## What is the percentage occurrence of the isotopes \({ }^{35} C l\), and \({ }^{37} \mathrm{Cl}\) is the average atomic mass of chlorine is 35.45 . amu?

Answer:

The weighted average of the isotopes is \(35.45 \cdot \text { amu….. }\)

Explanation:

And thus \(x_{1} \times 35 \cdot \mathrm{amu}+x_{2} \times 37 \cdot \mathrm{amu}=35.45 \cdot \mathrm{amu}\)

This is one equation in 2 unknowns. However, we can supply another equation because WE ASSUME that there are only the two isotopes of \(\mathrm{Cl},{ }^{35} \mathrm{Cl}\) and \({ }^{37} \mathrm{Cl}\), and thus \(x_{2}=1-x_{1}\).

And thus we get the equation: