How to find the natural abundance of antimony 121 and 123?

How to find the natural abundance of antimony 121 and 123?
You are given the mass of antimony 121 as 120.904 and 123 as 122.904 and we are supposed to find the natural abundance percentage by using the periodic table value of antimony(121.760)
Best answer:
Answer by athome
%(Sb-121) * 120.904 + %(Sb-123) * 122.904 = 121.760
%(Sb-121) + %(Sb-123) = 1
1 – %(Sb-121) = %(Sb-123)
%(Sb-121) * 120.904 + (1 – %(Sb-121) ) * 122.904 =121.760
1.144 = 2 * %(Sb-121)
%(Sb-121) = 57.2 %
%(Sb-123) = 42.8%
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The value on the periodic table is the abundance of each mass multiplied by that mass. So figuring that there has to be a total of 100% abundance, you have x% of one, and 100%-x% of the other. YOur equation is then
%A*m1 + (1-%B)*m2 = Mass on table
A*120.904 + (1-A)*122.904 = 121.76
120.904A + 122.904 – 122.904A = 121.76
-2A = -1.144
A = 0.572
So Sb121 has 57.2% abundance, Sb123 has (1-0.572) = 0.428 = 42.8% abundance