Chapter 31, Problem 16P

To determine

The energy released in the fission reaction.

Answer to Problem 16P

The energy released in the fission reaction is $126.5\text{ MeV}$ .

Explanation of Solution

Given:

Consider the reaction.

  $\text{n}{+}_{92}^{235}\text{U}{\to }_{38}^{88}\text{Sr}{+}_{54}^{136}\text{Xe}+12\text{n}$

Formula used:

Use Appendix B,

Calculate the required energy.

  $\text{Q}={\mathrm{m}}_{\mathrm{n}}{\mathrm{c}}^2+{\mathrm{m}}_{{}_{92}^{235}}{}_{\text{U}}{\mathrm{c}}^2-{\mathrm{m}}_{{}_{38}^{88}\text{Sr}}+{\mathrm{m}}_{{}_{54}^{136}\text{Xe}}-12{\mathrm{m}}_{\mathrm{n}}{\mathrm{c}}^2$

Calculation:

Substitute the values in the above equation.

  $\begin{array}{c}\text{Q}={\mathrm{m}}_{\mathrm{n}}{\mathrm{c}}^2+{\mathrm{m}}_{{}_{92}^{235}}{}_{\text{U}}{\mathrm{c}}^2-{\mathrm{m}}_{{}_{38}^{88}\text{Sr}}+{\mathrm{m}}_{{}_{54}^{136}\text{Xe}}-12{\mathrm{m}}_{\mathrm{n}}{\mathrm{c}}^2\\ =\left[1.008665\mathrm{u}+235.0439\mathrm{u}-87.9056\mathrm{u}-135.907220-12\left(1.008665\mathrm{u}\right)\left(931.5{\mathrm{c}}^2\right)\right]\\ =126.5\text{ MeV}\end{array}$

Thus, the energy released in the fission reaction is $126.5\text{ MeV}$ .