Transcript for:
Fundamentals of Atoms and Isotopes

all right so we're going to start this lecture talking about atoms and elements and probably the best place to start is with something called the atomic theory put forth by dalton and this was uh put forward around like the 1800s early 1800s and so um based on everything that was known at the time the these four things i have listed here as as the theory are actually quite impressive although there are some errors to them that we're going to correct um then we're going to kind of see why they are wrong and how we need to adjust the way that we look at these so the first one is that all matter is made of atoms and then atoms are indivisible and indestructible so so this one here is not quite correct and you know some of us may know this because we've had maybe a chemistry class before but the atom is not the smallest piece of matter right it can be broken down into electrons and protons and neutrons and so on and we'll and we'll look at that um and then the next one says all atoms of a given element are identical in mass and properties and this is also incorrect and we're gonna see this um and we're gonna we're gonna see this idea of what are called isotopes which are gonna kind of help us understand how one atom of an element can be a little bit different than one another atom of the same element so for instance not every hydrogen atom is the same and then third it says compounds are formed by a combination of two or more different kinds of elements so this is this is true and so one of the ways that i kind of want to draw this out is let's imagine that we have a let's imagine that we've got a hydrogen atom and then we've got another hydrogen atom okay and so i will label these as hydrogen atoms all right and um and then we have let's say an oxygen atom and an oxygen atom is going to be a little bit bigger and we'll learn about that so we'll just say this is an o atom right so an oxygen atom and what the third third point here says compounds are formed by a combination of two or more different kinds of elements so if i take two hydrogen atoms and two sorry one oxygen atom i can put those together to form water this is roughly what water would look like and we'll you know have a better picture of this as we go but this is something that we kind of picture as we you know we think about a water molecule so this is a compound of water um and so this part is actually correct right so compounds a water compound is formed by taking some oxygen atoms and some hydrogen atoms and and putting them together in a two to one ratio in this case um okay so kind of sticking with this idea of water right so we have this here where we can think of a you know water molecule is a combination of these two and so what i'm going to do is i'm going to get rid of this picture so i can draw a new picture and the fourth one says a chemical reaction is the rearrangement of atoms this is also true so let's again let's let's kind of take water as an example but let's say that we've got a now i'm drawing this a little different than i did the first time so these are hydrogen molecules so we would say these are h2 molecules and we're going to learn the difference between molecules and atoms and what all this means and then we're going to have a molecule of oxygen so this is an o2 molecule all right now when a chemical reaction takes place these are going to get rearranged so these two oxygen molecules are no longer going to be together and those hydro molecules aren't going to be together anymore they're going to rearrange and as we saw up here and i'll just kind of take this this here but we're going to form a molecule of water that's going to look something like that and then we're going to form another one of these right so we're going to get these two water molecules so we're taking these atoms that are connected in one way and we're rearranging them to make something else but notice that i still end up with this is kind of the key point here is that i started with one two three four hydrogen atoms and i end up with one two three four hydrogen atoms and i started with two oxygen atoms and i end up with two oxygen atoms so it's not like i change these atoms into something else right so all i'm doing is rearranging these atoms okay so three and four are pretty much correct we there are some what we call nuclear reactions which are gonna you know maybe disagree with this atomic theory but i don't think that that's very helpful at this point but we're going to look at at one and two in a little bit more detail because we do have to understand why these are wrong in order for us to kind of understand all the stuff that we need to get through in the class so we're going to start with one and talk about kind of this idea that all matter is made of atoms which is true um atoms are indivisible and indestructible this is this is not true so we know that we can break down an atom into something smaller which was not thought of as possible at the time so i'm going to say that you know we're going to modify dalton's atomic theory so in so around 1900 okay and i'm not going to ask you specific dates um the electron was discovered and i'll write electron out but the way that i'm going to abbreviate this is that so that means electron so okay so the electron was discovered and this is what's called the subatomic particle which basically means it's part of the atom and so this was the first time that something smaller than an atom was discovered before they thought that an atom was the smallest piece of matter and um and that is not true so here we have a subatomic particle and this is one of the pieces that actually makes up an atom okay now this is a negatively charged particle that is part of the atom okay so um okay and the other thing that's important about this that is that this the the electrons they're about 1 000th the mass of a hydrogen atom and at the time you know hydrogen atom being the lightest atom on the periodic table it was thought that that was the smallest particle that existed and so here they have these electrons that are 1 1000 the mass of a hydrogen atom and so they're very very tiny okay so we'll say they're negatively charged particle with a mass approximately equal to one one thousandth the mass of an h atom okay so that's pretty important so this is a very small piece of matter and um it it wasn't discovered you know earlier just because it's so small and you know technology had to come along that made it um it made it possible for us to discover things that were were so tiny basically okay um so now if you think about an atom and this is something that that might be intuitive may not be intuitive but atoms in general are neutral meaning they don't have a charge