Question

The atomic masses of ²⁰³Tl and ²⁰⁵Tl are 202.972336 and 204.974410 amu, respectively. The average atomic mass of thallium is 204.383 amu. Calculate the natural abundances of these two isotoped.

Percent abundance of ²⁰³Tl: ____%

Percent abundance of ²⁰⁵Tl: _____%

Answer 1

Assuming only the above mentioned isotopes exist in nature,,

Let x% be the abundance of ²⁰³Tl, then it is obvious that the abundance of ²⁰⁵Tl is 100-x%

The average atomic mass is the sum of individual atomic masses times their corresponding abundance.

Then we have,

202.972336 * x% +204.974410 * (100-x)% = 204.383

- 2.002074 x% + 204.9744410 = 204.383

0.591441/2.002074 = 0.2954

All measured in amu.

by solving for x we get, x = 0.2954 ie abundance of Li(6) is 29.54% aboundance of ²⁰³Tl

70.56 % aboundance of ²⁰⁵Tl