Question

Atomic Radius is of the order ${10}^{-8}$cm & nucleus order of ${10}^{-13}$cm. Calculate what fraction of atom is occupied by nucleus?

• A. ${10}^{-14}\times V_{atom}$
• B. ${10}^{-13}\times V_{atom}$
• C. ${10}^{-15}\times V_{atom}$
• D. ${10}^{-11}\times V_{atom}$

Answer 1

The correct option is C ${10}^{-15}\times V_{atom}$

We know the volume of a sphere varies to 3rd power of the radius and also nucleus and atoms are spherical in shape

$\frac{V_{atom}}{V_{nucleus}}=\frac{({10}^{-8}{)}^3}{({10}^{-13}{)}^3}$

$\frac{V_{atom}}{V_{nucleus}}=\frac{1}{({10}^{-5}{)}^3}$

$V_{nucleus}={10}^{-15}\times V_{atom}$

Hence, the correct option is $C$