Chapter 31, Problem 3P

To determine

To check: Weather the reaction $\mathrm{n}{+}_{92}^{237}\text{U}{\to }_{92}^{239}\text{U}+\mathrm{\gamma }$ is possible with the slow neutrons.

Explanation of Solution

Given Information:

The natural aluminium is all ${}_{13}^{27}\text{Al}$ .

Calculation:

Consider the mass of the reactants is ${}_{92}^{239}\text{U}=238.050783\mathrm{u}$ .

Here, the mass of the reactants is $\underset{0}{\overset{1}{\mathrm{n}}}=1.008665\mathrm{u}$ and the total mass of the reactant is $239.05948\mathrm{u}$ .

The mass of ${}_{92}^{239}\text{U}=239.054288\mathrm{u}$ . Then, the difference in the mass is,

  $\left(239.059449-239.052888\right)\mathrm{u}=5.16\times {10}^{-3}\text{u}$

Then, the equivalent energy is,

  $\begin{array}{c}\mathrm{E}=5.16\times {10}^{-3}\text{u}\left(931.52\text{MeV}/{\text{uc}}^2\right)*{\text{c}}^{\text{2}}\\ =4.80654\text{MeV}\end{array}$

Conclusion:

Thus, the energy released is $4.80654\text{MeV}$ then the reaction is possible with the slow moving neutrons.