there are charges that make them up and which we're going to discuss but um you know when you touch a wall it's not possibly charged like two particles can come together two two objects can come together they don't repel each other and they're not usually attracted to each other unless you know magnetic or something like that so if atoms are neutral right and everything's made up of atoms if atoms are neutral and they have found this negatively charged particle within the atom that must be mean there are positively charged particles within the atom as well because they have to cancel one and one another out okay so what this did when when in 1900 ish it was about 1897 but in around 1900 what this did was this started kind of the search for the um the positive part of the atom what what if we've got a negative part of the atom we must have a positive part of the atom because atoms are again overall neutral so let's kind of talk about how they went about trying to figure out where the positive part of the atom is and and whether that's actually true okay all right so what they did was they did a series of experiments called the alpha scattering experiments and these are um these took place roughly 1910 okay so it took them you know about about 10 years or so to kind of do these experiments and and gather enough information so that they were able to understand um the structure of the atom um to the best of their ability at the time okay so this picture i've drawn here okay there's a couple of things that are kind of important about it so this is the predicted model of the atom okay and so keep in mind that electrons had just been discovered right so they discovered these tiny negatively charged particles and that's what these are okay so this is a this is this is an electron and i've drawn this atom here that has four electrons in it right i could have drawn five or six i'm not i'm not pointing out one particular atom over another but just there's an atom here and we have these four electrons okay now what you'll notice is that i'm going to draw things that are negatively charged in red i'm going to draw things that are positively charged in blue and that'll be a theme throughout the lectures now the other thing is remember that the electrons are really tiny they're about a thousandth they make up about a thousandth of the mass of an atom and so what they thought which made sense and actually before i tell you what they thought i'll kind of explain why they thought this but if you think about again everything is made up of atoms right and i have i'm sitting here and i have a wall in front of me and that wall is made of atoms and my hand is made of atoms and when i try to push my hand through the wall it doesn't go and the idea is that those atoms that make up the wall they must be solid right that's why i can't push my hand through through the wall and so the model that they came up with was that the atoms were basically solid pieces of matter themselves and what they thought was that the atom was kind of this big sphere that was made up of all this positive material and then the electrons were embedded within that positive material so this is believed to have been what we call like a diffuse positive charge okay and again it kind of makes sense right you you think of atoms like you material has a solid feel to it so atoms which make up all the material they must be solid and since the electron is about a thousandth the mass of an atom that means that 999 parts per out of a thousand are the are whatever the positive charge is so it's probably going to take up the rest of the atom so this is kind of the idea that they had and i'm going to move this because i want to draw a picture here and this will kind of get in the way but i'm going to take this and just move this up here but it doesn't change the stuff that i said so this is the model that they have and it was actually called the plum pudding model and this model was put forward by someone in in europe and plum pudding is kind of like this cake that has raisins embedded in it so that was kind of the the picture that they had was that it was like this gooey dough which is this diffuse positive charge and then the electrons are kind of the raisins that are just floating around in there and if if this was if this model was put you know put forward in the united states it would probably be called the blueberry muffin model or something like that where you have this blueberry muffin and then the blueberries are the electrons embedded within the dough okay so kind of how maybe that that might be a more helpful picture but if you look it up it's going to be called the plum pudding model because it's actually what it was called at the time so they put they put out this model of what they think the atom looks like and again if we're going to study what matter is made up of and how it's going to behave and make new you know make engineer new products and new technologies we need to understand what we're working with and so they come up with this model and then again you can't just come up with a model and then not prove it so what they're going to do is they're going to test to see if this is correct so you'll notice up here i have this thing that i haven't actually mentioned yet but we have this this thing called the alpha scattering experiments okay and what that is is they took what are called alpha particles and what an alpha particle is it's a very dense positive charge okay so this is an alpha particle so that's the greek letter alpha so we'll call this an alpha particle and what they did was they took these alpha particles and basically shot them at atoms so you can imagine that i'm going to take this alpha particle and i'm going to shoot it at this atom and the question is what does it do when it interacts with the atom what's the prediction right so i have this also up here i have this you know predictions of what the experiments gonna gonna get now when i first thought about this when i was a student i thought oh well since that particle is positive and the atom is mostly this positive charge i expect that that is going to be repelled but when you look deeper into it you do the math what you realize is that that alpha particle which is incredibly dense like i'm not really drawing it to scale but it's this tiny tiny tiny positive charge that if it goes in and is shot at an atom the positive charge that the atom is believed to have that's spread out throughout this whole space since it is diffused right so we we use this this word here diffuse meaning it's spread out it turns out that that positive charge within the atom would not have enough focus or concentration to make this alpha particle basically get rejected or repel and so the prediction