A uniformly mixed core of is surrounded by a good neutron reflector

PHYSICS · Multi-part · CBSE · Physics · Nuclei · Nuclei

Problem

A uniformly mixed core of

^{235}\mathrm{U}

is surrounded by a good neutron reflector. Each fission releases, on average,

\nu=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}\mathrm{U}

. -

10\%

are captured in non-fission reactions. -

10\%

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

k

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

k

obtained above. (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. (iv) Assuming the assembly reaches a steady operating state at

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 as

200\ \text{MeV}

and

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