Question

In a liquid metal fast breeder reactor, no neutron moderation is desired and sodium is used as a coolant to minimize fission-neutron thermalization. How many elastic scatters with sodium, on the average, would it take for 2-MeV neutrons to reach an average thermal energy of 0.025 eV?

Answer 1

Answer:

219 scatterings

Explanation:

Given that:

The Coolant used In the liquid metal fast breed reactor = Sodium

The atomic weight (A) of sodium = 23

The initial energy $E_{i}$ = 2 - MeV

The final energy $E_{f}$ = 0.025 eV  (thermal energy)

The number of elastic neutron scatterings (n) needed to reach the given average thermal energy can be computed as:

$n = \dfrac{log \bigg(\dfrac{E_f}{E_i} \bigg)}{log \bigg [ \dfrac{A^2+1}{(A+1)^2} \bigg]}$

$n = \dfrac{log \bigg(\dfrac{0.025}{2 \times 10^6} \bigg)}{log \bigg [ \dfrac{23^2+1}{(23+1)^2} \bigg]}$

$n = \dfrac{log \bigg(1.25\times 10^{-8} \bigg)}{log \bigg [ 0.92014\bigg]}$

$n = 218.643$

n ≅ 219 scatterings