# How can I estimate isotopic abundances?

How do I determine the abundances of boron-10 and boron-11 to the nearest 10%?
Deb

Here's a quick and easy way to do it:
1. The atomic weight of boron is 10.81. This is an average of the isotopic masses of boron-10 and boron-11:
 average atomic weight of boron = abundance of boron-10 × isotopic mass of boron-10 + abundance of boron-11 × isotopic mass of boron-11 +...
where there is one term for each isotope of boron.
2. Assume the isotopic masses are roughly equal to the mass numbers. You only need 10% accuracy so this assumption is ok here.
 average atomic weight of boron = abundance of boron-10 × 10 + abundance of boron-11 × 11 +...
3. Assume that the abundances of all isotopes other than boron-10 and boron-11 are negligible. All of the isotopic abundances have to add up to 1 (they're fractions of the whole). Then if x is the abundance of boron-10, 1-x is the abundance of boron-11.
 10.81 = 10 x + 11(1-x)
4. Solve this equation for x.

Author: Fred Senese senese@antoine.frostburg.edu

General Chemistry Online! How can I estimate isotopic abundances?