Nuclear radius is of the order of `10^(-13) cm ` while atomic radius is of order`10^(-8)cm`. Assuming the nucleus and the atom to be spherical .What fraction of an atom is occupied by nucleus ?

Options

A. `10^-15`
B. `10^-10`
C. `10^-13`
D. `10^-14`

Answer

A

Explanation

(a) The volume of a sphere `= 4pi r^3//3`, where `r` is the radius of the sphere.
`:.` Volume of the nucleus `= 4 pi r^3//3`
`4 pi(10^-13)^3//3 cm^3`
Similarly, volume of the atom `= 4 pi r^3 //3 = 4 pi (10^-8)//3 cm^3`
Fraction of the volume of atom occupied by the nucleus
=`(4 pi(10^-13)^3//3 cm^3)/(4 pi(10^-8)^3//3 cm^3) = 10^-15`.