Q30 of 32 Page 464

Calculate and compare the energy released by a) fusion of 1.0 kg of hydrogen deep within Sun and b) the fission of 1.0 kg of 235U in a fission reactor.

a) Mass of hydrogen, m = 1kg = 1000 g


Since,1 mole of hydrogen contains 6.023×1023 atoms which is equivalent to 1 g of hydrogen then, 1kg of hydrogen contains,


N = 6.023×1023×1000 = 6.023×1026 atoms


In sun, 4 hydrogen atoms, combine to form one helium atom, in fusion process which releases 26 MeV of energy.


Thus,


Energy released from fusion of 1kg of hydrogen is,


……………….(1)


=


b) Mass of uranium, m = 1kg = 1000 g


Since,1 mole of Uranium contains 6.023×1023 atoms which is equivalent to 235 g of Uranium then, 1kg of Uranium contains,


N =


During fission reaction of 1 atom of releases 200 MeV of energy.


Thus,


Energy released from fission of 1kg of Uranium is,


………..(2)


Divide (1) by (2) we get,



Hence, Fusion reaction occurred in Sun releases 8 times more energy than energy released during the fission reaction of Uranium.


More from this chapter

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27

Consider the fission by fast neutrons. In one fission event, no neutrons are emitted and the final end products, after the beta decay of the primary fragments, are 14058Ce and 9944Ru. Calculate Q for this fission process. The relevant atomic and particle masses are

m(23892U) = 238.05079 u


m(14058Ce) = 139.90543 u


m(9944Ru) = 98.90594 u

 28

Consider the D–T reaction (deuterium-tritium fusion)


(a) Calculate the energy released in MeV in this reaction from the data:


m (21H) = 2.014102 u


m (31H) = 3.016049 u


(b) Consider the radius of both deuterium and tritium to be approximately 2.0 fm. What is the kinetic energy needed to overcome the Coulomb repulsion between the two nuclei? To what temperature must the gas be heated to initiate the reaction?


(Hint: Kinetic energy required for one fusion event = average thermal kinetic energy available with the interacting particles


= 2(3kT/2); k = Boltzmann’s constant, T = absolute temperature.)

 29

Obtain the maximum kinetic energy of β-particles, and the radiation frequencies of γ decay in the decay scheme shown in Fig. 13.6. You are given that

m(198Au) = 197.968233 u


m(198Hg) = 197.966760 u


 31

Suppose India had a target of producing by 2020 AD, 200,000 MW of electric power, ten percent of which was to be obtained from nuclear power plants. Suppose we are given that, on an average, the efficiency of utilization (i.e. conversion to electric energy) of thermal energy produced in a reactor was 25%. How much amount of fissionable uranium would our country need per year by 2020? Take the heat energy per fission of 23592U to be about 200MeV.