 Solution

ID: past-exam-of-the-mphil-in-nuclear-energy-course-of-the-university-of-cambridge/2021/paper-ne1/2/c/solution

At equilibrium, precursor production balances precursor decay:

0 = \frac{β}{Λ} n_{0} - λ c_{0} .

Therefore

\frac{c _{0}}{n _{0}} = \frac{β}{λ Λ} = \frac{0.007}{( 0.1 ) ( 0.5 \times 1 0 ^{- 3} )} = 140.

The delayed neutron precursor population can exceed the instantaneous neutron population even when the delayed neutron fraction is small: the delayed neutron precursor reservoir persists much longer than an individual prompt-neutron generation.

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