Question

The fraction of volume occupied by the nucleus with respect to the total volume of an atom is:

• A. ${10}^{-15}$
• B. ${10}^{-5}$
• C. ${10}^{-30}$
• D. ${10}^{-10}$

Answer 1

The correct option is A ${10}^{-15}$

As we know,
Radius of nucleus ($r_1$) is in the order of ${10}^{-13}cm$ and radius of an atom ($r_2$) is ${10}^{-8}cm$.
Volume of nucleus = $\frac{4}{3}\pi (r_1{)}^3$
Total Volume of atom = $\frac{4}{3}\pi (r_2{)}^3$
So, volume fraction = $\frac{volumeofnucleus}{Totalvolumeofatom}=\frac{4/3\pi ({10}^{-13}{)}^{3}c{m}^3}{4/3\pi ({10}^{-8}{)}^{3}c{m}^3}={10}^{-15}$