Transcript for:
Essentials of Nuclear Chemistry

all right so in today's discussion we're going to talk about the nuclear chemistry nuclear chemistry is one of those aspects um one of those topics in chemistry that tend to be overlooked primarily because what happens here or what happens in the nucleus does not necessarily translate to any observable change in the chemical properties of uh the uh substance the element or the compound we are more um focused on the chemical reactions and rightly so because chemistry is a study of uh chemical Transformations however nuclear chemistry is also very important and in fact it actually or in a sense the predecessor of nuclear chemistry um was the one that that ultimately led to the study of well ultimately ultimately led to chemistry as we know it remember Alchemists wanted to convert base Metals into gold metals like lead copper iron they wanted to convert it into something precious into gold in other words and the they were not able to do that at least we believe that they were not able to do that um however through nuclear processes we can now change one element to another not just lead into gold in fact you can change under certain of course logistical concerns and um conditions we can change or transform one element into another element all right okay nuclear chemistry has many applications for good and for ill as you're going to see later what is perhaps most important for you to know is that the energy that can be harnessed from the nucleus of the atom dwarf or rather um energy that can be harnessed from the from the nucleus of the at is so much much bigger the energy that we can usually obtain from chemical reactions these are talking about um energies that literally can destroy the world as we know it all right all right so the disc discovery of or one of the early studies in nuclear chemistry of course is um done in the past and this was this covered by scientists like Henry Beckel Mar curi and they were primarily interested back then with phenomenon called radioactivity all right so for example for example have here um a uranium Compound on a wrapped sheet of film produces like this um exposed part on the developed negative now what does that mean that suggests that there that this substance whatever that substance is is emitting particles that causes the film to become developed right okay this is or this yeah is antoan HRI beo right he is credited to be the father of radioactivity because it was his early studies on Pitch Blended the uh or or of uranium event led to the discovery of the phenomenon radioactivity okay now radioactivity or radioactive decay involves the um release of particles of small particles they can be charged particles but definitely they are highly energetic particles the release of Highly energetic particles by atoms that are unstable that are nuclearly unstable right he saw that photographic plates develop bright spots when exposed dur new Metals now what does that mean there's a I was hearing a sound so I'm not sure if somebody's trying to enter this meeting okay all right so let's go back to that all right so you have here uranium containing use my pointer uranium containing crystals right you have your black cloth in the plate now the development or the bright spots um is attributable to some high energy particles but they're emitted by the radioactive atom naturally it must have been the atoms of uranium in this UR uranium containing crystals uranium ore okay now this emitted particle is the one that's causing the development of the photographic plate now nuclear reactions can be um divided or classified into two those that happen on their own spontaneous decay of unstable nuclei we call that or refer to that as radioactive decay or radioactivity where the nuclear Decay spontaneously giving off an energetic particle as opposed to nuclear bombardment or nuclear transmutation which refers to the purposeful manipulation of the nuclei and transformation of the nuclei from one into another right so in nuclear bombardment reactions you shoot a high energy particle at the nucleus of another atom and see what happens right now here is how we typically represent the nucleus all right you have here your symbol of the element you have a is the mass number the sum of the number of protons and the neutrons and you have zet the atomic number right faly the number of protons all right to get the number of neutrons naturally you just need to subtract the atomic number from the mass number in our study of nuclear chemistry you will encounter the uh equations of this kind right these are nuclear equations and so we follow the conservation of mass principle the sense that number of protons uh rather the um number of U the atomic number right before has to add up to the some of the atomic numbers after the process the same with the mass numbers right the same of the mass numbers for example in this case have 90 so we have here hel volume to four why should be um in this case y should be um 88 right 88 + 2 equal 90 and X should be 228 228 + 4 adds up to 232 as as we expected okay now the energetic particles but we were referring to what are they exactly they can be alpha particles can be beta particles they can also be positron or what we call the positive electrons we're going to uh talk about that later and the gamma particles right high energy helium nuclear this are the alpha particles you can think of them as as um helium 2+ ions right because they are actually just the nuclei of helium you remove the electron from the helium atom and you're going to get the U um helium nuclei right we represented here as h242 plus to indicate that we're talking about helium ions beta particle is actually just a loose electron right it's an electron see here one minus because it has a charge ne1 zero because it definitely is almost massless pleas in comparison to a proton in a neutron so that's zero and E you have a negative here to indicate that it's negatively charge a gamma diation is energy right it's energy so it doesn't have any mass and it doesn't have any charge right so you can write it gamma z z that will be all right okay these are the typical particles that are emitted by a radioactive substance a Radioactive nucleid by the way when I when I say nucleid nuide IDE I'm referring to a nucleus with a specified number of protons and neutrons all right okay so Alpha radiation beta radiation and gamma radiation shown here well this is this attempts to explain the ENT of penetration by this particles right the penetrating power of this radiation notice that the alpha radiation um is able to be stopped on its Track by paper like metal foil thin clothing right beta radiation um can pass through that apparently it's more penetrating compared to Alpha radiation and to what do we attribute that the fact that it is very light right it's massless at least almost massless it's just a beam of electrons that's why it's able to pass through um this paper metal foiler thin clothing but as you can see it's unable to penetrate metal sheating dense wood and heavy clothing it gets trapped within such structures gamma radiation however is able to pass through all of those uh all I mean through vest two but it's able to um be stopped by thick walls of lead and concrete right of this three the most energetic is actually the gamma radiation it's a beam of high energy particles see gamma radiation um it has U unless I'm mistaken it even has higher energy than xrays right xrays are very energetic already okay all right so they are able to be stopped and they're tracks by thick walls of lead as well as concrete all right if you're going to to uh consider this thing um say for example you're this are called I this this particles or radiation are harmful definitely so if you're if you get exposed to this particles it's best to get I'm not saying it's best maybe it's less harmful to get exposed to alpha particles than to beta particles than to gamma radiation right because gamma particles are less able to penetrate you right or through you um uh the only problem with that is if you have ingested accidentally a radi active material even gamma radiation won't be even gamma radiation F will be very harmful because it already gone into your system if you have accidentally ingested like by drinking or eating um such um gamma radiation Source okay all right so here are the types of radioactive particles that are emitted through R in radioactive decay you have alha particles beta particles poetron um you have here another phenomenon it's called electron capture that has the same net effect as the poetron emission and you have a gamma emission all right so you can see here all the particles have a notation h24 because they're essentially just um helium nucleid all right um You have four atomic mass units that's the atomic mass approximate atomic mass the charge is positive two because they have helium um nucle use beta particles have already mentioned they should be e right it should be e not Z should be e um negative 1 Z approximate mass is zero the charge is negative one the gamma particles as you see gamma 0 0 there's no mass and of course there's no charge on that positron is a positive electron so you have plus one e z have approximately zero and you have positive one of charge neon is of course neutral so it doesn't have any charge but it has a mass of approximately one atomic mass unit you have a proton which has it's actually just what the nucleus of proteum the isotope of hydrogen most abundant isotope of hydrogen one one h11 approximately one atomic mass unit in a charge of positive one all right so alpha particle of or alpha particle emission is when you lose helium nucleus you have here an unstable radioactive nucleid that loses an alpha particle see here the alpha particle now the alpha particle you have two protons and two neutrons as you can see here all right of course what happens as a result is that a substance or an element becomes converted to another element and that is pretty much remarkable right because it converts one element into another element through changes in the nucleus that's the only way by which we can change really an element to to another by changing the number of protons in its nucleus okay all right so you have your a parent nucleid for example parent nucleid uranium 99 to 238 um decomposes into thorium 90 234 and you have here are the alpha particle this St of a daughter in nucleid of a parent nucleid duranium 92 238 okay um I will leave this to you as an exercise like something that you can do on your own you uh plutonium 239 loses an alpha particle helium nucleus I would like you to write the nuclear reaction in the same way that we have shown here the similar transformation for Uranium 92 or uranium 238 okay all right now another kind of radioactive decay is that of the beta emission in this case an electron is actually the releast by the nucleus or emitted by the nucleus and this is surprising why because are not supposed to be found in the nucleus right they're found outside the nucleus then again what happens here is a nuclear reaction where a neutron splits into a proton and an electron the the electron is then spit out as a beta particle see here radioactive carbon 14 nucleus c64 loses a beta particle and in the process it becomes nitrogen 14 nucleus what do you notice the number of protons Chang atomic number changed from six to seven means it gained one proton but look at the number of n the mass number the mass number remain the same 14 still is 14 after the process why because remember beta emission or beta Decay involves the conversion or the decomposition of a neutron into a proton and an electron what happens is yes the number of neutrons decrease but the number of protons increased by the same number and so the mass number Remains the Same but the number of protons as expected increased by one so the atomic number changed from six to seven this electron right it's a high energy particle now typically this kind of processes are accompanied by emission of gamma radiation as well high energy right okay so this is just uh what we have mentioned we have Neutron converted into a beta particle or an electron in a proton notice with the um subscripts add up as well as the superscripts 1 plus 1 it is zero and one +0 is one okay all right so here's another example you have a radioactive three tube right this streum loses a beta particle in the process it's converted into a stable he free nucleus all right it has two protons from having just one proton at the beginning now have two protons here we have lost one neutron as can be seen in this case okay now another example of a radioactivity is poetron emission poetron stands for positive electron so in this case a proton kicks out positive charge or positron to become a neutron so in this case a proton decomposes into a neutron and a positron a positive electron what's the difference between um electron or beta particle and the positron or positive electron the charge right one is a negative one charge the other one is a positive one charge what about the masses they have the same Mass here approximately massless all right okay um we give it a notation the beta plus to indicate that it's a positive electron um beta particle is just beta the positron collides with an electron annihilating both and generating energy so look at this what happened to say for example in this case fine 98 it under goes positron emission or positron Decay what happens is that remember a proton in that case decreases I mean the that number of protons decreases because uh one of their number is converted into a neutron so