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

Copyright © 1997-2010 by Fred Senese
Comments & questions to fsenese@frostburg.edu
Last Revised 02/23/18.URL: http://antoine.frostburg.edu/chem/senese/101/atoms/faq/estimating-isotopic-abundances.shtml