A small spherical assembly of enriched U operates with a neutron multiplication factor

MATHEMATICS · Multi-part · CBSE · Mathematics · Sequences and Series · Sequences and Series

Problem

A small spherical assembly of enriched 235^{235}U operates with a neutron multiplication factor k=1.20k=1.20. The mean generation time of neutrons is τ=1.0×10−4 s\tau = 1.0\times10^{-4}\,\text{s}. At t=0t=0 the neutron population inside the sphere is N0=1.0×106N_0 = 1.0\times10^{6}. (i) Write an expression for the neutron population NnN_n after nn complete generations. (ii) Calculate the neutron population after 3030 generations. (iii) Determine the physical time required for these 3030 generations to occur. (iv) If every neutron present at the start of a generation immediately initiates one fission, estimate the total energy released up to the end of the 30th30^{\text{th}} generation. Express your answer in kilowatt-hours (kWh). (Take energy per fission =200 MeV=200\,\text{MeV}.)

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