A thermal neutron is absorbed by a nucleus

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

Problem

A thermal neutron is absorbed by a

^{235}_{92}\text{U}

nucleus, forming an excited compound nucleus that promptly undergoes fission to produce barium-141 and krypton-92 as two of the fission fragments.

^{235}_{92}\text{U}+\,^{1}_{0}\text n \;\longrightarrow\;^{141}_{56}\text{Ba}+\,^{92}_{36}\text{Kr}+\,x\,^{1}_{0}\text n+Q

Measured atomic masses (in atomic mass units, u): •

m(^{235}\text{U}) = 235.04393\,\text u

•

m(^{1}\text n) = 1.00866\,\text u

•

m(^{141}\text{Ba}) = 140.91441\,\text u

•

m(^{92}\text{Kr}) = 91.92616\,\text u

1\,\text u

corresponds to

931\,\text{MeV}/c^{2}

. (a) Determine the integer value of

x

, the number of neutrons emitted, required to satisfy all relevant conservation laws. Show how you arrived at your answer. (b) Using the masses provided and your value of

x

, calculate the energy released

Q

for a single fission event. Express your answer in MeV. (c) In a reactor, an average of

2.4

neutrons are emitted per fission event of

^{235}\text{U}

. If exactly

1.6

of those neutrons on average succeed in inducing additional fissions, determine the effective multiplication factor

k

of the reactor core and state whether the reactor is sub-critical, critical, or super-critical.

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