the mass number the number of protons plus a neutron will remain the same but the atomic number will decrease right okay so from nine it becomes eight in other words from Florine it's become converted into oxygen now here's the interesting thing a positron is a positive electron and you have an electron nearby you see here a nearby electron it's it's it's it's natural the electrons are arranged in orbitals around the nucleus right and so there is a high probability of a positron um encountering an electron and they annihilate each other a positron annihilating an electron to in the process um generate vast amount of energy or huge energy in this case gamma gamma r R all right gamma ray or gamma radiation see vanishes in the burst of two GMA race okay now there is another transformation that is similar in its net effect to the poetron emission and that is electron capture electron capture occurs um with the it happens um on uh it's common to um heavy heavy element those which have high atomic number all right so what happens here is that you have an electron from an inner shell of the atom that is sucked into the nucleus to combine with a proton cor what happens is that the electron and the proton combines to form a neutron so the same net effect the number of proton decreases the number of neutron increases so as I've mentioned the same net effect as in the case of positron emission the only difference is that um in this case the electron is a reactant in the process while in the other case a positron or a positive electron is actually a product all right okay um so net effect again gives us common to heavy elements or to heavy nucle gamma emission is emission of high energy Photon from an unstable in so you see here fium 4399 m the m stands for metastable substance so that means it's a substance that is quite un unstable meaning it's um it's when you say meta stable it's something that is not really stable um the slightest disturbance will cause this substance to to undergo change all right so in this case technician 4399 m is converted into the more stable form of technici and you end up here with gamma gamma particle all right okay uh all right now the question then follows so how does an atom's atomic number change when its nucleus loses an alpha particle a beta particle or a gamma ray and how does that atoms mass number change Bel loss of each of these I believe we have considered them um already we have answered this question already again the case of an alpha particle the atomic number decreases by two the mass number however decreases by four the beta particle have what happens there is the loss of a what the loss of a neutron right the neutron becomes converted into a proton and so the atomic number increases by one excuse me but the mass number Remains the Same the case of gamma ray nothing happens if atomic number and to the mass number all right okay now the the uh positron and the electron capture in that cases or in those two cases um a casualty is of course a proton right the proton is decomposed or is transformed into a neutron and so the number of protons the mass rather the atomic number decreases by one while the mass number Remains the Same during positron emission electron capture now okay now you might be wondering exactly are we able to predict what kind of what sort of transformation radioactive decay certain radioactive nucleid will undergo okay now unfortunately our knowledge of the of the um Way by which the neutrons and the protons are arranged in the nucleus is um is rudimentary the we do not yet know exactly what are the what are the factors or we do not yet have Okay so let's put it this way we know that electrons are found in atomic orbitals and we have a fairly good way of assessing the relative energies of these electrons based on the quantum numbers are based on the orbitals in which they are found right we're able to assess and estimate or to characterize the chemical reactivity of a substance may it be an atom or a molecule based on its electronic structure we have a fairly good understanding of how the electrons are arranged in an atom or in a molecule that's what I'm trying to say we do not have the same level of understanding as or with with the um the nucleus it's still not very clear to us but there seems to be some parallelism scientists have noted that the same way that that the electron are arranged in in in in shells or in orbitals there seems to be some logic to the arrangement of the of the U nucle nucleons when you speak of nucleons you're referring to proton and neutron there seems to be um an arrangement or a number of nucleons that are stable right but are stable and later I'm going to show you the belt of nuclear stability you're going going to we're going to we're going to uh see or we're going to look at it ourselves and uh see or or be able to um um um generalize certain things but that's the best that we can do as I've mentioned um there seems to be like magic numbers involv although the origin or why those magic numbers are why they are such why they are they why they have such values is is not very clear to us yet okay now this is what we know or these are what we know so far the nuclear particles are held together by a strong attractive Force have you ever wondered what keeps the nucleus together intuitively we would have expected the nucleus to what to spontaneous disintegrate why because you're putting in there positively charged particles and we know that positively charg particles particles of the same charges will repel each other and not only are we putting them all together we're putting them in a very very very small region in space so you can only can only appreciate the intense repulsion that this particle experience towards each other the question is why do they stay together there has to be a force that keeps this particles together right okay as I've mentioned electrons or rather protons are thought to be arranged in Shell like electrons exactly what are the rules for such Arrangement is still unknown um or if he unclear but there are certain observation for example even numbers of protons and neutrons are most stable nucleid with even number of protons and neutrons are most stable and approximately one is to one Neutron to proton ratio the N should not be there is generally most stable but this this observation is only for for atoms or for nucleid that have low to moderate um atomic numbers as the number of protons increase the number the neutron to proton ratio for them to be stable um increases we're going to see that later so an atomic number greater than 83 is never stable all right okay so here is what I am talking about the band of stability so we do not know what exactly is going on in the nucleus but we do have some observations some helpful observations that can in one way or another guide us in helping to protect what radioactive transformation a nucleid will undergo so the region which this is a plot of the number of neutrons versus the number of protons right okay the region on a graph which indicates all stable nucle when the number of neutrons are compared to the number of protons for all stable nucle is called the nuclear belt or nuclear band of stability so here see here all of the atoms here in this band are stable all right here now here you see a line the neutron to proton ratio equal to one right that one and you have another line here the neutron to proton ratio equal to 1.5 of course you can compute the neutron to proton ratio for for a specific nucleid all right but you have to bear in mind that each point on the belt of stability represents stable nucle all right so as I've mentioned a while ago for atoms that for lighter atoms see for lighter atoms For What from number of protons from one to around let's just estimate let's just say up to 20 for example up to 20 the the number of neutron to proton ratio for stable nucleid is roughly one is to one right but as the atomic number increases for example if you have 30 protons if you have 40 protons 50 protons you see that the nuclear belt of stability is far way off from the one is to one uh Neutron to proton ratio l so it means that more protons or a nucleus or a nuclei a nucle with more than 20 protons must have more protons than rather more neutrons than protons in order to be stable right that's exactly what we're observing here and look at this part if you have around let's say 70 to 80 you must have approximately a neutron to proton ratio of 1.5 the number of U neutrons must be 50% higher than the number of protons right H what does that mean or or how do we rationalize that again because we do not yet know exactly what's going on the nucleus we can only conjecture we can only hypothesize and one of the things that we uh can easily say is that perhaps as a number of um okay first and foremost the neutron is doing something here right the neutron is more than just um a neutral particle or elementary particle that's that's just watching everything before it unfold before it's very eyes it is important here it it it has a role to perform um scientists and you're going to learn more of that tomorrow when we consider the computations the calcul involved that nuclear chemists and nuclear physicists believe that the neutrons have the ability or the ability of the nucle to stabilize itself um especially for heavy nucleid is dependent upon the number of neutrons that it has right so for now let's just consider the neutrons as the particles that sort of stabilize the uh protons what do we mean stabilize I mean that stabilize the nucle the nuclei um in the sense that it prevents the nuclei from disintegrating it prevents the protons from flying off out of the of of a nucleus all right apparently if you have just one to 20 protons you just need same number of neutrons as the number of protons but when you have more than 20 protons the number of neutrons that you need to counteract the repulsion between the protons is is now more than the number of protons that you have if you think of the number of if you think of the neutrons as a stabilizing force or stabilizing particles then this is this makes sense in the sense that you have more of the protons then the more intense the repulsion will be all right we have what we call nuclear binding energies and we will study exactly how to compute for nuclear binding energies tomorrow but this um binding energies are said to be somehow associated with the neutrons right with the neutrons there will be more about that tomorrow when the uh this cat but as a as um well we do not know much yet right but the nuclear belt of stability at least tells us exactly what's or at least allows us to predict what's going to happen if say for example you have an element um see okay um a p a pen or a highlight let's see a high High lighter all right so you say for example you have um somewhere here right see that yellow the region that I highlighted if your nuide is somewhere there then you know that that nucleid must as one of its um disintegrate as one of its radioactive processes must involve um Alpha DC right because in order to become in order to be in the belt of stability it has to lose protons excuse me in other words it has to move left and it has to lose neutrons it has to move down right so definitely if you are somewhere here sorry is that undo um if if you have if you are somewhere there you have to undergo a nucle have to or has to undergo um alpha decay as one of its um radioactive that's one of the one of its radioactive reactions okay now what if you are somewhere you're somewhere let's say somewhere here there okay it's to the left right and above the belt of stability it's to the left and above the belt of stability so it means that somehow it must um lose neutrons right it must lose neutrons and it must gain um protons right um let's see if I can use a so it has to move in that direction right it has to move in that direction in other words has to lose neutrons and it has to gain protons and uh what transformation will that be it has to undergo beta Decay it must release um a beta particle right Neutron must decrease and the number of protons must increase the opposite of course is true and say for example let me use the highlighter say for example you're um you're here right somehow in order for that um nuclei to become stable it must move in that direction so that means it must lose protons and it must increase its number of of uh neutrons right and how does that do that well there are two possibilities positron emission um or electron capture by the way we also call electron capture Kappa capture right Kappa capture so this two um what is most likely is a positron emission right because the it's not that heavy the uh atom or rather the um the nucleid is not that heavy but to say for example you have somewhere nuclei or nucle highlighter applied here right that's definitely heavy and so most likely this will undergo Kappa capture as one of its one of its one of the steps in the ractive series but it under goes to stability all right so again we can guess what's going to happen and we base that or those guesses on our knowledge of the belt of or the band of stability but the exact reason as to why certain number of protons are favorable and offs are not say for example having an even number of protons and neutrons are more stable why such is a case it's not very clear yet but then again um protons are thought to to be arranged in shells in within the nucleus the way electrons are arranged outside it okay all right now what we have discussed so far are nuclear or radioactive series these are reactions that happen on their own