Question

The atomic radius of F is 72 pm and that of $F^{-}$ is 136 pm. What is the percent increase (to the nearest integer) in volume that occurs when F(g) is converted to $F^{-}$(g)?

• A. $2$
• B. $3$
• C. $5$
• D. $6$

Answer 1

Answer: (D)

$6$

The volume V of an atom is given by the expression $V=\frac{4\pi }{3}{r}^3$.
Hence, the percntage change in volume when fluorine atom is converted to fluoride ion is $\frac{V_{fluorideion}-V_{fluorineatom}}{V_{fluorineatom}}\times 100=\frac{\frac{4\pi }{3}{r}_{fluorideion}^3-\frac{4\pi }{3}{r}_{fluorineatom}^3}{\frac{4\pi }{3}{r}_{fluorineatom}^3}\times 100=\frac{r_{fluorideion}^3-r_{fluorineatom}^3}{r_{fluorineatom}^3}\times 100$
Substitute values in the above expression.
$\frac{(136{)}^3-(72{)}^3}{(72{)}^3}\times 100=5.74\times {10}^2$ %.
Hence, the percentage increase is 6%.