# Atomic radius is of order 10^-8 cm and nuclear radius is of order 10^-13. calculate what fraction of atom is occupied by nucleus?

Sep 14, 2017

$\frac{1}{10} ^ 15$

#### Explanation:

The idea here is that you need to calculate the volume of the nucleus and compare it to the volume of the atom.

In order to be able to do that, you need to assume that both the nucleus and the atom itself are spheres. The volume of the nucleus will be

V_"nucleus" = 4/3pi * (10^(-13) color(white)(.)"cm")^3

The volume of the atom will be

V_"atom" = 4/3pi * (10^(-8)color(white)(.)"cm")^3

Divide the two volumes to get the fraction of the atom occupied by the nucleus

V_"nucleus"/V_"atom" = (color(red)(cancel(color(black)(4/3pi))) * (10^(-13))^3 color(red)(cancel(color(black)("cm"^3))))/(color(red)(cancel(color(black)(4/3pi))) * (10^(-8))^3 color(red)(cancel(color(black)("cm"^3))))

You will end up with

${V}_{\text{nucleus"/V_"atom}} = {\left({10}^{- 13} / {10}^{- 8}\right)}^{3}$

${V}_{\text{nucleus"/V_"atom}} = {\left({10}^{- 5}\right)}^{3}$

${V}_{\text{nucleus"/V_"atom}} = {10}^{- 15}$

This means that the nucleus occupies $\frac{1}{10} ^ 15$ of the volume of the atom.