all right so now we know what is inside the nucleus now let's talk about describing the nucleus the nucleus is described using two numbers the atomic number and the mass number the atomic number is the number of protons in an atom's nucleus you can find the atomic number on every periodic chart if you look at a periodic chart and i'm going to draw a square for us to talk about here that's supposed to be a square most periodic charts have a number up at the top your elemental symbol and then another number down at the bottom the top number right here is your atomic number your atomic number is the number of protons in the nucleus of an atom the periodic table is arranged in order of increasing atomic number remember earlier when we said that dalton was wrong about atoms of um the same element all having the same mass but they did have something in common all atoms of of an element have the same atomic number it turns out that it is the number of protons that defines the identity of an element every single atom of carbon will have six protons if it doesn't have six protons it's not carbon it does not matter the number of electrons or the number of neutrons only only the number of protons determines whether or not an atom is of a certain element the number of electrons and the number of neutrons are like resistance it's their futile right you only care about the number of protons for a neutral atom meaning it doesn't have a charge the number of protons equals the number of electrons so for a neutral atom of carbon it would not only have six protons but would have six electrons one of the reasons where another area where dalton was wrong was atoms of the same element can actually have different masses atoms of the same elements that have different masses are referred to as isotopes now how can they be atoms of the same element and have different masses by differing in the number of neutrons remember only the number of protons determine the identity of an element so they're allowed to have different neutrons the mass number is the sum of the neutrons and the number of protons in the nucleus of an atom the mass number does not appear on the periodic chart the only way you know the mass number of an atom the only way you know the mass number of of an atom is if it is given to you how is it given to you there's a couple ways that can be given to you carbon has three isotopes it has carbon 12 carbon 13 and carbon 14. all of these are isotopes of carbon therefore all have six protons but all of them have different mass numbers when you see the name of an element written hyphen and a number that number is the mass number so carbon has three isotopes possible they all have six protons but they differ in their number of neutrons you can determine the different number of neutrons in an atom by taking the mass number and subtracting the number of protons so carbon 12 has a mass number of 12 because it's carbon it has six protons so 12 minus six because remember mass number is protons plus neutrons then 12 minus six is six so it has six neutrons 13 carbon 13 has a mass number of 13 because it's carbon it has six protons so it must have seven neutrons carbon 14 because it's carbon it has six protons if it has a mass number of 14 then it must have eight neutrons in other words you can't look at the periodic table and determine a mass number it has to be given to you either by writing the name of the element and a dash or there's another form of notation that will work here another way to write it is to write the elemental symbol and then write the mass number as a superscript on the left hand side here are some more examples of that notation in this notation where we're doing an isotope we write the elemental symbol we write the mass number and then we write although it's optional the atomic number for example i have nitrogen here with a 14 superscript so that means its mass number is 14. its atomic numbers written down here you'll often see this number admitted people will often just write this like that why do they write it like that instead of writing the seven well look at your periodic table nitrogen has the atomic number of seven if it's nitrogen there are seven protons if there are seven protons they're nitrogen so a lot of people will review writing that second seven down there as redundant um so that's your atomic number how do you calculate your number of neutrons this is why i love this notation because they've got your subtraction all lined up for you nitrogen 15 15 minus seven eight neutrons chemistry is easy life is hard all right this is me trying to make a hard question about isotopes okay how many protons electrons and neutrons does this isotope have and by that they mean phosphorus 31. all right well let's start with the easy thing the protons they tell us the number of protons right down here or we could simply say we've got phosphorus we go to the periodic table we find phosphorus and it's element number 15. so we know that we have 15 protons how about electrons well there's no charge denoted over here and since there's no charge noted the number of protons and the number of electrons must be equal then the neutrons the only thing that ever causes people trouble on exams is they will forget that the mass number is the number of neutrons plus the number of protons so to get your number of neutrons you have to do that subtraction 31 minus 15 is 16. so 15 15 16. oh what do you know about that why don't you write down nora write down nora n-o-r-a nora why don't you write down nora how come is it they how come is it that they put two werewolves in the show but we only get one vampire and the ghost doesn't even stay a ghost for most of the last two seasons but anyway i digress you wrote down nora n-o-r-a all right let's work another example this time we're dealing with uranium 235. how many protons neutrons and electrons does uranium-235 have well let's do the easy ones first here's our atomic number so that's our number of protons and since it's a neutral atom that 92 is also our number of electrons to get our number of neutrons we're going to have to subtract this right up here is our mass number remember which is our number of neutrons plus protons so if we subtract our number of protons we'll be left with our number of neutrons or 143 neutrons chemistry's easy life is hard and why don't you write down danny write down danny d-a-n-n-y danny the ghost danny alright element x is toxic to humans in high concentrations but is essential to life in low concentrations identify element x then write the symbol for the isotope of x that has 28 neutrons all right first of all they tell us that x has 24 protons so we have to go to our periodic chart and find out what element number 24 is element 24 is located in the middle there and it's chromium which has the elemental symbol cr so for the isotope of chromium that has 28 isotope 28 neutrons we have to add our protons and neutrons together to get the mass number of 52. so that would be the isotope symbol so the name and how we would say that isotope would be chromium dash 52 all right i told you that the mass number is not on the periodic table so if the mass number is not on the periodic table what is this number down here at the bottom of the block then that number down there is the atomic weight the atomic weight is the weighted average of the atomic masses of the element naturally of the of the masses of the match of the elements naturally occurring isotopes what that means and what this number really is is but well let me back up a little bit isotopes chemically don't make a difference in terms of the normal chemistry you're going to be undergoing the presence of one isotope compared to another does not make a difference in the chemical properties therefore as chemists unless we're wishing to label something with a particular isotope we don't care about separating isotopes it's expensive and unnecessary therefore what we as chemists want is we want a number that if we were to grab a million random carbon atoms what would their average mass be that's what the atomic weight represents if we were to grab a random sample of all the isotopes as they exist in nature for an element what would their average mass be that's what your atomic weight is so if i grabbed a million random carbon atoms their average mass would be 12.011 amu or atomic mass units mathematically how do you calculate atomic weight the formula is as follows whoa the atomic mass equals the fractional abundance of one element of one isotope sorry the atomic mass equals the fractional abundance of one isotope times its mass plus the fractional abundance of the second isotope times its mass plus the fractional abundance of the third isotope times its mass so forth and so on what do i mean by fractional abundance abundance here has to be in a fraction most of the time however abundance will be given in the first form of a percent how do you turn a percent into a fraction you divide by 100 right so if we're wanting to solve for if so if we're wanting to solve for the atomic mass of carbon what we're going to do is we're going to take the percent natural abundance of carbon 12 and change it into a fraction so 98.89 percent divide by 100 times the mass of that isotope 12 amu plus the fractional abundance of the second isotope divide by 100 times its mass and then you multiply add and you get the mass of the carbon to be 12.01 amu let's take a look at a couple more examples all right let's calculate the atomic mass of bromine remember atomic mass equals the fractional abundance of the first isotope times the mass of the first isotope plus the fractional abundance of the second isotope times the mass of the second isotope our first isotope is bromine 79 it has a percent abundance of 50.69 to change it into a fraction we're going to divide by 100 it has a mass of 78.9183 our second isotope is bromine 81. it has a fractional abundance of 49.31 change it into a fraction by dividing by 100 times its mass of 80.916 punching it into my calculator now and i have 0.5 0 whoops my calculator is going to give me a long number now if you look i've got four sig figs and six sig figs so the most sig figs i can really have coming out is four i'm going to carry an additional one forward in my calculation punch that into my calculator and again i get a long number but i've got four and six so i should be limited to four sig figs coming out i'm going to carry an additional two in to avoid some rounding there now i need to add together and i add together and i get 79.90 which happens to be choice a chemistry is easy life is hard all right we can do some algebra with this one too the average atomic mass of boron 1081 of boron is 1081. it is composed of two stable isotopes boron 10 and boron 11. the atomic mass of boron 10 is 10.05 and it has an isotonic abundance of 20 percent what is the atomic mass of boron 11. well first of all let's solve for the low hanging fruit first if we're going to solve for atomic mass we need the abundance of each if the abundance of 10 is 20 then the abundance of 11 must be 80 why is that because percents have to equal 100. so now we have atomic mass equals the fractional abundance of 10 times the mass of 10 plus the fractional abundance of 11 times the mass of eleven they gave us in the problem the atomic mass they gave us the percent abundance of ten we need to change it into a fraction they gave us the mass of ten they gave us the fractional abundance of eleven indirectly as eighty percent times the mass of eleven now it's plug in chug city that's sloppy there and we've got 0.2 times 10.01 subtract 2.2 10.81 minus 2.002 and that gives me a mass of 11.01 amu