based on the math was that this alpha particle would go right through the atom and come out the other side that is the prediction okay and if they did this experiment and the alpha particles go through and just like they predicted then this is one piece of evidence to support this what we call again the plum pudding model or we'll call it a blueberry muffin model however we want to say it so that's going to support this idea that this is what the atom looks like okay now this is not what happened right so they do the experiment and then on the next slide i'll kind of talk about the actual results so here what they're going to do they're going to take this alpha particle right and again i'll draw this as this you know this tiny little positive charge and and they're going to do this and they have a whole source of these right so what's going to happen is let's say we take an alpha particle and we shoot at the atom and notice i've drawn the atom a little different now i've put the blue in the middle of the atom and it's not spread out through the whole atom so what's going to happen is i'm going to take this this alpha particle here and i'm going to take this and i'm going to shoot it at the atom and it's going to go right through you know and i just said that that that's not what happened so i feel like i'm contradicting myself here but the first one goes through then i take another one and i shoot it at the atom and this goes through as well so again here i am saying that that they didn't get the result that they expected um and but now i'm telling you that they shoot alpha particles through the atoms and they go through but notice what happens here when i take and i shoot another one through the atom where i shoot another one at the atom if it comes near that blue dot that i put in the middle it actually gets repelled and it doesn't go directly through the atom it actually gets moved and what's happening here so again some of us may know this already but this blue dot i put in the middle is what we call the nucleus of the atom and here we have this alpha particle that's going toward the atom and then it's getting repelled and pushed up and we would not have expected that to happen if the positive charge of the atom was all spread out but it turns out that every once in a while that alpha particle goes in to the atom gets too close to the nucleus which is a very dense positive charge also and that repels the alpha particle that's coming in all right and it turns out we don't really need to know the math for this but it turns out that if you were to shoot about 20 000 of these alpha particles at an atom about one out of every 20 000 would would be rejected okay and that actually tells us a little bit about the kind of the the size of the nucleus of the atom relative the size of the entire atom so it is important maybe you know as we move forward in this class we'll talk more about that so this was the discovery of the nucleus of the atom and so now we have and and that that's where all the positive charges so around uh around 1900 they discovered the electron the negatively charged particle right so we've got the electron was the first thing to be discovered and then now what we've discovered is the nucleus now within the nucleus there are actually two pieces so one of them is what's known as a proton so we'll call this the electron and if you read more about this they were they were known as cathode ray particles at the time but now we call them electrons this is what we call a proton which is inside the nucleus um and you know one of the things that's interesting is you know when we when we discover things or when we learn things um a lot of times when things are charged they're easier to to find or discover or you know come across in an experiment and so electrons and protons were easier for us to find than what um is called the neutron which is the other piece that's in the nucleus okay we'll talk about that on the next slide all right so we've got electrons that were discovered then and then and it turns out that they were discovered kind of by accident they weren't expecting them right because they thought atoms were the smallest piece of matter they did some experiments and electrons just happened to be discovered once they discovered the electron they knew that there has to be something in there that's positively charged so then they designed these alpha scattering experiments to do that okay so again one of the things that's kind of important about this is that the electron even though the electron is you know a tiny particle and the nucleus is this tiny little piece of the atom the nucleus still contains most of the mass within the atom and that's important so most of the mass of an atom is inside that nucleus or yeah most of the mass of the atom is inside that nucleus and then you have these tiny little electrons flying flying around and then most of the atom if you think about it is just empty space which is a little counter-intuitive because again we start off this this discussion by saying that you know a wall that i'm touching is a solid object so and it's made of atoms so atoms must be solid but that's not the case okay atoms are mostly empty space okay um and kind of an example of this is if you imagined you were like at a basketball game at like the sport at a sports arena of some sort and you were looking down you looked at the entire arena and if the arena was the atom if you were to put a marble in the middle of the arena that's the amount of space the nucleus takes up in terms of the volume of the atom so all the rest of it is empty space it's kind of mind-boggling if when you try to think about it so i will leave it up to you whether or not you want to really think about that okay now the other thing that's that is important about that is even though that tiny tiny amount of space that marble in the middle of the entire arena is the nucleus that's where most of the mass of the atom is it's in that tiny tiny particle in the middle okay and so the nucleus is an incredibly dense object more dense than it than any one of us can probably imagine um if you were to do the calculation if i drew like a period like this on the end of at the end of a sentence so think about how small a period is at the end of a sentence in a textbook if i were to take the mass of about 40 40 suvs like some you know chevy tahoes or something like that and put that into that period that's how dense that's how much mass is in that tiny of a space to make up the nucleus okay all right so you know what have we you know what have we kind of got from this what did we learn so the this is this is kind of the current structure of the atom that we're going to look at right so we've got our atom which we