Question

The binding energy per nucleon of deuteron \[{{(}_{1}}{{H}^{2}})\] and helium nucleus \[{{(}_{2}}H{{e}^{4}})\] is 1.1 MeV and 7 MeV respectively. If two deuterium nuclei react to form a single helium nucleus, the energy released is –
A) 13.9 MeV
B) 26.9 MeV
C) 23.6 MeV
D) 19.2 MeV

Answer 1

Hint: We need to understand the relation between the binding energy per nucleon of a nucleus and the energy it can release when these nucleons are separated to find the energy that will be excess after the formation of another nuclei.

Complete answer:
We are given a deuteron nucleus which has a proton and a neutron in its nucleus and a helium nucleus which consists of two protons and two neutrons in its nucleus.
We know that the binding energy per nucleon is the binding energy possessed by each nucleon (protons and neutrons) in a given nucleus. The binding energy is regarded as the energy that is utilised by the nucleus to overcome the electrostatic repulsion between the positive protons and neutral neutrons in a nucleus. It is the energy equivalent to the mass defect experienced by the nucleus by Einstein's mass – energy equivalence.
We are told that two deuterons react to form a single helium nuclei. One deuteron consists of two nucleons, so there are nucleons which combine to form the helium. The energy required to break the nuclear force in the deuteron nuclei is –
\[\begin{align}
  & {{E}_{req}}=4\times 1.1MeV \\
 & \therefore {{E}_{req}}=4.4MeV \\
\end{align}\]
The energy released due to the formation of a helium nuclei with four nucleons is given as –
\[\begin{align}
  & {{E}_{released}}=4\times 7MeV \\
 & \therefore {{E}_{released}}=28MeV \\
\end{align}\]
The net energy released out of this nuclear fusion reaction is given as –
\[\begin{align}
  & E={{E}_{released}}-{{E}_{req}} \\
 & \Rightarrow E=(28-4.4)MeV \\
 & \therefore E=23.6MeV \\
\end{align}\]
This is the required solution.

The correct answer is option C.

Note:
The mass – energy equivalence proposed by Einstein solved a lot of problems like the mass defect in the nuclear mass in Physics. The idea of atom bombs and nuclear bombs also came from this simple relation between this mass and energy inter convertibility.