Question

The atomic radius of K is 216 pm and that of K${}^{+}$ is 133 pm. The percent decrease in volume that occurs when K(g) is converted to K${}^{+}$(g):

• A. 76.66%
• B. 65.42%
• C. 54.24%
• D. 38.33%

Answer 1

The correct option is A 76.66%

Volume of K atom $=\frac{4}{3}\pi r^3=\frac{4}{3}\pi (216{)}^3$
Volume of K${}^{+}$ ion $=\frac{4}{3}\pi (133{)}^3$
Decrease in volume $=\frac{4}{3}\pi \left[\right(216{)}^3-\left(133{)}^3\right]$
% decrease $=\frac{\frac{4}{3}\pi \left[\right(216{)}^3-\left(133{)}^3\right]}{\frac{4}{3}\pi (216{)}^3}\times 100$
$=$ 76.66%