Question

The ratio of volume of atom to volume of nucleus is

Answer 1

Hint: As we know that the atom is the smallest particle which is found in a chemical element. Each solid, liquid, and gas are composed with ionized or neutral atoms. The size of the atom is extremely small, around $100$ picometers across. And the atomic nucleus is a subatomic particle which contains a positively charged proton, and a neutron which is electrically neutral. Both protons and neutrons are made up with quarks.

Complete answer:
The size of the atom is extremely large which is made up with three subatomic particles which are smaller than the atom. And that is, protons, neutrons and electrons. The neutrons and protons are located at the nucleus.
Here we have to find the ratio of volume of the atom to the volume of the nucleus. Hence, let’s consider the ratio of the atom which is denoted as ${r_1}$ and it is equal to ${10^{ - 10}}$. And the ratio of the nucleus which is denoted as ${r_2}$ and it is equal to ${10^{ - 15}}$.
The volume of the atom is directly proportional to the ${r^3}$, $V \propto {r^3}$. Hence, we can write that,
${V_{atom}} = \dfrac{{{r^3}_{atom}}}{{{r^3}_{nucleus}}} \propto {V_{nucleus}}$
The ratio of the atom $ = {r_2} - {r_1}$
$ = {10^{ - 15}} - {10^{ - 10}} = {10^{ - 5}}$
Hence, the ratio of nucleus and atom can be written as,
$\dfrac{{{r_{nucleus}}}}{{{r_{atom}}}} = {\left( {\dfrac{1}{{{{10}^5}}}} \right)^3}$
By simplification will get, ${V_{atom}} = {10^{15}} \times {V_{nucleus}}$
Therefore, the ratio of volume of the atom to the volume of the nucleus is equal to ${10^{15}}$.

Note:
 The size of the nucleus of an atom is around ${10^{15}}$ m in size. Which is almost equal to around ${10^{15}}$ m of the size of the atom. Hence, we can say that, the size of the nucleus is very much smaller than the whole atom. An atom is made up of three subatomic particles and that is, neutrons, protons and electrons. And most of the atoms are stable.