The nucleus of an atom is spherical. The relation between radius of the nucleus and mass number A is given by `1.25xx10^(-13)xxA^((1)/(3))cm`. If radius of atom is one`Å` and the mass number is 64, then the fraction of the atomic volume that is occupied by the nucleus is `(x)xx10^(-13)`. Calculate x

Options

A. `1.0xx10^(-3)`
B. `5.0xx10^(-5)`
C. `2.5xx10^(-2)`
D. `1.25xx10^(-13)`

Answer

D

Explanation

Radius of nucleus = `1.25xx10^(-13)xxA^(1//3)cm`
= `1.25xx10^(-13)xx64^(1//3)=5xx10^(-13)cm`
Radius of atom = `1Å=10^(-8)cm`.
`("Volume of nucleus")/("Volume of atom")=((4//3)pi(5xx10^(-13))^(3))/((4//3)pi(10^(-8))^(3))`
= `1.25xx10^(-13)`