A spherical lump of a fissile material emits on average neutrons per fission

PHYSICS · Single correct · CBSE · Physics · Nuclei · Nuclei

Problem

A spherical lump of a fissile material emits on average

\nu = 2.4

neutrons per fission. The probability that a neutron escapes without causing further fission is approximated by

P = e^{-R/10}

, where

R

(in cm) is the sphere’s radius and the neutron mean free path is 10 cm. Criticality is reached when

k = \nu (1-P) = 1

. The minimum radius required for criticality is closest to (a)

12\ \text{cm}

(b)

5.4\ \text{cm}

(c)

3\ \text{cm}

(d)

8.1\ \text{cm}