Copper (Cu) consists of two naturally occurring isotopes with masses of 62.9296 and 64.9278 u. (a) How many protons and neutrons are in the nucleus of each isotope? Write the complete atomic symbol for each, showing the atomic number and mass number. (b) The average atomic mass of Cu is 63.55 u. Calculate the abundance of each isotope.

Video transcript

Hey everyone in this example, we're told that magnesium has three stable isotopes with the following atomic masses. We need to identify the number of protons and neutrons for each of these isotopes and identify the isotope symbol. Our first step is to recall what an isotope symbol looks like. So we would have our element represented by X. We would have our atomic number represented by the symbol Z. And then above that we would have a representing our atomic mass. So we should recall that Z is our atomic number and A. Is our atomic mass A. K. A Our mass number. We want to recall that also our atomic number, Z is equal to our number of protons. And we also want to recall the fact that we can find atomic mass By taking our number of protons and adding that to our number of neutrons. So when we find magnesium on the periodic table, we're gonna find it in group two a. And we see that it corresponds to an atomic number or Z equal to a value of 12. And this tells us that we therefore have 12 protons for each of our isotopes of magnesium. So so far we can fill in our isotope symbol with our atom magnesium and we can fill in our atomic number as 12 here. So all we're missing is our atomic mass which is our a variable here. So given our first isotope mass were given a mass of 23.985 am use. And we're going to subtract this mass from our number of protons, which we just confirmed is 12 protons. And this difference gives us our number of neutrons equal to 12 neutrons. So to complete our first isotope symbol, we want to recognize that that atomic mass represents our atomic mass of our isotope. And so for our atomic mass symbol, we would just round this to about 24 since we have 23.9. So we can say that we have 24 for our atomic mass for our isotope symbol for our first isotope. And this is going to correspond with having neutrons. So this is our first answer for our number of protons and our number of neutrons As well as our isotope symbol for our first isotope here. We're going to take that second mass given 24. am use and subtract that from our number of protons in magnesium which we confirmed is 12 protons. And this difference gives us a value of 13 neutrons. And so to complete our isotope symbol for our second isotope, we would still have magnesium, we would still have the atomic number 12. However, we will have now the mass which we can round to 24.9. So we can round this to 25. So our mass number is now 25 for our second isotope. And this is our second answer which includes our number of protons are number of neutrons and our isotope symbol for the second isotope. And now we have that third given mass listed as 25. am use subtracted from 12 protons, which gives us a difference of 14 neutrons. And so to complete our third isotope symbol, we still have magnesium, we still have the number of protons or the atomic number is 12. And our mass number we can round from 25.9832. Now 26 for our third isotope. And so our third final answer is this isotope symbol here, the 12 protons and the 14 neutrons associated with this third isotope. So this will complete our answers for this example. If you have any questions, please leave them down below and I will see everyone in the next practice video.