Question

The volume of nucleus is ______ as compared to the volume of complete atom.

Answer 1

Step-1: Calculate the volume of nucleus

As nucleus is considered to be spherical, therefore formula to calculate volume of nucleus

$V_n=\frac{4}{3}\pi r_n^3$

where $V_n$= Volume of nucleus

$r_n$= radius of nucleus

As $r_n$= ${10}^{-15}$ m

Therefore, $V_a=\frac{4}{3}\pi {\left({10}^{-15}\right)}^3$

Step-2: Calculate the volume of the atom

As atom is also considered to be spherical, therefore formula to calculate volume of an atom

$V_a=\frac{4}{3}\pi r_a^3$

where $V_a$= Volume of an atom

$r_a$= radius of an atom

As $r_a$= 10^-10 m

Therefore, $V_a=\frac{4}{3}\pi {\left({10}^{-10}\right)}^3$

Step-3: Calculate the ratio of Volume of nucleus to the volume of an atom

$\frac{V_n}{V_a}=\frac{{\displaystyle \frac{4}{3}}\pi {\left({10}^{-15}\right)}^3}{{\displaystyle \frac{4}{3}}\pi {\left({10}^{-10}\right)}^3}={10}^{-45+30}$

$\frac{V_n}{V_a}={10}^{-15}$

$V_n={10}^{-15}{V}_a$

Hence, the volume of nucleus is 10^-15 as compared to the volume of complete atom.