Question

The nuclear radius is of the order of `10^(-13)` cm while atomic radius is of the order `10^(-8)` cm. Assuming the nucleus and the atom to be spherical, what fraction of the atomic volume occupied by the nucleus ?

Answer 1

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