Question

An element Z contains two naturally occurring isotopes ³⁵Z₁₇ and ³⁷Z₁₇. If the average atomic mass of this element be 35.5 u, calculate the percentage of two isotopes.

Answer 1

Let the percentage of ${}_{17}{}^{35}\mathrm{Z}$ = X$\raisebox{1ex}{$0$}\!\left/ \!\raisebox{-1ex}{$0$}\right.$
Then the percentage of ${}_{17}{}^{37}\mathrm{Z}$ = (100 $-$ X)$\raisebox{1ex}{$0$}\!\left/ \!\raisebox{-1ex}{$0$}\right.$

The average atomic weight of Z = 35.5u

Now, the average atomic mass is given by,

$$\begin{gathered} 35.5=\frac{35.\mathrm{X}+37.(100-\mathrm{X})}{100} \\ 35.5=\frac{35\mathrm{X}+3700-37\mathrm{X}}{100} \\ 35.5\times 100=3700-2\mathrm{X} \\ 3550-3700=-2\mathrm{X} \\ -150=-2\mathrm{X} \\ \mathrm{X}=75 \end{gathered}$$

Therefore, ${}_{17}{}^{35}\mathrm{Z}$ = 75%
And, ${}_{17}{}^{37}\mathrm{Z}$ = 100 - 75 = 25%