think of as kind of spherical we'll talk more about that we have electrons that are moving around and then we have the nucleus and the the protons are the positively charged part of the nucleus and then it really didn't it didn't happen for you know another 20 25 years where they they discovered the the neutrons that are also part of the nucleus okay so the protons and the neutrons are within the nucleus you know i could ask why did it take them so long to find the why did it take them so long to find the the neutrons and and the answer is because they were neutral right it's a lot easier to find things that are charged um going back to the alpha scattering experiments the nucleus rejected the alpha particle because the nucleus was positively charged and the alpha particle was positively charged neutral objects don't interact with other matter in the same way and they're a lot harder for us to study okay um and then again we have our electrons which are the negatively charged particles um now i've written down the masses for these and notice that they're all very very small right 10 to the minus 31 for the electron and 10 to the minus 27 for the k for the um for the proton and the neutron and those are incredibly small numbers okay um now what i want you to kind of take away from this though is that the proton and the neutron are much heavier than the um than the electron okay they're again they're about a thousand times heavier and so these are you know one one thing i'm going to one term i'm going to use here is i'm going to say that these are within the atom these are the massive subatomic particles okay and so um the neutrons and the protons are much much heavier than the electron okay so let's that's important to remember and then the other thing i i want us to kind of know and again i don't expect anybody to know the actual masses of these if you need them they will be provided to you but what i do want you to know is that if i was to say which of the three subatomic particles is the heaviest or the most massive the answer would be the neutron right the neutron is a little bit heavier even though we have to go all the way out here to you know this third decimal place to see that the mass of a neutron is a little heavier than the mass of a proton but neutrons are heavier than protons but they're very very close in their mass and then electrons are much lighter than that by a factor of about a thousand okay um all right so our nucleus is composed of neutrons and protons which are this tiny tiny piece of matter in the middle of the of the atom and then the electrons are flying around you know in the rest of the space now the other thing to to note here is um if i ask the question you know why so the electrons are flying around they're doing their thing and that's like a whole other discussion of what electrons are actually doing but why don't electrons just leave right like the electrons are negatively charged they don't want to be around the other electrons so why don't they just leave and the answer is they don't leave because they're attracted to the nucleus so the structure of the atom where you have this positive charge in the middle and these electrons kind of moving around outside they don't leave sometimes they do but we'll talk about why they leave other times but they don't usually leave because they're attracted to the nucleus so that's what keeps them drawn in all right and it turns out that the at the shape or the size of an atom is is dependent on you know the electrons being attracted to those protons in the nucleus and if i were to change the number of protons those electrons will be more attracted to the nucleus and so on um so that's something that we need to kind of keep in mind as we go forward okay so now let's look at this picture i've drawn here and this is just a whole bunch of carbon atoms okay so these are all carbon atoms and you'll notice that one of them looks a little different than the others this one here is different from the others but as i said they're all carbon atoms so this goes back to one of the other issues that we have with dalton's atomic theory that all atoms of the same element are the same and they're not it turns out that some atoms of carbon can be heavier than other atoms of carbon which is a little bit weird because you know all carbon atoms pretty much for the most part behave the same way and when i think about a carbon atom if it if it is neutral it will have six protons in it every carbon atom has six protons and it will also have six electrons and if this is a carbon atom two like i said this has to have six protons in the nucleus and then it's also got to have six electrons right and again the reason those electrons don't leave is because they're attracted to the protons and and if they weren't attracted they might get a little further away from the nucleus but they may not leave but they're going to you know get a certain distance away from the nucleus now if this black carbon atom that i've drawn is different than these gray carbon atoms that i've drawn um if if they're different they're different because of the number of neutrons and so for this example that we've drawn let's just say that these have six neutrons in them all the gray atoms have six neutrons and this black one has seven neutrons these two different carbon atoms the the one that has the six neutrons versus the seven neutrons they're going to behave identically chemically because they have the same protons same number of protons same number of electrons so the way that things interact with each other is very much based on the way they are charged and if i have one more neutral particle in there that's not going to change the way that a carbon atom is going to interact with an oxygen atom the carbon atoms and the oxygen atoms are going to interact because of their protons and electrons not because of those neutrons but we have to know and it actually helps us when we do research we have to understand that some carbon atoms are going to be heavier than others right and keep in mind that neutrons were the heaviest particles so if i take a carbon atom that looks like this and then i add a neutron to it and i make it into this one that carbon atom that i just made is going to be a little heavier than the the carbon atom was before so not every carbon atom has the same mass okay all right so let's go to the next slide so these two atoms that we were talking about these two different atoms they're called isotopes and so if we write this out right so this is going to have this has six protons six electrons this one has six protons and six electrons okay and again this is the important stuff in terms of how carbon does what it does and why it behaves the way that it does why it