Question

${}_{17}^{35}Cl$ and ${}_{17}^{37}Cl$ are two isotopes of chlorine. If average atomic mass is $35.5$ then ratio of these two isotopes is:

• A. $35:37$
• B. $1:3$
• C. $3:1$
• D. $2:1$

Answer 1

Answer: (C)

$3:1$

Let $x$ and $y$ be the fraction of ${}_{17}^{35}Cl$ and ${}_{17}^{37}Cl$ in ${}_{17}^{35.5}Cl$.

Therefore,

Average at. mass $=\frac{x\times 35+y\times 37}{x+y}$

$35.5=\frac{35x+37y}{x+y}$

$\Rightarrow 35.5x+35.5y=35x+37y$

$\Rightarrow 35.5x-35x=37y-35.5y$

$\Rightarrow 0.5x=1.5y$

$\Rightarrow \frac{x}{y}=\frac{1.5}{0.5}=\frac{3}{1}$

Hence the ratio of ${}_{17}^{35}Cl$ and ${}_{17}^{37}Cl$ in ${}_{17}^{35.5}Cl$ is $3:1$.