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