# What is the percentage occurrence of the isotopes ""^35Cl, and ""^37Cl is the average atomic mass of chlorine is 35.45*"amu"?

Feb 11, 2017

The weighted average of the isotopes is $35.45 \cdot \text{amu.....}$

#### Explanation:

And thus ${x}_{1} \times 35 \cdot \text{amu"+x_2xx37*"amu"=35.45*"amu}$.

This is one equation in 2 unknowns. However, we can supply another equation because WE ASSUME that there are only the two isotopes of $C l$, ""^35Cl and ""^37Cl, and thus ${x}_{2} = 1 - {x}_{1}$.

And thus we get the equation:

${x}_{1} \times 35 + \left(1 - {x}_{1}\right) \times 37 = 35.45$

So $37 - 2 {x}_{1} = 35.45$

And ${x}_{1} = \frac{37 - 35.45}{2} = 0.775$

And ${x}_{2} = 0.225$.

And thus % ""^35Cl=77.5%, and % ""^37Cl=22.5%.

Capisce?