interacts with oxygen or nitrogen or hydrogen is because of these protons and these electrons okay now as i mentioned this one had seven neutrons and this one had six neutrons now the other thing that i pointed out was that the protons and the neutrons are much heavier than the electrons right so if i if i think about that i'm going to say okay well this has six protons and six neutrons it has 12 of the heavier particles or 12 of the massive particles this has six protons and seven neutrons this has 13 of the massive particles in there all right so this one here we're we're going to call this carbon 12. this 12 is telling me that i have 12 massive particles this one we're going to call carbon 13. this 13 is saying that we have 13 massive particles all right now one of the things that's very important is that so these are two different isotopes so the definition of an isotope atoms of the same element that differ in the number of neutrons so these are both carbon atoms carbon 13 is a different isotope than carbon 12 and it has one more neutron than carbon-12 does okay so it's a little bit heavier but chemically they're going to behave the same way again because they have the same number of electrons in the same number of protons and then one thing that's really important is that an atom is defined by the number of protons it has so notice that when i added another neutron i didn't make a different atom it's still carbon all carbon atoms have six protons so atoms are defined based on the number of protons they have if i were to somehow take a proton away and only have five protons um sorry if i was taking a yeah i only have five protons i would have a boron atom so i would have changed the atom i would have changed the way it behaves because i would have changed the number of protons okay so we're going to look at different ways that we write this but two things here that are important on this slide one is that so the definition of an isotope right atoms of the same element that differ in the number of neutrons and the other thing that i mentioned which will become more clear on the next slide is the number of protons within the nucleus that's what defines which atom we're talking about okay okay now i've drawn these top two already and then i drew another one down here that's a little bit smaller and we'll talk about why i drew it smaller but this is carbon 12. and we're going to write it a little different than we did on the last one we're going to write it like this okay so this is how we would denote that we have a carbon 12 isotope and this one we said was carbon 13 okay and you'll notice that i'm writing like a 12 and the 13 which hopefully makes sense based on what we talked about on the previous one and but i'm writing six below each of those and so that might be a little bit confusing um so the the technique that i'm using here is is to write them out like this okay so this this is the elemental symbol okay so a c for carbon this is what is known as the mass number okay this is the number of protons plus the number of neutrons that's what that is so this is the number of protons plus the number of neutrons okay now the way i remember this is that protons and neutrons are the massive subatomic particles so the mass numbers how many of those do i have and again with carbon 12 let's just look at this one for carbon 12 we said that i in there i will have six protons plus i will have six neutrons right so i have 12 of the massive particles and then in carbon 13 i have six protons because it's carbon but i have seven neutrons right so the mass number is 13. okay now this z is what is known as the atomic number this is the number of protons and the reason we call it the atomic number is because again the number of protons tells me what atom i have so if i have six protons i have carbon and if you were to be looking at a periodic table let's say you had seven protons that would be nitrogen and if you had eight protons that would be oxygen so that's what we have with our atomic number and our mass number the atomic number tells us what atom we have the atomic number tells us the number of protons and the number of neutrons now if i know what atom i have i have i will know how many protons i have so then i can figure out how many neutrons i have okay now i want to do one thing here so i drew this other one um and i again i drew it a little bit smaller and there's a couple kind of key parts to this but um now i drew it the same color as the carbon 12. so what i'm going to do is i'm going to say that this is also carbon 12 but it can't be exactly the same because i drew it different right so like if i draw them if i draw it smaller that's got to be some difference now this has a mass number of 12 which means it has 12 pro sorry six protons and and six electrons sorry six protons and six neutrons and then the atomic number is six which tells me that it's carbon the one way i want to modify this is i'm now going to say that this is a plus so this is a carbon-12 that has a plus charge what this means this means that it lost an electron so somehow an electron was removed and i told you before that that electrons like to stay with the atom because they're attracted to the nucleus but something can come along that the electron maybe is more attracted to and the electron would then go with that other item okay that other that other atom now the reason why this is important is because this positive charge here there's two ways that i can imagine something would become positively charged either i add a proton or i remove an electron and if i ask the question how do i know that i didn't add a proton and the answer would be because i have carbon still carbon has six protons a c plus does not mean that you have seven protons if you had seven protons you would have a nitrogen atom so it turns out and again going back to kind of the structure of the atom the nucleus is right in the middle and the electrons are flying around outside so atoms can have electrons taken off or put on but they don't change their number of protons in in the middle okay now i again the other thing i want to point out is that i said that you know the size of the atoms are kind of defined by where the electrons move around well if i were to ch and then those electrons are attracted to the nucleus if i have fewer electrons they're not going to be repelling each other so they're going to be more attracted to the nucleus and they're going to get pulled in closer which is why a carbon plus is actually a little bit smaller okay now the other thing is you know i want to just draw this because sometimes this this is how you'll see it but i use this technique here without writing the z in and the z is kind of redundant it's helpful in some senses in in when we do what's called nuclear chemistry it's helpful but um it's not necessary here because the atomic number tells me how many protons and in the case of carbon that's six the elemental symbol tells me that i'm dealing with carbon and those those are kind of like synonymous with one another if i know i have carbon i know i have six protons and if i know i have six protons i know i have carbon so sometimes we'll write it where we just do this okay and we don't have to say what the atomic number is it's kind of understood what it would be okay so now let's let's kind of practice this so i have a table here and so we're going to just write out a an elemental symbol so let's say we have this okay now in order to do this we're going to need um to have a periodic table with us so this is n a which is sodium and um so sodium is the 11th element which means it has 11 protons okay um and actually i'm gonna yeah i'll uh i want to i'm going to color code this so i'm going to change this to a different color because i want us to know that's what we started with so when we look back at our notes um we'll kind of be wondering like well what information did we start with to get our answer so we have 11 protons because it's sodium now there's no charge indicated here so it's not like it's an n a plus or an n a minus and so that means that i have to have the same number of electrons right if electrons and protons have the ones positive ones negative they have to be equal if something is neutral now the number of neutrons here what i'm going to how i'm going to get that is i'm going to look at that that is my mass number remember the mass number is the number of protons and the number of neutrons i have 11 protons which means that i must have 12 neutrons because 11 plus 12 is 23 okay when i see sodium i know i have 11 protons i don't know how many neutrons i have until i look at that mass number okay right so let's look at this in a a different way let's say that we've got something with two protons two electrons sorry two protons two electrons and two neutrons okay so again the stuff i'm writing in purple is what we're given in the problem so if i have two protons that means i have helium right so helium is the element that has two protons now if i look at my protons and my neutrons together that equals four so that means i have a mass number of four which is what i would put there and then i look at my protons and my electrons and they are the same so i don't have a charge on this and so i can come up with my elemental symbol of this isotope by looking at my number of protons and my neutrons okay all right and then let's look at another one here so let's do so this would be oxygen 16 and again so i'm going to go and look at my periodic table and oxygen is the eighth element which means it has eight protons since it's neutral it must have the same number of electrons and my mass number is 16 and my number of protons is eight which means that i need eight neutrons to make a mass number of 16. okay all right let's do one with a charge now let's say we've got magnesium 24 with a two plus charge all right so first off i have magnesium so i look on my periodic table magnesium is the 12th element which means it has 12 protons the mass number is 24 which means that i also have 12 neutrons because 12 plus 12 is 24. and then that two plus charge again when i have a plus charge it does not mean that i've added protons what it means is i've removed electrons so i'm going to have two electrons less than i do protons so i'm going to have 10 electrons and then we'll do one more of these all right so i have chlorine i look i have 17 protons because that's chlorine i have a negative charge so that means that this picked up an electron which means that it must have 18 electrons there's one more electron than it does protons because it's negatively charged and then i have a mass number of 35 which means that since i have 17 protons i must have 18 neutrons because 18 plus 17 is 35. so if i'm given enough information i can figure out what how i should draw my elemental or my isotope symbol and if i'm given the elemental symbol or the isotope symbol i should be able to figure out these other pieces just by the way we write our notation if you think about that's pretty valuable um if you know instead of saying i have something with 17 protons and 18 electrons and 18 neutrons if i just say you know this is what i have we can figure all of that out just by the notation as long as we understand what the notation is okay all right so now um we've talked about the you know how we write things how we write um isotope symbols how we can figure out how many protons or neutrons or electrons um and then we talked about this thing called the mass number which is just the number of protons in the neutrons um but if you were to look at a periodic table you know the the number that so the top number you see is the atomic number which is how many protons it has then you have your symbol and then below it is what what is known as the mass but there's a distinction between the mass and the mass number and that's the subtlety that we're going to have to get used to the mass number is just the number of protons and neutrons and the mass is something that we're going to be talking about shortly okay so here i have this is this is kind of the picture i've been using for a carbon-12 atom okay now what i have over here is is something a little you know it's not an atom so imagine that you know so this is a balance right so i've got this balance and i've got a carbon 12 atom on one side of the balance and then i have 1 2 3 4 5 6 7 8 9 10 11 12. 12 of these little red dots so each one of these red dots represents what what's called one atomic mass unit or what we would call an amu for sure and notice that this is balanced so i have 12 amus which are like little what we might think of as like standards if we were gonna you know be trying to calibrate a scale i i have 12 amu's which is equal to one carbon-12 atom so that's the definition of an amu and and this is this will become more clear as we go um but an atomic mass unit is exactly that's the symbol i use for exactly exactly exactly equal to 1 12 of carbon 12 okay and it's very important when we make measurements that we have definitions that we rely on but that's what an atomic mass unit is is is defined as it's defined as 1 12 of carbon 12. now if i was to put another atomic mass unit on there and it was still balanced then i would say that an atomic mass unit is 1 13 of carbon 12 which actually wouldn't be very useful but which is why we don't do it but this is how we define an atomic mass unit and then we're going to use these atomic mass unit numbers as we as we progress through the rest of the lecture okay the importance of defining it on based on carbon 12 will come um will become more apparent as we go all right um but an atomic mass unit is 1 12 of carbon 12. now again if you think about it and and i've obviously had more time to think about these things than most of you have but um within a carbon-12 atom there are 12 of the massive particles right you've got six protons and six neutrons so an atomic mass unit is roughly the mass of a proton or roughly the mass of a neutron remember the mass of the approach on the neutron are very close it's not exactly a proton it's not exactly a neutron but it's close to both of them okay so that's kind of something to just maybe keep in mind as we as we progress here all right so let's go back to this picture so here we have this picture of our carbon-12 our our carbon atoms and um i've just kind of made a little smaller because i want to do a calculation here but this is a sample of carbon and in this sample i have 21 carbon 12s and i have one carbon 13. okay that's just i counted all of these up and you can verify that if you want you can press pause and count those and you'll have 12 carbon 12 sorry 21 carbon 12s and 1 carbon 13. now carbon 12 has a mass of 12 atomic mass units right that we just kind of talked about that so it takes 12 atomic mass units to be equal to carbon 12. so i'm going to write this so this is exactly 12 but i'm going to write some zeros after this um and i want to write seven zeros after it just okay i'm doing this because um it's going to help with our calculation but i could write as many zeros as i want um i could leave it off because i'm i because i'm saying that it's exactly equal to so it's understood that there's an infinite number of zeros that follow this carbon 13 has a mass of has a mass of that and so let's see actually to i i'm going to get rid of two of these zeros um i only really wanted five i wanted to have the same number of decimal places as the carbon 13 number i'm using and this is in terms of amu's as well okay now notice that carbon 13 weighs about one amu more because i've added one neutron and a neutron is about an amu but it's not exactly 13 it's just close to 13. the only isotope that has an exact mass is carbon-12 because that's how we define an amu all right now if i wanted to know what the mass of the average carbon atom was in this sample right so what i wouldn't do is i wouldn't just average these two numbers because i have a lot more carbon 12 than i do carbon 13. so it wouldn't make sense to say that the average is 12 and a half right so what we're going to do is we're going to calculate what's called the weighted average and in the weighted average we take into account how many of each type we have so one thing that i would ask before we do the calculation is to think to yourself is the weighted average like the average of these carbon atoms all of them in there is this going to be closer to 12 amuse or is it going to be closer to 13 i would expect it to be closer to 12 because i have a lot more carbon 12s so the kind of the um the makeup of this sample is going to be much more closely related to carbon 12 than it is carbon 13. so the way we're going to calculate what's called the weighted average of this sample is we're going to take the fraction that is carbon-12 so there's 21 out of 22 total carbon atoms that are carbon 12. and i'm going to multiply this by the mass of carbon 12. and then i'm going to say plus the fraction of these so 1 out of the 22 is carbon 13 i'm going to multiply that by the mass of carbon 13. so this is going to give me the weighted average i'm multiplying the fraction this is the fraction of carbon 12 and this is the fraction of carbon 13. and again i want to emphasize this is for this sample okay this one that i made up i i made up a sample that had 21 carbon 12s and 1 carbon 13. so now when we do this we're just going to have to pay attention to our significant figures as we go okay so the number of each atom is an exact number there's exactly 21 carbon 12s in there right like i don't have a fraction of a carbon 12. so i have exactly 21. so i'm going to do 21 divided by 22. there's exactly 22 atoms and i'm going to multiply this by 12. this number and i'm going to just write this in blue so that i can kind of keep track of which number is which but this is 11 okay my units are amu's so that and i'm going to make this a little bit more clear just so we're not thinking that i'm doing a division here um that's that number okay and the way that i wrote it out so this this has kind of an unlimited amount of significant figures right because this 12 is exact the 21 and the 22 are exact so now what i'm going to do is i'm going to add it to this number here these numbers are not exact so again we're following our significant figure rules so i'm going to do 1 divided by 22 times 13.00354 and the 1 and the 22 are exact but the the atomic mass unit number is not but it has one two three four five six seven significant figures my calculator and this is actually a good lesson so this is what my calculator gives me right so just again one two three four five six seven significant figures my calculator is giving me a number with only five significant figures and so i need to put two more decimal places there because i should have seven significant figures this number is significant to here okay so now what i'm gonna do is i'm gonna add these two numbers together and the number that i come out with 12.045 6 1 5 4 5 amuse and i have one two three four five six seven decimal places one two three four five six seven so there so the answer that i'm going to come out with is going to be 12.0456 one five four right so i've got one two three four five six seven decimal places so i should have seven decimal places in my answer and so i'll put my units on so this is amu's that is the weighted average of carbon in this sample that again i made up that i had one carbon 13 and 21 carbon 12s okay and i was just a reminder when before we did all the math we asked ourselves should the weighted average be more like carbon 12 or more like carbon-13 and we said to be more like carbon-12 because there's a lot more carbon-12 in this sample so it's going to behave a lot more like carbon-12 right and this is what we find okay so now now what i'm going to do is and again i will i will point out here because some of you might be thinking wait a minute he doesn't know how to round as we discuss in our significant figure lecture if i have an even number followed by a 5 and there's nothing after it i keep it even right so so i rounded it the way that i'm supposed to all right so now let's look at a question that we will be faced with you know coming up on like an exam or a homework so