Question

Two deuterons undergo nuclear fusion to form a Helium nucleus. Energy released in this process is: (given binding energy per nucleon for deuteron = ${\rm{1}}{\rm{.1}}\;{\rm{MeV}}$ and for helium = $7.0\;{\rm{MeV}}$)
A. $30.2\;{\rm{MeV}}$
B. $23.6\;{\rm{MeV}}$
C. $25.8\;{\rm{MeV}}$
D. $32.4\;{\rm{MeV}}$

Answer 1

Hint: We know that, in the nuclear fusion reaction, a huge amount of energy is released. It is one of the examples of the exothermic reaction. The nuclear fusion creates a single heavy nucleus from two different lighter nuclei. Generally, this process is termed as the nuclear reaction.

Complete solution
As we all know, the two lighter hydrogen atoms are commonly fused to create a bigger atom of helium. This chemical reaction generally explains the phenomena of nuclear fusion.
The nuclear fusion chemical reaction of two deuterons to form helium is shown below.
${}_1^2{\rm{H}} + {}_1^2{\rm{H}} \to {}_2^4{\rm{He}} + {\rm{Energy}}$
As we all know, the mass of one deuteron atom is $2.013550$.
Hence, the mass of two reacted deuteron atoms is $2 \times 2.013550 = 4.42981$.
Similarly, the mass of produced helium atoms is $4.013490$.
The energy released during the nuclear fusion chemical reaction can be shown below.
$
\Delta E = 4.013490 \times 7\;{\rm{MeV}} - 4.0271 \times 1.1\;{\rm{MeV}}\\
 = 28.09443 - 4.42981\;{\rm{MeV}}\\
 = {\rm{23}}{\rm{.66462}}\;{\rm{MeV}}\\
 \approx {\rm{23}}{\rm{.6}}\;{\rm{MeV}}
$
Where, the coefficient $\Delta E$ is the difference in the energies of two different elements.
Hence, the energy released in this process by two hydrogen atoms that are deuterons and from one helium atom is $23.6\;{\rm{MeV}}$.

Therefore, the correct option for this given question is B that is $23.6\;{\rm{MeV}}$.

Note:
The exothermic reaction is that in which a large amount of energy is produced to the system from its corresponding surroundings. The combustion is one of the best examples to explain the exothermic reaction by forming a product like carbon dioxide and water. The nuclear reactions are of two types one is nuclear fusion and other is nuclear fission. The nuclear fission usually gives the endothermic chemical reaction.