Question

Atomic radius is of the order of ${10^{ - 8}}cm$ and nuclear radius is of the order of ${10^{ - 13}}cm$ . The fraction of atom occupied by the nucleus is:
A. ${10^{ - 5}}$
B. ${10^5}$
C. ${10^{ - 15}}$
D.None of these

Answer 1

To solve this question we need to find out the ratio of volume of nucleus to the volume of atom. By finding this ratio we will get to know the fraction of atoms occupied by the nucleus. Basically a nucleus is a positively charged center of an atom that contains protons and neutrons.

Complete step by step answer:
A nucleus is also known as the atomic nucleus. Basically a nucleus consists of a positively charged center of atom containing protons and neutrons. The nucleus of an atom is the central region of an atom where the majority of the mass is concentrated. Moreover, there are two heavy particles i.e. the protons and neutrons and $99.9\%$ of the mass is concentrated inside the nucleus.
Now, in the given question we have to find the fraction of atoms occupied by the nucleus. So, first of all we will find the volume of the nucleus and volume of the atom. After that we will find the ratio between both of them.
So, volume of nucleus $= \dfrac{4}{3}\pi {r^3}$
Where r is ${10^{ - 13}}cm$
Therefore, volume $= \dfrac{4}{3}\pi {({10^{ - 3}})^3}c{m^3}$
Now, volume of atom $= \dfrac{4}{3}\pi {r^3}$
Here, $r = {10^{ - 8}}cm$
Therefore, volume of atom $= \dfrac{4}{3}\pi {({10^{ - 8}})^3}c{m^3}$
Now, the ratio of volume of nucleus to volume of atom will be,
$\dfrac{{{V_N}}}{{{V_{atom}}}} = \dfrac{{{{10}^{ - 39}}}}{{{{10}^{ - 24}}}}$
So, $\dfrac{{{V_N}}}{{{V_{atom}}}} = {10^{ - 15}}$

Hence, option C is correct.

Note:
There are electrostatic forces of repulsion acting inside the nucleus because the protons are very close to each other. Moreover, the total number of protons is equal to the number of electrons revolving around the nucleus and therefore, the atom as a whole is electrically neutral.