naturally occurring carbon is 98.84 percent carbon 12 and 1.16 carbon 13 what is the weighted average of naturally occurring carbon so this is kind of like if i just went out and i grabbed a handful of carbon i would see that it's going to be 98.84 carbon 12 and 1.16 carbon 13. so i'm going to calculate what the weighted average is of a naturally occurring sample not one that i made up but like what would actually be out there if i just went and grabbed some randomly so i'm going to do the same i'm going to do the same math okay so we're going to calculate our weighted average which we're going to call x now it's 98.84 carbon so that means that the fraction is 98.84 out of every 100 is going to be carbon 12 and then the mass of carbon 12 is 12 amuse i'm just going to write 12 amu's here because i want to start getting used to numbers that i can use that are going to be exact so this has exac this is exactly 12 amuse and then the amount of carbon 13 is 1.16 out of every 100 okay now this 98.84 is not 100 is not exact and the 1.16 is not exact somebody had to do some measurements to figure out the percent of each of these so these are not exact numbers and then the mass of carbon 13 which we use in the previous problem which i'll use here and you're not expected to know this number you would be given this okay but since we used it in the previous problem i assume we still have it so this is how i'm going to set this up and and we'll do it the same way we just did it so i'm going to do this one first and then i'm going to do this one okay so we're going to say x is equal to and i'm going to have some number here so i do 98.84 divided by 100 times 12. okay now the number i get on my calculator is 11.8608 amus and this has four significant figures because of that 98.84 number 1.16 divided by 100 times 13.00354 all right this number comes out to be that this is significant to three significant figures because at 1.16 when i add these two numbers together the number i come out with is this now when i'm trying to figure out where i'm significant to the number i have in blue has two decimal places i'm adding to a number with three decimal places so my answer can have two decimal places right this is my addition rule for significant figures so my final answer is going to be sorry i underlined the wrong place there should have two decimal places so the number i get here is 12.01 amu's okay now what i didn't do before we did this problem is i didn't ask which one do you think it's going to be closer to but hopefully if i did ask we would have picked 12 because there's a lot more 12 than there is 13. but the other thing i want you to notice is that this number is the number that's on the periodic table and so the numbers on the periodic table are the weighted average of naturally occurring isotopes of those elements so the mass that the mass not the mass number but the mass of carbon that's on the periodic table is the weighted average of all of the isotopes of carbon okay now carbon 12 and carbon 13 make up the most of them but there are there some of you probably heard of carbon 14. carbon 14 is there's a very very very small portion of carbon out there that is carbon 14. um and it it it doesn't there's so little of it that it doesn't really register in this calculation but if i was to carry this calculation out to like let's say seven or eight decimal places it would factor in okay um but the number on the periodic table is the weighted average of all of the the isotopes that occur okay so we're gonna do one more of these and then we'll we'll get practice of this on the homework and in in you know future practice problems okay so here i have so what i've done is i've given you two isotopes boron 10 and boron 11. i've given you their masses in atomic mass units and i will give you the percentages i haven't given you the percentages yet because what i want to do is i want to kind of ask a question first so if i look at boron on the periodic table now again boron 11 is about 11 amuse and boron 10 is about 10 amuse if i look at the number on the table i notice that the number is 10.81 so what that tells me is that or i should ask the question which of these isotopes do you think is more abundant is the number on the table closer to the boron 11 number or is it closer to the boron 10 number it's closer to the boron 11 number so if i was going to say which one of these makes up a higher percentage i would expect the higher percentage to be boron 11. and sure enough if i do that if i if i then go look up these percentages i find that 19.7 percent of it is four on 10 and 80.3 percent of it is boron 11. and that goes along with like my prediction based on looking at the periodic table and looking at the masses and so on so let's say that you know i gave you this information that's currently in front of us and i said calculate the weighted average of boron that is naturally occurring so that again this is a naturally occurring sample and so we would then do what we just did for carbon and i would say okay well 19.7 out of every 100 is going to have 10.01 amu's plus 80.3 out of every 100 is going to be boron 11 and so here i have what is set up to solve this problem and so we'll just do it the same way we did the previous two right so this is the this is the most like math intensive stuff that we've been doing so i want to do a couple of these or i guess this is the third one of these just to make sure that you see a number of examples so i'm going to do 10.01 times 19.7 divided by 100. this works out to be 1.97197 the units are amu's and i have three significant figures because of my percentage so i'm significant to there and again i'm color coding the numbers just so it's going to be easier for us to follow this okay so now i do the next calculation and i come out with this and i am significant to three significant figures um and now i'm going to add those two numbers together which is the next step that i would do and this comes out to be so i'm going to be significant to two decimal places when i do this addition so i'm just going to write that out and this is the number that i get and that is the number that i predicted right because if this is my if this is my naturally occurring then i should get the number that's on the periodic table that's what that number on the periodic table represents okay so this ends this lecture on atoms and elements and what the masses mean and you know how to picture atoms in terms of protons and neutrons inside the nucleus the electrons are orbiting around so all of that stuff or that's all stuff that we need to kind of keep in mind as we're thinking about atoms thinking about why they have the sizes that they have you know why do they have the masses that they have and so on okay