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It is proposed to use the nuclear fusion reaction, { }_{1}^{2}

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It is proposed to use the nuclear fusion reaction, $_{1}^{2} H +_{1}^{2} H \to_{2}^{4} He$ in a nuclear reactor $200 MW$ rating. If the energy from the above reaction is used with a 25 per cent efficiency in the reactor, how many grams of deuterium fuel will be needed per day? (The masses of $_{1}^{2} H$ and $_{2}^{4} He$ are $2.0141$ atomic mass units and 4.0026 atomic mass units respectively.)

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Optics And Modern Physics (DC Pandey)

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It is proposed to use the nuclear fusion reaction,

_{1}^{2} H +_{1}^{2} H \to_{2}^{4} He

in a nuclear reactor

200 MW

rating. If the energy from the above reaction is used with a 25 per cent efficiency in the reactor, how many grams of deuterium fuel will be needed per day? (The masses of

_{1}^{2} H

and

_{2}^{4} He

are

2.0141

atomic mass units and 4.0026 atomic mass units respectively.)

7 mins ago

Discuss this question LIVE

7 mins ago

Text solutionVerified

Mass defect in the given nuclear reaction,

Δ m = 2 (

mass of deuterium)

-

(mass of helium)

= 2 (2.0141) - (4.0026) = 0.0256

Therefore, energy released

Δ E = (Δ m) (931.48) MeV = 23.85 MeV

= 23.85 \times 1.6 \times 1 0^{- 13} J = 3.82 \times 1 0^{- 12} J

Efficiency is only

25%

, therefore,

25% of Δ E = (\frac{25}{100}) (3.82 \times 1 0^{- 12}) J

= 9.55 \times 1 0^{- 13} J

i.e. by the fusion of two deuterium nuclei,

9.55 \times 1 0^{- 13} J

energy is available to the nuclear reactor. Total energy required in one day to run the reactor with a given power of

200 MW

E_{Total} = 200 \times 1 0^{6} \times 24 \times 3600 = 1.728 \times 1 0^{13} J

∴

Total number of deuterium nuclei required for this purpose,

n = \frac{E _{Total}}{Δ E /2} = \frac{2 \times 1.728 \times 1 0 ^{13}}{9.55 \times 1 0 ^{- 13}}

= 0.362 \times 1 0^{26}

∴

Mass of deuterium required

= (

Number of g-moles of deuterium required

) \times 2 g

= (\frac{0.362 \times 1 0 ^{26}}{6.02 \times 1 0 ^{23}}) \times 2 = 120.26 g

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Question Text	It is proposed to use the nuclear fusion reaction, $_{1}^{2} H +_{1}^{2} H \to_{2}^{4} He$ in a nuclear reactor $200 MW$ rating. If the energy from the above reaction is used with a 25 per cent efficiency in the reactor, how many grams of deuterium fuel will be needed per day? (The masses of $_{1}^{2} H$ and $_{2}^{4} He$ are $2.0141$ atomic mass units and 4.0026 atomic mass units respectively.)
Topic	Nuclei
Subject	Physics
Class	Class 12
Answer Type	Text solution:1
Upvotes	91

Text solutionVerified

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