Q. The nuclear radius of a certain nucleus is 7.2 fm and it has charge of $1.28\ \times \ 10^{- 17}\ C$. The number of neutrons inside the nucleus is
A) 136
B) 142
C) 140
D) 132
Explanation
(a) $R = R_{0}A^{1/3}$
Here, $R = 7.2\ \times \ 10^{- 15}\ m,\ R_{0} = 1.2\ \times 10^{- 15}\ m$
$\therefore A = \left( \frac{R}{R_{0}} \right)^{3} = \left( \frac{7.2\ \times \ 10^{- 15}}{1.2\ \times 10^{- 15}} \right)^{3} = (6)^{3} = 216$
Also, atomic number $Z = \frac{q}{e}\ = \frac{1.28\ \times \ 10^{- 17}}{1.6\ \times 10^{- 19}} = 80$
Therefore, number of neutrons
$\ \ \ \ \ \ \ \ N = \ A - Z = 216 - 80 = 136$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.