they are spontaneous right they're of course purposeful manipulation of the um purposeful manipulation of the nucleid converting it from one into another and we call this processes transmutation right changing one element to another by shooting a nuclear particle at its nucleus all trans uranium elements all right those which have more than 92 protons were created synthetically in particle ACC accelerators that's why they are called transuranium right Beyond uranium okay so here's an example of a transm a reaction you have nitrogen converted into oxygen this is the alchemist's dream right this is what they wanted conversion of one element to another well they focus on the conversion of Base Metals into gold but this is essentially what they were trying to do so this case nitrogen is converted into oxygen you have here how do you do that you shoot nitrogen nucleid with helium nucleid or alpha particles the process converting nitrogen into oxygen and releasing a A prot in the process right so you have here your original particle you represent it this way you have your original particle n73 you have here the bullet or the particle with which you shot the original particle P this is the particle that's been emitted that's the proton right the prote nucleus so that's particle emitted is the proton and you have alpha particle is the bullet here's a new atom 0817 that's how we represent the uh transmutation reaction okay now you know what one of the most interesting things about nuclear reactions is that the masses never seem to add up they never add up for example you have lithium reacted with or shot with prot the process you end up with two helium atoms one is helium three the other is helium 4 if you add up their masses like the mass before is 7.02 294 the mass after is 7.1 863 atomic mass unit so there is a disparity in mass and where did that mass go well that apparently has been converted into energy or that's the the way we rationalize it remember Einstein's famous equation eals mc² right that's how we interpreted the energy the vast amount of energy that is released from this process um um accounts for the disparity in masses before and after the nuclear reaction right call that the mass defect right some of the mass can be converted into energy all right shown by the very famous equation of Albert Einstein right E equals MC squar all right okay now let me um let me okay where was I nuclear chemistry one [Music] okay I'm having trouble with my screen all right so here is um the energy the mass and the speed of light all right apparently some of a mass has been converted into energy and what a vast amount of energy it is even the smallest because that difference in mass is very small right right but that small difference in Mass amounts to a vast amount of energy is that remember that's the speed of Life MC squar right okay and that okay all right let me stop sharing because I think there's a problem with this figure it all this okay I should be quick at it okay so all right okay now at this point in time then we have to emphasize the difference between nuclear reactions and chemical reactions um chemical reactions which as chemists were primarily concerned with follow the law of conservation of mass right the masses before and after are are the same the sum of the masses of the reactants and those of the products are equal to each other there's relatively small energy changes of course the energy of a of a um say for example of of an explosive that's huge um but that is relatively small in comparison to the energy released by a nuclear reaction right there's no changes in the nuclei they involve only the veence electrons that is true for chemical reactions now for nuclear reactions there are small changes in Mass which translates into huge vast energy changes right the numbers of protons neutrons electrons and gamma rays can be um lost or gained all right now here is Thea um here is one of the greatest demonstrations of the vast power the vast energy that can be released from a nuclear nuclear process this is the Sun and you can see the solar flares ejected from it right solar flar is ejected from the sun right now here is the where the energy that sun releases is powered by fusion fusion reactions right where small nucle um combined together and form to form heavy nucleid all right okay nuclear fusion as I've mentioned is a joining of two light nuclei into one heavier nucleus right see here diffusion of hydrogen nuclei can see here all right now in the core of the Sun two hydrogen nuclei join under tremendous heat and pressure to form a helium nucleus all right this is a stable helium nucleus right when the helium atom is formed huge amounts of energy are released right as it can see here energy and this energy is the energy that powers the entire solar system it's energy that powers the Earth all right because in one way or another energy on the earth can be traced back to the sun right to the solar energy okay um the energy I cannot emphasize it enough the energy that is released by Fusion reactions it's very very very huge okay scientists in fact cannot yet find a safe and manageable method to harness the energy of nuclear future all right it would have been um awesome right to be able to harness that amount of energy just imagine the U Energy Event would have what would have been able to enjoy the of energy that we would have been able to enjoy have we found a way of harnessing the energy from a nuclear fusion reaction right but we cannot we haven't yet found a way to do that cold fusion would would occur at temperatures and pressures could be controlled but we haven't figured out how to get it to happen all right now there is a technology that has been proposed we have proposed to um to uh handle the because if you're going to remember a sun is a plasma right the it's it's the temperature is too high the elements the atoms in the sun exist as ions right no container on Earth can withstand such high temperatures that's why see here we haven't yet found a safe and manageable method to harness the energy of a nuclear fusion reactor um one of the things the idea that have been floated is the use of the magnetic field like can use potentially according to the magnetic field to contain to contain the energy of such a nuclear fusion reactor I'm not sure if you have watched Spider-Man but in one of those one of those installments I seem to remember and I was then back in college um there was this Dr o right Dr o he is uh harnessing right the I think it's nuclear fusion nuclear if my memory serves me correctly nuclear fusion reactor that he was that he has managed to develop and if you're if you're also interested you can watch that or you can also watch Chain Reaction Chain Reaction it's a it's an old a relatively old movie featuring K Reeves and U racial Vice they and and Morgan Freeman they found a way way or at least the story evolves around the university I think the University of University of university of University of Chicago in the United States they found a way to harness the energy from from from nuclear fusion you know what this is actually um if if people or scientists can find a way to do that that would be very it's a big deal it's a very huge deal why because we have unlimited supply of hydrogen water water we have water on Earth right we can use that as a source of fuel right so if you want uh you can watch that it's titled chain reaction and again it it featured Morgan Freeman K Reeves as well as racial vience okay now nuclear reactions have many applications right in medicine in agriculture is again as energy sources see chemotherapy um um here is one of the applications so food irradiation for example food can be irradiated with gamas from Cobalt or and um and why do you do that you want to kill the bacteria you want to uh you want to um ensure that it's what is that what is it term um sanitized accordingly right it's clean uh of unwanted microorganisms irradiated milk as a shelf life of three months imagine that three months without Refrigeration right the only thing I'm concerned about is what happens to the proteins in the milk right because uh gamma radiation actually um the Nature's proteins the Nature's biological molecules that's a not sure game the Hollywood is right um with with films that uh in one way or another eludes the nuclear processes Hulk right Hulk The Green Man or that green muscular man he was um um transformed into that by nuclear I'm not sure if it's nuclear it's a nuclear process I just can't remember if it's nuclear fishion or nuclear fusion right but then um the point that I'm trying to get at is that biological mole are denatured by exposure to um radiation so we have to be very careful okay but the USDA us Drug Administration amazingly has approved irradiation of meats and eggs so they must have a reason for that they must have deemed it safe enough to allow such a practice to occur okay so this is another example you have exra examination of luggage at a security station those of you have trial Tred um um through planes okay go to the airport and that's done um um done regularly and routinely all right here's an image of a thyroid gland obtained through the use of radioactive iodine right you uh use them in imaging the FID and human lungs obtained from gamma ray scan all right okay and of course a cancer patient that is receiving radiation therapy all right one of the things that you have to bear in mind however is that this mode of of therapy or medicine is okay it kills the cancer cells the problem is that it also kills the healthy cells so there is a field now in medicine that U specifically um nanom medicine that seeks to to uh delivered drugs only to the cancer tissues or only to those tissues that are deceased and not um affect healthy healthy tissues all right okay now nuclear reactions as an energy source right uranium 235 I'm not sure if you've heard of this but uranium 235 is a source of nuclear power it's the fuel that powers nuclear reactors right and nuclear reactors what happens there is fishing right it's the splitting of one heavy nucleus into two or more smaller nuclei as well as some subatomic particles and energy all right the energy released here I must say is a is a is um large it's huge and it's it's huge it's very huge but compared to nuclear fusion reaction it's it's not as much okay here a heavy nucleus which is usually unstable due to having many protons is used as the fuel all right notice that when or note that when fishing occurs energy is produced more neutrons are given off like okay so what happens here is here or what happens here is shown here you have a neutron and you have a Target you're fuel all right your fuel you you expose it in or you shoot that with a neutron happens is that gamma radiation is released and you form an unstable isotope that unstable isotope under goes disintegration in the process releasing other particles like in this case beta particles gamma radiation and you have this product all right um there's an observation noted here it is much easier to crash and neutral Neutron then a positive proton into a nucleus to release energy and I'm sure you understand why that is the case right because a neutron is neutral it will not be repelled um by the protons of the nucleus right right okay that's why it's easier to use a neutron as your bombarding particle okay so here are the nuclear fishing reactions and that I will just ask you to uh balance it yourselves at home all right and do some mathematics balance the nuclear um reactions nuclear efficient reactions what actually happens in this I'm not sure if you have it here yeah I have it here so here you have uranium 235 for example when you um expose it to a neutron what happen is as I mentioned you generate this unstable isotope this unstable isotope fur under goes further disintegration into barium as well as cryptum all right and look at that how many neutrons in turn have been released during the process we have one two three a single process that is single ficient reaction that has been um initiated by one Neutron led to the formation of what this nucle all right this nucle and three neutrons look at that each fishion reaction first and foremost is highly energetic it's Rel it releases a large a huge amount of energy and notice that one one Neutron gives rise to three neutrons if this process goes unchecked you're going to end up with a chain reaction right wherein one Neutron causes um the the one fishing reaction which releases three neutrons and then this three neutrons will lead to the formation of nine neutrons and so on and so forth remember that the process becomes or the the the chain reaction occurs exponentially at a rate that gives off too much energy all right too much energy how do we assess the rates of radioactive decay and how then do we estimate the amount of of uh Radioactive nucleid that remain after such disintegrations all right in order to answer that questions we turn our attention to the concept of the Half Lives now I'm not sure which um course it is discuss nowadays but I believe that you have been introduced into you have been introduced to the concepts of chemical genetics and in um one of those uh discussions I hope you have been familiarize with the order of the reaction and the integrated great laws in any case we're going to revisit them in passing and and uh order to remind you what it is that you should should know at this point in time now we turn our attention as I've mentioned to the rate of rate of radioactive decay okay radioactive decay all right the disintegration of a nuclear of the nucleus into smaller pieces is