Atoms And Nuclei Question 345

Question: The nuclear fusion reaction $ 2H^{2}\to _{2}He^{4}+\text{Energy } $ , is proposed to be used for the production of industrial power. Assuming the efficiency of process for production of power is 20%, find the ass of the deuterium required approximately for a duration of 1 year. Given mass of $ _{1}H^{2} $ nucleus = 2.0141 a.m.u and mass of $ _{2}He^{4} $ nuclei = 4.0026 a.m.u and 1 a.m.u. = 31 MeV

Options:

A) 165kg

B) 138kg

C) 180kg

D) 60kg

Show Answer

Answer:

Correct Answer: B

Solution:

  • Mass defect $ \Delta m=2\times 2.014-4.0026=0.0256,a.m.u. $

    Energy released when two $ _{1}H^{2} $

    nuclei fuse $ =0.0256\times 931=23.8MeV $

    Total energy required to be produced by nuclear reaction in 1 year $ =2500\times 10^{6}\times 3.15\times 10^{7}=7.88\times 10^{16}J $

    No. of nuclei of $ _{1}H^{2} $

    required $ =\frac{7.88\times 10^{16}J}{23.8\times 1.6\times {{10}^{-13}}}\times 2=4.14\times 10^{28} $ Mass of Deuterium required $ =\frac{4.14\times 10^{28}}{6.02\times 10^{23}}\times 2\times {{10}^{-3}}kg=138kg $



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