Question

The average atomic mass of a sample of an element ${}^{\prime }{X}^{\prime }$ is $16$. What are the $\%$ of isotopes ${}_8^{16}X$ and ${}_8^{18}X$ in the sample?

• A. $80\%$ and $20\%$
• B. $90\%$ and $10\%$
• C. $70\%$ and $30\%$
• D. $40\%$ and $60\%$

Answer 1

The correct option is B $90\%$ and $10\%$

$\begin{array}{c}\text{let total}\%=100\\ {}_8^{16}X{,}_8^{18}X,y,(100-y)\end{array}$

$\begin{array}{c}\text{Average Atomic mass}=\left(\frac{m_1{y}_1+m_2{y}_2}{y_1+y_2}\right)\\ 16.2=\frac{y}{100}\times 16+\frac{100-y}{100}\times 18.\\ 16.2=\frac{8y}{50}+\frac{1900-9y}{50}\end{array}$

$y=960-810=90$

$\begin{array}{c}100-y=100-90=10\\ \text{so}\%\text{of isotopes are}90\%\text{\&}10\%\end{array}$