and example of a first order reaction right it's an example of a first order reaction and therefore it will follow the first order kinetics before we go into the details of such um kinetics or such process such process let's consider the case of the following strum um 3 strum 38 [Music] 90 disintegrates into um 39 0 in the process um release beta particle or an electron right now the the disintegration of strum into itum as already alluded to it's an example of a first ordinary action in first ordinary actions speak of the quantity called halflife right half life half fly us should given the symbol T12 is the time necessary for the um substance for the substance's concentration for very AC concentration to be reduced to half its original value can think of it as the time elapse um um before or the time it takes for the substance concentration or the substance's amount to be reduced to half its original value okay now the Half Lives can be as short as millions of a second can be as long as billions of years all right depending on the particular nuclei in question now strum 90 undergo beta Decay as you can see here under go beta Decay and half lifee perious process D12 is equal to 29 years now what does that mean it take it means that it takes 29 years for stune for the amount of stum radioactive strum to become half of its original value right now as in the case of all first order reactions the half lives or nuclear Decay are unaffected by external conditions such as temperature pressure and the state of chemical combination right so and like toxic chemicals which you can neutralized by addition of appropriate reagents like if you have an acid you can simply neutralize that the base if they have a powerful oxidizing agent then you can add a reducing agent to neutralize that and like toxic chemicals excuse me the radioactive atoms cannot be rendered harmless by chemical treatment right or any other practical treatment for that matter so in that case then we cannot do anything but to allow this nucle Radioactive nucle to lose radio activity at their characteristic rates in all the while protecting ourselves from the harmful radiation that they might um Emit and that they are actually emitted all right the halflife as you can see here is an important parameter because it allows us to determine the amount of substance that will remain after some time the time not necessarily equal to the half life or we can simply estimate Thea um the amount that will remain after certain multiples of the half for example let's consider the following example okay this is more of qualitative later we're going to go into the details examples we have a the half life the half life of cobal 16 is 5.3 years so how much of a one um milligram sample of cobalt 6 is left after uh 15.9 year period all right so what is the solution all right how do you solve for this okay so what I want you to notice or take note is the fact that you're looking for the amount that remains of Cobalt 60 after excuse me after 15.9 years you're going to look 15.9 years is actually a multiple of half right 5.3 * 3 is a um 15.9 and so that means that um you're looking at a span of three half lines right so if you start with a 1 milligram sample can here you have a 1 milligram sample 1.00 milligram sample of a Cobalt 60 after one half life or after 5.3 years that will become 0.5 millam right after another half 5.3 years that the the become 0.250 mgam after the third half life in other words after a span of three times 5.3 years or 15.9 years going to end up with 0.125 of a millgram of Cobalt 60 now notice that this example it's quite straightforward right um the um the uh time that we're talking about is a multiple a whole number an integral multiple of the half life of the sample what if you are asked to determine the amount of the substance that remains or even the amount of the substance that is consumed after a time that is not an integral multiple of the half life in that case you would have to go into the details the calculations as we're goinging to consider later but before we go into that um details I want to talk about dating specifically the process of determining a date of a particular sample and artifact in archaeology for example or a mummy or any sample any biological sample now you might have heard of radiocarbon dating right now it's one of VI most important tools that archaeologists use to determine the age of certain artifacts or of artifacts now it it had its chemical basis or should I say nuclear basis is as follows you will um have a take note of following reaction first nitrogen right in the um upper atmosphere actually reacts or actually captures a neon right so Z One n there's a neutron capture and this happens in the upper atmosphere it's a natural process that occurs in the upper atmosphere so nitrogen 7 14 the um Regular common isotope of um nitrogen captures a neutron in the process producing carbon for carbon 14 is a radioactive form of carbon remember the most stable form of carbon is carbon 12 so plus a proton P11 right so you have a neutron that is captured by a nitrogen nucleus process nucleus is transformed into a carbon 14 nucleus causing the um um um release or in the process of a concomitant release of a proton again this happens in the upper atmosphere so I've already mentioned carbon is um radioactive so it will undergo Decay right the point that you have to bear in mind in this case is that this reaction um provides a small provides a small but reasonably constant right source of carbon 14 this is your source of carbon 14 this your let me highlight that um this reaction is your Source carbon 14 right it provides a small but reasonably um constant um source of carbon 14 now the carbon 14 is radioactive right carbon 14 is radioactive this substance undergo what under goes the composition back into nitrogen 7 um 14 the process however um this what do you notice look at the um okay let us balance the equation so that you will be able to see what is the substance what is the particle that is emitted so 7 six so this has to be 1 the mass number should be zero particle that is charge ne1 there a mass number of zero is natured the electron so this is an example of another beta Decay so carbon 14 decays into nitrogen process releasing beta particles okay all right now the let me highlight that okay this is very important because this process is used in dating artifacts okay um halflife for such decomposition is uh um um quite a long time all right the uh um um halflife purpose is 5,000 [Music] T2 okay 5,730 years half life the time it takes for the carbon 14 nucle to um become half number of carbon 14 nli to be reduced to half its original um value okay before I go into the application of this remember that the uh the chemical reactions do not discriminate between the nucle that is for example the formation of carbon dioxide or yeah the formation of carbon dioxide in the upper atmosphere will not discriminate the LI your carbon source is carbon 12 or carbon 14 you're going to the theaction will assimilate whatever carbon you have right and so in the upper atmosphere then and in the atmosphere for that matter you're going to have carbon dioxide that has carbon 14 and carbon dioxide that has carbon 12 okay remember that carbon 14 is a small amount is a is a small fraction of the carbon um it's the less abundant isotone right and not surprising because it's radioactive Okay so the carbon dioxide that is found in the atmosphere is a mixture of carbon dioxide that contains carbon 14 and carbon dioxide that contains carbon 12 okay what's going to happen the trees are going to assimilate that or we're going to assimilate that process converting carbon dioxide and the process ofes into glucose right so the carbon atoms will essentially be um will not be part of the glucose molecule the carbon framework of the glucose molecule now this molecules can be assimilated by animals right ultimately enters into the um food chain right and so a human being for example or an animal will take in um glucose that has carbon 14 and carbon 12 right for as long as that individual that plant or rather that human that animal even the plant the plant lives it will have a steady and more or less constant ratio of carbon 14 to carbon 12 right why because for as long as that animal for example or that plant is alive sorry is alive that animal or that plant is taking in um carbon dioxide in the case of plant or glucose in the case of animals um from the ultimate source of carbon dioxide the one which is produced in the upper atmosphere or if it is found in the atmosphere right for as long as it's alive now the moment the moment that the plant or the animal dies right what happens is that carbon for disintegrates okay I think that statement should be clarified carbon 14 disintegrates even if even if the um the animal or the plant is still alive okay so it's it's disintegrating but there that the amount of carbon 14 is more or less constant why because it's constantly assimilating the in the case of plants the carbon dioxide from the atmosphere in the case of animals the glucose right there is a steady constant Source or supply of carbon 14 but the moment the um the animal or the plant dies the integration of carbon 14 happens as expected but the carbon 14 is no longer replenished right it's already dead it's no longer going it's not going to eat anymore it's a plant it's not going to assimilate carbon dioxide in the atmosphere anymore so but this integration of carbon 14 um causes the carbon 14 the carbon 12 ratio to decrease right decreases when the animal or the plant dies okay and so from that point onwards you're able to date you're able to date the artifact or the um the mummy for example but remember when you date a mummy or you date an okay just a mummy for example when you date a mummy you're dating it from the time it has died right because that's the moment where that mummy or that individual is no longer able to replenish its source of carbon 14 or its carbon 14 all right okay now the process of radiocarbon dating can be used to date objects that are old but not older than 50,000 years because Beyond 50,000 years BM um radio activity coming from carbon 14 can no longer be detected accurate okay of course other other um other radioactive nucleid can be used for dating depends on what you want to date for example um it takes uh 4.5 look at that it's long time 4.5 * 10 to the 9th years all right for half of a sample of uranium 238 to Decay to lead 206 so this is the half life for the um conversion of uranium 238 to lead um 2006 so if you're say for example you're you're um trying to dat um a rock sample like you're talking about um the geologic time scale the geologic the old of a sample of rock um then it's more appropriate to use such as a basis for ding bat samples and just than using um carbon as a basis all right okay now let us be more mathematical and more quantitative now we'll remember that in the case of a first order reaction first order reaction the case of a first order reaction the rate is directly proportional to the concentration of a substance or concentration of a reactant so in this case you can say you have um how do you represent this let's just say R right a radi active nucleid that is converted into products it's disintegration products okay so the rate of the reaction will naturally be proportional to the number or to a concentration of r or if you want the number of um atom rather the number of nucleid of R so the rate at which the rate at which the uh number of nucleid change with time is equal to a constant multiplied by the number of nucleid it's directly proportional it's a first order reaction for Simplicity I'm going to remove the r right so it's when I say n it's a number of nuc okay and so you can integrate this as you typically do in calculus so you combine similar terms in same side of equation you have DN Over N is equal to K DT then you do your integration between limits from Z to T for example NS Sub Zero the initial amount initial number of nucleid um to any number of nucleid corresponding to time T the integral of DN / n as you know is lnn right this is definite integration so you end up with lnn from N Sub Z to n is equal to K T integrated between limit 0 to T so you end up with Ln n minus Ln N Sub z um equals um netive K T all right right okay now you can combine the logarithm remember it the difference logarithm the difference of logarithms is a logarithm of the quo so that becomes lnn over N Sub Z is equal k d this is the equation for a first order reaction right you have you must have had encountered that in the past okay all right um how do we get the expression for the half line all right at T equals E12 what do we know the number of nucleid is equal to 12 the initial number of nucleid and so we end up with Ln 12 N Sub Z Over N Sub Z just cancel out term end up with k t 12 right and so you end up with ln2 are simply Nega ln2 is equal to K T12 manipulate the equations you have the half life is equal to natural logarithm 2/ K this is the equation that we use in evaluating the value of the constant for the process or the half life from Vice from from one or the other can evaluate the half life from the rate constant the first order rate constant or the first order rate constant from the half life and you will notice that the halflife is a constant like it does not vary with the amount of substance right it's natural logarithm of two divided by the rate constant the rate constant does not depend in temp temperature I mean it depends on temperature all right it depends on temperature but at constant temperature um the value rate constant will not change okay all right so it's not depend on the number of nucleid okay using this equation then you're able to evaluate the half life from the r constant and vice versa and using these more generally this's more General equation able to evaluate the amount of a nucle after any given period of time okay now one of the things you have to emphasize is the concept of activity now the activity is the rate at which a sample decays right it's the rate at which the sample decays in other words it's simply V it's simply this one right the rate at which the sample decays of a rate of change of a number of nucle and you multiply that by negative by the way because you want positive number DN over DT is negative and you speak of R you speak of positive numberers so that's why it's necessary to multiply by negative one this is the activity that we are talking about right the rate of this integration okay um so what do you notice the rate of this integration is directly proportional to what the rate of this integration is directly proportional [Music] to the amount of the number of nucle right that is very important because tells us that we can replace here we can replace this ratio by the ratio of the rates of disintegration or simply activity now I'm going to use a symbol a for the activity okay activity so that means that how they do this let me see okay okay that means that the natural logarithm of what activity over initial activity is equal to Nega K T right and why is that the case because the activity is just directly proportional to the um concentrate over to the number of nucle so if you factor out okay if you want to know exactly how that happened notice that this can be represented as n is equal to negative d n over DT over K right and so um can see that they are directly proportional to each other so you can simply replace n there and notice that the negative K simply cancels out um or if you want remember that the activity is negative DN over DT so that means it's a over K so we can substitute the values for n/ and and n/ N Sub z n and NS OB zero end up with a over k divided by a sub Z over K and so the K simply cancels out you end up with that the point that I'm trying to make here is that you can either use the mass of the radioactive nucleid as the basis for your computations or the activity right as measured by the number of dist Integrations observe for unit time all right um okay let's consider the following example example a rock contains 0.257 mgram of lead 206 for every milligram for every milligram of uranium 238 okay halfly for the de the half life excuse me for the decay of uranium halflight for the decay of uranium um 238 to lead 1006 is 4.5 * 10^ the 9 year how old is The Rock how old is The Rock okay all right let's try solution okay so you have here a rock that contains 0.257 milligrams of lead 206 for every milligram of uranium 238 okay um half life for V Decay V 238 to Le 206 is uh 4.5 * 10 9 years so you're ask here how old is The Rock okay so in order to determine the age we're going to use the equation we have here if you want to know of the age let's use a different highlighter purple okay you want to know the age T then you either have to know the number of nucleid like the milligrams of nucleid at now or at this point in time and the number of nucleid at the beginning right ends of zero or you can computer the same quantity if you're given the activity now and the activity at the beginning of the uh process okay looking at the problem you're given what you're actually given the the what the masses right the milligrams if you look at the problems you get the milligram of lead 206 for every milligram of uranium 238 okay that's a ratio right you have a ratio you do not have um the um actual do not have the uh actual masses you're what you're given is a ratio of masses okay you will think that you need the actual masses right but in truth you're going to look at our formula you're taking a ratios and when you're taking ratios the root constants I mean the constants will just cancel out okay what I'm trying to say is as follows Let's uh solve this okay so I'm not fond of assuming that you have one for example in this problem you say a rock a rock contains 0.257 milligrams of lead 1006 for every milligram of ranium 238 um some people will just simply say assuming we have one milligram of uranium at present right because this is the amount at present right this is the ratio at present that's the present r okay and uh I'm not fond of doing that so what we're going to do is we're going to generalize let a or let uh yeah let a be the weight or a mass I'm using the weight and the mass interchange weight of a of uh uranium um 238 U 238 at present in other words now okay that is the case what is the um um weight of lad 206 so that means that the weight of lead 206 0. 2 2 57 that's mgram over mgram right milligram your R of lead 206 per milligram of uh of uranium 238 since it's just milligram I will simply just take that as a multiplier I mean as I will simply cancel that out okay s257 over um 1 Point uh let's just say 1.0 0 Z per consistency three decimal places times a right because you have 0.257 milligrams or every one milligram so if you have a can be a let's specify milligrams the weight of your 308 at present in milligrams okay in milligrams so that will be this one 0.257 over 1 * a is the weight of over L what is that 206 at present in milligrams okay so what do we want we want the N the weight of the um the uh uranium 238 at present and you actually have that we said said it's a right it is a um what about the weight of uranium 238 at the beginning like at the start okay that is what we need to find out but you will remember that the process is as follows uranium 238 becomes converted into lead 2006 right so if that's the case how do you compute for the amount of uranium 238 at the beginning in other words it's original amount how do you uh compute for that it should be the amount of uranium 238 at present plus the amount of uranium 238 that has been lost due to the disintegration right and look at his stomry have 1 is to one so that means that the you're talking about the number of moles for every one mole of uranium 238 you form one mole of lead 206 all right but you have one nucle of uranium 238 you form one nule of lead 206 okay H so that means that the original let's write original weight of uranium 238 will be equal to the weight of uranium 238 at present which is a all right plus what the weight of uranium 238 that has disappeared has been converted into lead qu 6 do not know that but you can certainly compute for that and that means it is how much how do you relate that to the weight of um um to the weight of lead 206 how do you relate that you know that it's 0.257 over 1 * a milligrams right 0.257 just not going to write one anymore times a but that is the weight of lead 206 how do you convert that into the weight of um the uranium just multiply that by 206 in the denominator and 238 in the um numerator okay now how did you get that before I tell you the answer to that question what's going to be the answer here um the answer is going to be simply [Music] 1 297 * 8 right that's the original weight in milligrams okay of uranium 238 all right you might be wondering where did you get b um this one okay remember we're looking for the weight of uranium 238 that disappeared I'm just going to say this disintegrated or disappeared and we say that um it has to be related somehow to the um to the uh weight of of lead 206 but the weight of uranium 238 that disappeared must be equal to the number of moles of uranium 238 that disappeared right this or disintegrated times the M mass or V omic Mass let's just say m mass of uranium 23 remember we're talking about the nucle the nucleus here all right okay according to vetry what is the number of moles of U uranium 238 that has disappeared one is to one so that means it's equal to the number of moles of lead 206 that has been formed assuming that there's no other source of lead 206 right okay times molar mass of uranium 238 now what is the number of moles of uh lead 206 number of moles of lead 206 is equal to V weight of lead 206 divided by the molar mass of lead 206 times I here A M mass of uranium 238 simply to get the weight of uranium 238 that has disintegrated or it has disappeared you multiply the weight of lead 206 that you have at present by the molar mass of uranium 238 divided by the molar mass of lead 206 which is what simply already know what this values are 238 over 206 as you can see here highlighted all right this one what is this this is simply 0.257 a that's the weight of lead 206 at present in milligrams and that's exactly what we need to multiply by 248 over 206 in any case right you now have what you're looking for original weight of uranium 238 and you have the weight of uranium um to frate at present here which is a all right how do we solve for this Ln what is that n Over N subz is equal to um negative KT right okay before we are able to solve for this we're given the half life we're not given the rate constant we're given the half life which is 4.5 * 10^ the 9 years or um sorry 4.5 * 10 the 9 years so that means what is the relationship between the half life and the rate constant there T12 is equal to ln2 over K or k is ln2 over T12 right so here where I plug in the values I want to simplify this what is K ln2 Over T2 have here l Ln n / n0 * T right we're looking for the value of T so just substitute the values okay let me uh admit your class first all right now let the substitute the values the natural logarithm of what is n the amount of uranium 238 or the weight of uranium 238 now it is equal to a right it is equal to a all right where is that it's here a so a what about the original amount or weight in milligrams of uranium 238 it's there original weight of uranium 238 1. 297a okay equal to negative ln2 over what is a half life the half life is 4.9 4.5 * 10^ 9 years 4.5 * 10 to 9 years um then T just SOL for and when you use your calculator what are you going to get going to get 1.7 * 10 to the 9 years this is the answer we're looking for so via Rock apparently is of an old drop 1.7 * 10 to the N9 years that's extremely old okay all right now I would like you to uh bear in mind that had you assumed that the amount or the weight of uranium 248 at present is simply 1 milligram you would have ended up with the same answer all right because notice that a here a right where is that but a year this a simply cancels out so yes people are justified in assuming so but only because the um um value of the uh substance like in this case the amount of uranium at present um cancels out in the working equation all right okay um I want you to uh assignment assignment one righted a wooden object I want you to answer this a wooden object from an arch ological site our chological site is subjected to R carbon D is subjected to radio carbon dating activity of the sample activity of a sample due to carbon for carbon 14 is measured to be 12.4 is Integrations per second the activity of a carbon sample sample of equal Mass from fresh wood fresh wood is [Music] 19.5 this Integrations per second the half carbon for 14 is 5,730 years what is the age of the archeological the archaological sound all right show your complete Solutions show your complete Solutions and encircle your final answer right that's important very important encircle your final answer so it will be easier for me to find your answers I will post um I will create a bin for submission um in canvas after our meeting today and this will be due tomorrow before our meeting which um will happen at 10:00 in the morning okay I makeup class tomorrow which will happen at 10:00 in the morning all right so I hope that concept of radioactivity rather the rate of associated with radioactive decay or disintegration is clear and the calculations involved with it okay now yesterday we also alluded to the observation also mentioned the observation that VM nuclear reactions involve changes in masses like the U masses of the nucle prior to the nuclear reaction is not the same not exactly the same as the masses after after the um reaction there seems to be a disparity between the masses and we we said that portion of the mass has been converted into energy similarly or following the same line of reasoning is also possible for energy to be converted into Mass right Einstein's famous equation equals mc² allows us to compute for such um equivalencies in mass as well as in energy all right let us consider the energy changes in nuclear reactions energy changes in nuclear reactions okay okay perhaps E mc² is Einstein's most famous equation E energy m is the mass and C of course is the speed of light which has a value equal to 3.0 * 10 to 8 m/ second right notice that if you're going to take or to use this equation as a way which we can compute energy from mass and mass from energy the proportionality constant c^ s is actually a huge number it's 3 * 10 8 SAR at mean it's 9 * 10 to the 16th that is a very huge number right and so it is not surprising that um small changes in masses nuclear reactions translate into significant significant amounts of energy all right okay for example let us consider the following the change in mass accompanying the radioactive decay of a mole of uranium um is as follows let's consider a reaction first uranium 248 Anum 92 238 coming converted into thorum 90 and 234 plus this is a beta this is the alpha decay helium two and four okay now if we're going to look at that the atomic numbers the subscripts and the superscripts do um add up right okay if