Help with Chemistry and Fractional Abundance?

Question

The two naturally occurring isotopes of copper are copper-63, with a mass of 92.9298u and copper-65, with a mass of 64.9278u. If the tabulated atomic mass of copper is 63.546u, what must be the percent natural abundances of the two isotopes? Please solve for x - it has been too many years since algebra.

Thanks

Answer 1

there is a typo in your question, the first mass is not 92.9298, but 62.9298

I think the way to do this is:

It is presumed that the observed atomic mass is just the weighted average of the two isotopes.

So let x = the fraction of the heavier isotope;

63.546 = 62.9298[1-x] + 64.9278x

63.546 = 62.9298 - 62.9298x + 64.9278x

63.546 = 62.9298 + 1.998x

0.6162 = 1.998x

0.3084 = x

So 30.84% Cu 62.9298 and 69.16% Cu 64.9278

Observed values: 30.91 and 69.09%

I hope this is of some use to you