Physics

Problem

A uniformly mixed core of

^{235}

U is surrounded by a good neutron reflector. Each fission releases on an average $ u = 2.5$ neutrons that enter the next generation. In one generation of neutrons the following fractional losses are observed: •

80\%

of the neutrons cause further fission in

^{235}

U, •

10\%

are captured in non-fission reactions, •

10\%

leak out of the core despite the reflector. Answer the questions that follow. a. (i) Calculate the effective multiplication factor

k

for the core. b. (ii) State whether the chain reaction is self-sustaining, damped or increasing. Give reason based on the value of

k

obtained above. c. (iii) If improvement in moderation raises the fraction of neutrons that cause fission to

85\%

(all other fractions changing proportionately), find the new value of

k

and comment on the fate of the reaction. d. (iv) Assuming the assembly reaches a steady operating state at the value of

k=1

, estimate the thermal power produced when the steady fission rate is

8.0\times10^{18}

fissions per second. (Take energy released per fission

=200\,\text{MeV}

;

1\,\text{eV}=1.6\times10^{-19}\,\text{J}

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