you're going to examine the change in energy associated with this reaction you're going to inevitably have to consider the masses before and after the reaction okay now let us consider what happens first let's consider the mass of the U product right mass of products it's the mass of volum all right the mass of thorum 234 and that's 233 9942 it's actually 233 9942 AMU or atomic mass units but notice that the atomic mass units that that's the mass of one nucleus right one nucleus or one nuide of sodium 234 if you have one mole of that right that means you have [Music] 23399401 one mole of this reaction right let's talk about one mole of reaction okay so 23.99 42 G that is for thorium what about for um helium nucleid it's 40015 AMU but we're talking about one mole so that's in GRS right okay now let me move this okay so what uh all right so that one minus the mass of reactant reactant in this case is uranium 238 and the atomic mass of uranium 238 is 2 2 3803 AMU but again we're considering one mole so that's GRS all right too much okay so you have what is the difference in Mass the difference in Mass you can see here Del m is equ Al to what just use our calculators and you're going to get the following 0.46 GRS see that you're missing 4.6 mgram right where did that mass go what happened to that mass all right okay now the fact with the system has Lo Mass suggests that the process is exoic which is true right this process is exothermic it actually releases energy so the mass the Lost Mass can be accounted for by considering the fact that it's converted into energy excuse me so the change in energy or the the energy associated with that process can think of that as what is our equation E is equal to m c^ 2 so you can think of that change in mass as becoming converted into energy right the energy that it's converted to must be equal to well Delta M time c^ 2 all right and what is that equal to let me move this to the left it's equal to um netive 0.46 GS but what is one gr that is um 10^3 of a kilogram right times 10^ the kilogram why are we using we're using the um SI unit excuse me so C is remember um meters per second it's in unit of meters per second so that's going to be 3. * 10 to the 8 m per second squared so the answer what you're going to get here is4 1 * 10 to the 11 kilog per kilogram square meter per um Square second and kilogram met squ per second squ that's the unit of energy Jews -4.1 * 10 to the 11 Jew that is a huge amount of energy right right that's 10^ the 11 Jew and that's just one mole one mole of such a reaction right okay that this calculation emphasizes the fact that even the slightest change in the amount even the slightest loss in Mass which in this case is just 4.6 milligrams translates into a huge energy right 4.1 * 10 to the 11 right actually I would preferred to Simply drop the negative sign because uh well understood of course that the U sorry understood of course that that amount of energy has been released in the course of a reaction counting for the Lost Mass okay now yesterday we also talked about the fact that the nucle tend to be or some nucleid tend to be more stable than the others and that this nucleid are found in the belt or the band of stability right okay we made certain observations and we said that well we do not know exactly what's going on but we just think or there is a reason for us to believe that the the protons are arranged in shells inside the nucleus then again the uh neutrons play important role in this in in maintaining the Integrity of the nucleus right that the more protons you have the more nut must there be or must there must be there in the nucleus in order to stabilize it in order to prevent the protons from spontaneously um um shooting out or or or spontaneously um firing out of the nucleus okay now talk about the nuclear binding energy the nuclear binding energies one of the most interesting things that have been discovered in study of nuclear chemistry or Nuclear Physics was the fact that the mass of the actual nucleus is smaller than the mass of the nucleons from which it took made for example consider the case of uh helium right helium 4 helium 4 has two protons and what two neutrons right there two protons and two neutrons we know the weight of a proton and the weight of a neutron accurately we're able we know that values or we know those values also able to measure the weight of a nucleus of helium so we're going to add up so the mass of two protons and the mass of two neutrons in other words the nucleons these are the nucleons 2 * 1.007 um 28 AMU two times what is this 1.0 867 AMU you get the total amount the total masses and you're going to get 4.03 um 1 n0 atomic mass unit all right that's the mass that's the mass that you expect right because a the nucleus is just two protons and two neutrons so you expect that mass okay all right surprisingly however when they measured the mass of the helium nucleus mass of the helium nucleid they found out that its mass is actually 4.15 atomic mass unit but notice there is a defect right there is a difference in Mass it appears that the nucle the nucleus or the nucleid is lighter than we expected right we expected it to be 4.0 3190 uh atomic mass units in in weight but we have just 4.15 atomic mass unit the mass defect we call that the mass defect Delta m is a um 0 um z30 40 atomic mass unit that's the missing Mass the missing Mass all right apparently that missing mass or we rationalize that missing mass by considering it to have become converted into energy right and as before you are able to um compute excuse me you're able to compute for the um energy um by using the equation E is equal to M c² all right um you simply need to uh do the uh calculations on your own and uh you will be able to compute for the corresponding value again or again as we have done um a while ago we use e isal to Delta M time c^ 2 right the value of energy that you're going to get here is for for helium right this is for helium is um um 4.54 I'm going to leave it to you to substitute in the values 4.54 * 10^ the -12 of a jewel right okay 4.54 * 10 -12 Jew right okay that's the binding energy that's the nuclear binding energy and that energy is thought to bind the nucle together to hold the protons together the energy that is used to prevent the um nucleus from spontaneously disintegrated to prevent the protons from shooting out of the nucleus right now when they you can compute for the nuclear binding energies for different different um nucleid of course for as long as you know the actual weights of the nucleid and the masses of the protein since I've already mentioned are known so can can just use it from the you can just use the values that I have used here in problems for you have to be given the mass of a nucleid right the mass of a nucleid in in many instances um we can use the atomic mass why because the electrons are essentially massless they they do not have any significant mass and so the mass of the nucleus is the mass of the atom itself right okay now they did um compute for The Binding energies of many different elements and they they computed for The Binding energy per nucleon all right The Binding energy per nucleon what is that you just get your um nuclear binding energy and divide that by the total number of nucleons that you have number of neutrons plus the number of protons and they observe that all right plot of the uh binding energy per nucleon against the mass number they noticed that you have something like that right um here is uh let's say you have your helium this is not drawn to scale right helium 4 and say you have here iron 56 and you have here uranium 235 now what do you notice or what what do we expect we expect those nucleid which have high nuclear binding energies for nucleon to be stable they are stable and since they are stable all the other nuclei tend to become like them tend to become like other words tend to become something like iron 56 right in the case of helium and other lighter elements they are able to become stable in other words they are able to have to to AC to to acquire an identity where um they're able to become converted into stable nucleid by fusing together right into becoming that intermediate mass or intermediately sized nucleid like iron 56 and so you expect them here to undergo fusion and we know that in our discussion yesterday we've learned that um hydrogen the Isotopes of hydrogen under go Fusion to the process produce helium in the Sun and in fact the other elements other heavier elements can be synthesized from Helium and hydrogen from the reactions that occur in the sun other Fusion reactions that occur in the Sun what about the heavy elements the heavy elements become stable in other words they become converted into nucleid in the vicinity of iron in 56 like somewhere here right somewhere here by what by breaking apart into smaller into smaller particles in other words they undergo fishing right they undergo fish all right and what else does this diagram tell you it tells you or it confirms what we already know the amount of energy that is released in in the process of fusion right that energy is much greater than the energy that is released as a result of fusion as a result of fishion right the amount of energy released during Fusion is much greater than the amount of energy released um during fishion all right tomorrow we're going to continue with our discussion we're going to turn your attention to the um measure to the different ways of expressing um the um doses of radiation and consider some examples of the terrible use of uh of nuclear nuclear very knowledge of nuclear chemistry and nuclear physics the case of hirosima and nasaki in Japan all right been obliterated during the second world war all right the previous discussion we have considered the um rates of radioactive decay as well as the the uh nuclear binding energies said that the nuclear binding energy at least the nuclear binding energy gives us a parameter you can use to gauge the tendency of of a a nuclei to either undergo fusion or to undergo fishing this too we have mentioned that fishing gives off much gives up smaller amount of energy comparison to Fusion that currently we're unable to harness um energy from Fusion reactions we are however able to for a long time already able to harness energy from fishing nuclear reactors are powered by Fishin okay it do review what Fishin is and how they are how this process is appropriated for the generation of energy now nuclear fishion involves the splitting of a heavy nucleus into two or more smaller nucle as well as some other subatomic particles in energy so we learned already that having nucleus usually unstable due to the many positive protons that tear that tend to push um each other part or that tend to tear the nucleus and tend to push each other away all right when fishion occurs you know that tremendous amount of energy is produced and that more neutrons are given up for every one one fishing reaction we usually use a neutron as a a bombarding particle because a neutron is a neutral a neutral particle and therefore will not be subject to repulsion by the um nucleus the target um nucleus once it is bombarded is converted into an unstabilized to which then under goes um nuclear change nuclear reaction it killes off particles like alpha beta particles and a tremendous amount of energy and of course V stable product um I give it to you as an exercise to the identity of the daughter nucle that is where the particle that is produced from this um reactions again bearing in mind that the mass numbers in very reactant in the products must be the same and that rather a sum of the mass numbers and the reactant in the products must be the same and some of the atomic numbers also have to be the same okay now you will notice that each fishion reaction produces as in the case of uranium 235 the fishing reaction of uranium 235 converts it into a very unstable nucle sh under goes the composition into bar 140 in Crypton 93 what is interesting to note is the fact that aside from the tremendous amount of energy is generated in this process the fishion reaction also gives off one two and three three more neutrons each of these neutrons will cause another efficient reaction so one Neutron causing one fish will generate three neutrons which will generate three fishs and then three fishs will generate um three neutrons each going to give up nine neutrons going to generate nine fishion going to generate 27 neutrons and 27 fishion going to generate um 81 um fishion and uh um 81 * 3 neutrons it is easy to see that the uh process is a chain reaction right that the rate of reaction proceeds exponentially therefore the amount of energy generated from such a system is magnified um astronomically unless you figure out a way of controlling this reaction this process this um will lead to well destruction Annihilation essentially um if you're are aware of it the uh uranium is actually used as um fuel for making nuclear bombs all right okay this is the first um atomic explosion in New Mexico in the United States usually test this in the desert in the United States in plenty of desert so they test their um nuclear uh bombs in the uh um in the uh desert okay so this is the uranium bomb right see here the uranium um we call it the little boy and uh this is um fueled or uh the explosive material here the nuclearly explosive material is uranium okay so when you want to consider what happens there you have to take note of some terms like critical mass subcritical mass and super critical mass the critical mass is just the right amount of the um fuel for for a sustained reaction like it's