Answer to Question #337592 in General Chemistry for Sese

Question

An unknown element D has two stable isotopes, ¹⁸⁵D and ¹⁸⁷D with masses of 184.9523 amu and 186.9564 amu. The average atomic mass of element D is 186.2071 amu. 

Determine the percentage abundances of the two isotopes.

Answer 1

Ler x is a share of ¹⁸⁵D and y - share of ¹⁸⁷D. Then

x+y=1

184.9523x+186.9564y=186.2071

184.9523x+186.9564(1-x)=186.2071

x(184.9523-186.8564)=186.2071-186.9564

1.9041x=0.7493

x=0.3935=39.35%

y=1-0.3935=0.6065=60.65%