# How would you find the percent abundance of 2 isotopes of an element, given the atomic weight and mass number of each isotope?

Nov 11, 2015

See explanation.

#### Explanation:

The average atomic mass of elements is calculated by:

$M a s {s}_{a v r g .} = \sum \left(\text{isotope mass")*("percent abundance}\right)$

For example, suppose we want to find the percent abundance of chlorine isotopes ""^35Cl and ""^37Cl given that the average atomic mass of chlorine is 35.45 "a.m.u..

Assume that the percent abundance of ""^35Cl is $x$, therefore, the percent abundance of ""^37Cl is $1 - x$.

Thus, $35.45 = \left(35 \times x\right) + \left(37 \times \left(1 - x\right)\right) \implies 35.45 = 37 - 2 x$.

Solve for $x$, $x = 0.775$

Therefore, the percent abundance of ""^35Cl is 77.5% and the percent abundance of ""^37Cl is 22.5%