Isotope Composition (Example)

October 9, 2019

In this problem, I have a mixture of three silcon isotopes. And I’m giving their exact atomic weight And then this mixture has an average atomic mass of 28.0855 atomic mass units The question is: given how much of silicon-29 is in this mixture, we want to know how much silicon-28 is in the mixture? I’m gonna show you my approch to solving this problem which I have not worked out the solution ahead of time So what I want to do first is list the information that I have. So I have silicon-28, silicon 29, and silicon-30 And the silicon-29 is 4.67 percent We’re trying to find the percent for silicon-28 let’s call that x. Now we know the total percent is 100 100 minus x minus 4.67 is the percent of silicon-30 and we know the average, and that’s 28.0855 So essentially, it’s asking us how much of each of these we add together to give us this average, which means We would say x, that percentage, times the atomic mass of silicon-28 which is 27.9769, plus 4.67 times silicon-29, plus this percentage So this percentage, 100 minus 4.67, 95.33 minus x times it’s atomic mass, number, 29.738 and all this adds up to 100 percent with an average So essentially, just need to do the multiplication so I can solve for x. I’m going to have 27.9769 minus 29.9738, times x plus these other two numbers . So this shows multiplying out the numbers. So I can rearrange and have x on the left side and on the right side I then have and notice I have to be careful here, beacuse this was actually a minus sign, that I don’t want to forget the minus sign And I noticed that when I check on my calculator that I typed in the wrong numbers, so this number Multiplies 2857.40, and so then right side of this equation is -184.17. and when I solve for x it’s 92.23. And I’m gonna keep in this case four significant figures. So 92.23 percent of the mixture of isotopes is silicon-28

Leave a Reply

Your email address will not be published. Required fields are marked *