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Energy Released in Nuclear Fusion of Deuterium to Helium

The energy released if hydrogen atoms are combined to form 24He_2^4\text{He} is ________ MeV\text{MeV}.
(Take binding energies per nucleon of 12H_1^2\text{H} and 24He_2^4\text{He} as 1.1 MeV1.1\text{ MeV} and 7.2 MeV7.2\text{ MeV}, respectively)

Options

A

6.1

B

24.4

Correct
C

26.6

D

5

Topics & Concepts

NucleiNuclear Reactions

Step-by-Step Solution

To calculate the energy released in the nuclear fusion reaction 212H24He2 \,_1^2\text{H} \rightarrow \,_2^4\text{He}, we determine the difference between the total binding energy of the product and reactant nuclei.

The total binding energy of two deuterium nuclei is 2×(2×1.1 MeV)=4.4 MeV2 \times (2 \times 1.1\text{ MeV}) = 4.4\text{ MeV}, while the total binding energy of the helium nucleus is 4×7.2 MeV=28.8 MeV4 \times 7.2\text{ MeV} = 28.8\text{ MeV}.

The net energy released is Q=28.8 MeV4.4 MeV=24.4 MeVQ = 28.8\text{ MeV} - 4.4\text{ MeV} = 24.4\text{ MeV}.

Hence, the correct option is (B).

Energy Released in Nuclear Fusion of Deuterium to Helium | Physics PYQ Solution - JEE Challenger