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In the fusion reaction { }_{1}^{2} {H}+{ }_{1}^{2} {H} { }_{2}

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Solving time: 3 mins

In the fusion reaction $_{1}^{2} H +_{1}^{2} H ⟶_{2}^{3} He +_{0}^{1} n$ , the masses of deuteron, helium and neutron expressed in amu are $2.015, 3.017$ and $1.009$ respectively. If $1 kg$ of deuterium undergoes complete fusion, find the amount of total energy released. $1 amu \equiv 931.5 MeV / c^{2}$

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Updated on: Feb 11, 2023

Book:

Optics And Modern Physics (DC Pandey)

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Scarlett Discussed

In the fusion reaction

_{1}^{2} H +_{1}^{2} H ⟶_{2}^{3} He +_{0}^{1} n

, the masses of deuteron, helium and neutron expressed in amu are

2.015, 3.017

and

1.009

respectively. If

1 kg

of deuterium undergoes complete fusion, find the amount of total energy released.

1 amu \equiv 931.5 MeV / c^{2}

14 mins ago

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14 mins ago

Text solutionVerified

Δ m = 2 (2.015) - (3.017 + 1.009) = 0.004 amu

∴

Energy released

= (0.004 \times 931.5) MeV = 3.726 MeV

Energy released per deuteron

= \frac{3.726}{2} = 1.863 MeV

Number of deuterons in

1 kg = \frac{6.02 \times 1 0 ^{26}}{2} = 3.01 \times 1 0^{26}

∴

Energy released per

kg

of deuterium fusion

= (3.01 \times 1 0^{26} \times 1.863) = 5.6 \times 1 0^{26} MeV

\approx 9.0 \times 1 0^{13} J

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Question Text	In the fusion reaction $_{1}^{2} H +_{1}^{2} H ⟶_{2}^{3} He +_{0}^{1} n$ , the masses of deuteron, helium and neutron expressed in amu are $2.015, 3.017$ and $1.009$ respectively. If $1 kg$ of deuterium undergoes complete fusion, find the amount of total energy released. $1 amu \equiv 931.5 MeV / c^{2}$
Updated On	Feb 11, 2023
Topic	Nuclei
Subject	Physics
Class	Class 12
Answer Type	Text solution:1 Video solution: 3
Upvotes	361
Avg. Video Duration	5 min

Text solutionVerified

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