not a chain reaction you're just um allowing the fishing reaction to proceed at a rate where one fishing leads to one fishing reaction what does that mean that means that one Neutron leads to the formation of one Neutron it has to be clarified because always three neutrons are always generated so it means that that one Neutron leads to the formation of only one active Neutron how do you do that in nuclear reactors you control you have some control rods which effectively absorb exist neutrons the process controlling the rates of reaction okay so if you have a mass that is less than the critical mass then the reaction will not be self sustained and it will not will after some time come to a halt if it's more than critical mass then you risk an explosion okay so you have here a uranium bomb you have two subcritical masses um I think you have you have a subcritical mass of uh uranium 235 and you have a subcritical another subcritical Mass you're designed as a tube and a plug right have a cube in a PL when you this is harmless because you have two subcritical Mass um however when this two masses are combined into one they generate a super critical Mount right or in amount that is um more than what's necessary or that is just above what is necessary for for um the sustained reaction so in that case it's going to be a chain reaction a chemical explosive is typically used Us in order to um detonate the bomb and to fuse the two subcritical masses to each other okay so you produce or generate in a pure explosion a plutonium bomb has been designed in similar way but there's just a different schematic so you have here a sphere of plutonium right you it's subcritical because you have a hole right at V Center uh you line the um periphery with conventional explosive conventional explosive then you detonate that the sphere is going to be compressed and it's going to collapse on itself to produce a critical mass or a super critical mass gain generating a nuclear explosion right now see here what happens as a result of uh the uh bombing at hirosima all right it's total Destruction okay the Japanese I'm not sure if you watch History U uh documentary the Japanese even after Germany is has um surrendered already the Japanese still will not okay and so the Americans um were debating and that what to do what to do with with the Japanese because they really did not want to surrender in fact they were using themselves as Weapons like kamikazi kamikazi bombers right um they are attacking I think the uh whatever Fleet of the United States and Australia is in the Pacific so um they fought that the only way in which Japanese will be forced to surrender is um by dropping ball at hirosima and the gaki right it's a a horrific horrific incident in human history immediately after the bomb has been dropped and uh the devastation happened Japan surrendered un conditioning all right now I was talking about the uranium also being used as a the fuel in nuclear reactors here is a schematic of the core right perhaps I should show you this first here is the schematic diagram of a nuclear power plant you have here the core all right and in the core you find the nuclear fuel rods excuse me you have the nuclear fuel rods and you have here the control rods I will tell you more about what they do and what they are for later so you have here a coolant right the coolant essentially is the fluid that um flows through the reactor all right now this can be just water like typically usually heavy water gated water in other words some of substance okay what happens is that or if you're going to look at the schematic the uh coolant all right passes through a region here where you have just water this is not radioactive right because it is protected from the coolant that flows um circulates within the core now the water is effectively heated up because you can imagine the coolant to be um or sorry whatever circulating fluid here um whatever circulating fluid they use um must be hot must be very hot and so it vaporizes water into steam steam is connected to a turbine all right steam turbine here and you have um you generate electricity of course as a result the uh steam is condensed okay and uh as you can see here it's simply um really generated or at least mix with the water from which it came from okay all right so what we're interested with be the control rods and the nuclear fuel rods so you have here the nuclear fuel rods they contain the uranium fuel okay now what is the function of a control rods so control rods can be adjusted up or it can be moved down depending on what you want depending on the condition of a nuclear reactor the um control rods contain a substance like one of one of the materials that they use is bordon so bordon effectively captures the neutron all right Bon captures the neutron and so if you see that the nuclear reaction of a nuclear fishing process is occurring at an alarming rate and explosive rate then you're going to move the control rods downward in order to absorb the excess of the neutral right you want the nuclear fishion reaction to occur in such a way that one fishion reaction leads to just one fish not three fish reactions you want want to let it occur or you want to make it occur at a constant rate right the steady rate you don't want it to happen you don't want the rate to magnify itself exponentially okay if you see that the um reaction is actually proceeding very slowly then you simply have to lift the rods up that case less of the neutrons will be captured and the rate of re reaction deficient reaction will be enhanced answer will be increased okay okay uh this is enrio thur and I believe you have in one way or another heard of him uh he built the first atomic pile and produced the first control chain Rea look at that on December 12 1942 okay here are examples of the cooling towers of the nuclear power plant and I think this is in the states okay all right here is another a a disaster the the uh nuclear power plant chobble in Ukraine all right um that is a disaster um accident happened in April 16 1986 which caused the release of radioactive material in chern okay um this is now a ghost St the only thing living there will be the wild animals that is amazing you know what because I'm not sure if you if you watch um there's a series in Netflix it's our planet our planet narrated by David attenberg they featured that animals have been coming back to churn that means that the levels ofation is no longer as intolerable as before right the fact that um the animals like the Wolves the deers some of our small animals have and birds have come back to chle means that the environment has somehow managed to heal itself right and to restore itself to its previous state I'm not sure if it's already complete but at least the uh environment is healing okay um so this is one of the um um one of the worst disasters ever happened you have can just imagine what happened in April 16 1986 they needed to evacuate an entire an entire um region right the chobble region and if you watch that documentary i' one I've already mentioned you will see houses buildings completely empty and uh the only things living there the the animals they have reclaimed the the uh space okay um okay but this are quite rare the uh fallout the nuclear fallout of this kind accidents of this kind the United States for example is very much reliant on on nuclear power I think uh fance as well Germany has started to uh I think three years ago the German government decided to to uh stop relying too much on nuclear power okay all right there is a there's something there's a Power Nuclear Power Plant in ban they abandoned it right I don't know exactly why they abandoned it but maybe it's for the better right don't know maybe it's for the better okay um now here are the challenges of uh having nuclear power as your source of energy how do you dispose of waste products the waste products here tend to be radioactive right so that's a problem see what they do or what they do in the stat is they construct they bury their nuclear waste deep under ground very clever right very clever because this um as you've already as we've already mentioned and discuss this radioactivity won't won't penetrate um concrete for example so that's what they do they have lots of this places this kind of places in the states here is a construction of a tunnel that would be used for burial of radioactive waste deep within the commountain in Nevada okay all right or they can also dispose of them in a in a shallow bit but I don't know I think the first one is more is more preferable okay all right I think I've already covered this um topics all right I do want to uh I do want to uh show you this photographs these are great scientists of uh the 20th century this is uh Madame marce clova all right she I believe she is the only one correct me if I'm wrong but I believe she's the only one who has two Nobel prizes one in chemistry and the other one in physics she first she first got a Nobel Prize in physics for her study with on radioactivity and uh I think the second is a Nobel Prize in chemistry for discovery of the elements Ru I can't remember the other one I'm not sure if it's Pon but one is R definitely right so she's the only one who has two Nobel Prize uh after her name and she right was a woman Ernest rofer Ford he discovered Alpha rays and beta Rays okay and CH James chadrick the [Music] neutron okay this are other great scientists Le mner and otan and and okay opheim and uh Groves they were the first people who tested the atomic bomb and of course greatest scientist of the 20th century Albert Einstein right it is C discovered V creation as you already know that relates mass and energy all right and [Music] he he called caution people the use of nuclear weapon right he uh caution people in the use of nuclear we he said that um the next war that will be fought if if if if if if people use nuclear weapons as means to destroy each other then the war after that will be fought with sticks and stones right and that's the danger right that's a danger nowadays we live in a world of nuclear Powers the United States is a nuclear power the um Russia is a nuclear power and of course our neighbor China is also nuclear right so let's hope and pray that um war will not come during our lifetimes your children your children's Children's lifetimes but I think war is inevitable okay hopefully hopefully it won't happen but I think it will happen but hopefully it won't prev discussion or just in our discussion a while ago we considered the possible um effects disasters terrible effects of nuclear um nuclear weapons to you to society in general now we turn our attention to the uh more specific one the effects of of uh the effect of where is that the effect of H okay the effect of um radioactive Emissions on living tissues okay in other words the biological effects of radiation biological effects of radiation biological effect of radiation we mentioned already that the um that the radioactive emissions are high energy emission all right and there are two you can classify them into two kinds you can either call them ionizing or nonone ionizing radiation the ionizing radiation of course leads to the generation of ions specifically they are able to knock out electrons out of a molecule or out of an atom nonionizing radiations are those emissions that are just simp be able to exite an electron from a lower energy orbital to a higher energy orbital in the process exiting the molecule or the atom from ground state to a higher energy State okay this too of course the more detrimental is the ionizing radiation right the ionizing radiation um now most of the living tissue contains at least 70% water it is therefore not surprising that um the term ionizing is U defined um by saying that an ionizing radiation is radiation that can cause the ionization of water right I mean all the process requires around 12 16 kilj per mole gain V ionizing radiation is commonly defined as those radioactive emissions or radiation in general it's able to cause the ionization of molecules of water the ionization of water typically requires 1,26 KJ per mole right so based on this classification or based on this criteria alpha beta and gamma rays as well as of course xrays and higher energy ultraviolet light um are ionizing radiation because they possess energies that are in excess of 1,216 K per mole all right so it is relevant then to ask the question what happens when water under goes ionization okay so let's see this is a molecule of water when this is exposed to ionizing radiation let's just say h new um perhaps it's best to call it just ionizing radiation you have already studied organic chemistry so you would know that of these electrons in the oxygen atom the easiest one to dislodge would be the electron in the lone pair or in the um non-bonded pair of electrons right so this is going to generate following o h h in other words you're going to have that radical all right okay here is a thing when you have or when you generate this species in water what's going to happen is it it's it's so unstable right it's so unstable but it's going to react with with whatever substance that's in the vicinity and that will be able to make it more stable by the way has a charge of positive one because it has lost an electron all right so it's going to react with another molecule of water because that's what's in abundance right water going to reative another molecule of water in the process generate a hydronium ion perhaps it's best to draw it right generate a hydronium ion and a hydroxy pH radical okay hyrogen and you have there alone um electron so we also call