Q. The binding energy per nucleon of deuteron ($_{1}^{2}{H)}$and helium nucleus ($_{2}^{4}{He)}$is 1:1MeV and 7MeV respectively. If two deuteron nuclei react to form a single helium nucleus , then the energy released is

A) 13.9MeV
B) 26.9MeV
C) 23.6MeV
D) 19.2MeV
Explanation

(c) As given
$\ _{1}H^{2}\ + \ _{1}H^{2} \rightarrow \ _{2}He^{4}\ + energy$
The binding energy per nucleon of a deuteron$(\ _{1}H^{2})$
$= 1.1MeV$
$\therefore$ Total binding energy of one deuteron nucleus
$= \ 2\ \times \ 1.1 = 2.2MeV$
$\therefore$ The binding energy per nucleon of Helium$(\ _{2}He^{4})$
=7MeV
$\therefore$ Total binding energy
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \ 4\ \times \ 7\ = 28MeV$
Hence, energy released in the above process
$\ \ \ \ \ \ \ \ \ \ \ = 28 - 2\ \times 2.2$
= $28\ –\ 4.4\ = \ 23.6\ MeV$

Dr. Abubacker
Reviewed by Dr. Abubacker

Physics Educator & NEET/JEE Specialist

Ph.D. in Physics with 19+ years of teaching experience.

Want more practice?
Practice Nuclei MCQs