that or we simply write that an O radical or hydroxy radical I'm not sure if you've already uh studied biochemistry but of course you would have if you had then you would have been made familiar with biological molecules and their important functions in living systems the hydroxy radicals will react with proteins or nucleic acids carbohydrates um even with lipids to U form um other radicals and uh ultimately this molecules will react with other compounds in the body until the until in the end you end up with the biological molecules no longer being able to perform their function all right so naturally diseases more usually cancer and shoes right and cancer is U when the cell control is dividing uncontrollable when the cell is no longer able to control the rate at which it under go cell division right uncontrolled proliferation of cell occurs when the growth um uh regulation mechanism of the cell has become impaired and cancer is one of the um possible effects of having a lot of this kind of radicals in the B okay all right and this is primarily as I've mentioned the culprit hydroxy radicals which as I've mentioned will react with u react with biological molecules proteins um nucleic acids Etc produce more radicals okay all right the um exposure to radiation and their corresponding effects are expressed in terms of well units of a of absorbed dose okay and effective absorb dose let's consider those you have radiation doses radiation dosis okay all right now in order to uh um estimate the um radiation that that is absorbed the amount of radiation that is absorbed by the um body or by an individual we must first have a way of expressing activity of a a ractive material all right there are several different units that are used for meas in radiation of this the SI unit is the um um beel right that's one beel one BQ is equal to um one disintegration per second all right one this integration per second so this is a unit of activity of a radioactive material one disintegration per second now there's an older unit it's aury right Ci or cury um it's an old unit but it's still widely used it is defined as [Music] 3.7 * 10^ 10 disintegrations per second if you're wondering why 3.7 * 10 10 in other words why 3.7 * 10 10 beel then um the number 3.7 * 10 10 is important number because it's actually the rate of decay of one gram of radium that's why it's called a c right because Madam C has discovered radio okay all right so very important to take note of that one be is one disintegration per second one C is 3.7 * 10 10 be or 3.7 * 10 10 disintegration per second okay now how do you then measure the um exposure to R these are just the activity of the radioactive material or a radioactive substance how do you measure its effect living tissues in terms of how much of varation energy has become absorbed now two units are commonly used to measure the amount of exposure to radiation and these are the gray one sorry one gray the gray and thead gy right now one gray gray by the way is SI unit of um absorb dose one gray is equal to or it corresponds to the absorption of one Jewel of energy per kilogram of tissue right one Jewel of energy per kilogram of tissue okay that's one grade now another another um unit that is more commonly used when gray is rad one rad all right rad stands for radiation absorb dose radiation absorb dose so one rad corresponds to the absorption of 1 * 10 -2 Jew of energy per kilogram of dissue all right kilogram of dissue so it's obvious or it's apparent that one gray is equal to 100 rad all right clinically the use um red more than uh gray but as a unit of absorb those is the gray okay so the gray and the red all right okay now not all forms though of of um radiation have the same efficiency for damaging biological isssues we already mentioned already saw that um the radiation have different degrees of penetration they penetrate um an object at different to different degrees and therefore they would impart different levels of damage to a biological material right so um for example one rad of alpha radiation um can produce more damage apparently than R of beta radiation this can be associated with the fact that the um that the uh alpha particles are heavier than the electrons right much heavier than the beta particles the electrons to correct therefore for the differences in the damaging capabilities of the different kinds of radiation we multiply the absorb dose by the relative biological effectiveness of radiation all right rbe should highlight this first okay we multiply the absorb dose I fail to indicate that this is absorbed dose the unit of absorb do now the effective absorb dose or the effective dosage of absorb radiation takes into account not just we absorb those but also the relative biological effectiveness of the radioactivity all right and the rbe varies from one particle to another in the exam you will be provided with the corresponding RB or in the question you must be provided that okay um okay the exact value of the relative biological Effectiveness um varies with the dose rate the total dose all right and the type of tissue affected it's natural or it's expected some tissues will be more assistant than others all right and um the U the uh product of the absorb dose in RADS and the rbe gives you the effective dosage in rem all right or renen equivalent for man so you write here the number of RMS or the effective dossage in rims I write that number of RS right what is the what does REM stand for Ren equivalent of man is equal to the number of RADS all right of absorb [Music] those multiplied by the relative biological Effectiveness okay well the RS is is a is used often clinically right it's used often clinically but it's not the SI it's not the SI unit of uh um uh it's not the SI unit of U of U effective dosage Thea sorry Thea SI unit of effective dosage is a sh out right so one she SV shiv is equal [Music] to 100 Rin equivalent for ma right 100 RS actually you're going to notice you get the number of shs right number of shiv or SV effective dossage in terms of the number of she is obtained by multiplying the dose in Gray number words number of um Gray multiplied by rbe right so it's there um it's therefore um not surprising that one shiv as we see here is equal to 100 G because what do you notice we just multiply that relationship one gray is equal to 100 d right okay if you do that let's do that so one gray is equal to 100 okay if you multiply both sides of the equation by um the RVE like multiply both sides of equation by the rbe you get one gray multip by the rbe is equal to 100 R multili by the rbe right already mentioned gray times the rbe will just give you the number of she one sheer and you have rad times the RVE will give you the um number of RS so you end up with 100 rad times rbe is just R so one shiv it is indeed one 100 them all right okay um all right the r as I've already mentioned is a unit of radiation damage that is usually used in clinical setting in in medicine for example I think there's there's a field called nuclear medicine right so those those are the unit typically um use in their calculations right the effects of shortterm exposure to uh radiation or um as follows I want you to get an idea of what happened so if for example you're exposed to Z to 25 Rim gr engine equivalent per man there's no detectable clinically effect excuse me however if they're exposed from exposed to a dose or they have an an um an exposure of 25 to 50 of them you're going to suffer from slight or temporary decrease in white blood cell CS I'm not going to ask you this in the exam or in the quiz I'm just I just want you to have any an idea what's going to happen apparently if you're exposed to a um I mean if you have um an effective dosage of 100 to 200 RMS you're going to suffer nausea right and the mark decrease in white blood cells and if you have 500 you have an effective dosage of 500 RMS um you're going to uh guarante um there's a chance that you're going to die right they observe that half of the exposed population died within 30 days and after exposure that's why if you're you're a member your advice not to take X-rays of yourselves I can't remember how how not how how often or how not often but from what I remember you your advice not to take it I may be wrong I'm not I'm not a physician but from what I remember I think you're advised not to take it more than twice in a month right because xray is an ionizing radiation so naturally there's a um there's a possibility of suffering from are suffering from a from a disease or from a condition it's brought about by Too much exposure to such ionizing radiation okay all right all right now let us consider an exercise H let's consider an exercise okay let's example sorry a laboratory rat is exposed to an alpha radiation alha radiation Source Alpha radiation Source was activity is 8.7 M CU 8.7 mli cuy what is a what is the activity of the radiation in this Integrations per second and B the rat has a mass okay the r has a mass of uh 250 g 1/4 of a kilo and is exposed to the radiation um for two seconds absorbing [Music] 65% of the emitted alpha particles of the particles each having an energy each having an energy of 9.2 * 10 to the 13 Jewel calculate the absorb dose [Music] in mads and gray C if V is the uh rbe of the radiation is um 9.5 the RV of the radiation is 9.5 calculate the effective absorb do in m and okay so solution a let's look at the problem a laboratory rat is exposed to an alter radiation Source there activity is and is A7 mq what is activity of the radiation in this Integrations per second so think this straightforward right the activity excuse me is equal to what is that 28 M um 8.7 8.7 yeah 8.7 M so 8.7 M so that means 8.7 * 10^ the3 of a c right what is 1 c um look at our 1 C 3.7 * 10 10 10 3.7 * 10 10 3.7 * 10 10 I'm just going to write this meaning this integration per second so let's use our calculators and solve for that it's going to be 3 8.7 exping to the 3.7 exponent 10 okay so it's going to [Music] be 3.22 * 10 to the 1 2 3 four five six 7 8 eight this integration for second okay 3.22 * 10 8 is Integrations for second letter B what we asked uh the rat has a mass of 250 gram and is exposed to the radiation for two seconds absorbing 65% of the emitted alpha particles oh each having an energy 9.12 * 10^3 calculate we absorb those in mads and inre okay so let's first compute the quantity in grade because I think the grade you remember where is our unit the gray is one absorption of one Jewel of energy per kilogram of tissue right so let's first um compute for the uh dosage perhaps I should write absorb do okay equal to want um so this is more or less your your dimensional analysis right um two seconds so you multiply your number of disintegrations by two so it will give you the number of disintegrations for every disintegration you naturally have one alpha particle but only 65% of that gets um absorbed so you multiply it by 65 and then each having each ala particle has 9.12 * 103 Jew okay so it's going to be 3.22 * 10 to the 8 this per second multiplied by 2.0 second second cancels out one alpha particle for every this integration so this this um so that will give you the number of ala particles right because the units cancel out but you are given that only 65% gets absorbed so you multiply it by six by 0.65 or 65% or 65 over 100 but we're talking about the energy right absorb those is the energy in Jewels per kilogram of tissue um what is the energy of one alha particle it's uh 9.2 * 103 okay 9.2 * 10 the3 [Music] Jews 13 Jews what is the weight of the U rat the rat has a mass of 250 grams what is our what is gray it's the amount of energy in Jewel right you see there in Jewel per kilogram of tissue so you have to divide that by 0.25 kilogram or 0.250 kilogram use your calculator okay times 3.22 * 10 8 * 2 * um um .65 what else times 9 12 exponent to the3 ided by 0.25 okay the answer is 1 53 * 10^ the -3 um Jew per kilogram or simply 150 3 um * 10 to the3 gray let me re check the computation yeah 1.53 exponent of a negative3 gray what else you're also being asked to an in milar R okay sure H what do you know one gray is equal to how many rods one gray is equal to 100 rad right one gray is equal to 100 rad one rad is equal to how many mill RADS 1,000 right so it follows that one gray is equal to what 10^ SAR * 10 Cub or 10 the 5th other words 100,000 100,000 mil oh so that's why that's why we wanted to give it in m r a more realistic like value in the sense that it's not a negative power of 10 so 1.53 * 1 exponent to the 5th it's going to [Music] be 53 m r okay letter c this is the effective dosage and it's straightforward right um you're asked to calculate VM if if rbe the relative biological Effectiveness is 9.5 calculate the effective absorb dose in millam and in so we remember that if you want to determine the effect dosage in shiv you just need to multiply the number of Grays to absorb those by the rbe okay so that's 153 or 1.53 rather times 10^ the -3 gray multiplied by the rbe which is 9.5 okay it's um 9.5 that is 0 um 0145 sh or again you have the same relationship you have one CH that means you have how many rims you have I think yeah I I showed it here 100 RMS so if you're looking for MMS of course you need to multiply that by 10 the 5th right times 1 exponent to the 5 which is um um 1,450 this is units of millam can simply multiply 15 153 by 9.5 okay so that's the uh answer that we obtain that is how we express the effective absorb do um from in information about the activity of the ractive materials and of course the absorb dosage or dose of radiation I hope that you have learned something from this discussion