Chapter 31, Problem 18P

To determine

The number of fissions takes place per second.

Answer to Problem 18P

The number of fissions is $6\times {10}^{18}\text{ reactions per second}$ .

Explanation of Solution

Given:

The reactor is of 200 MW

Formula used:

The expression is given by,

  $\mathrm{P}=\frac{\text{Energy}}{\text{Reaction}}\left(\frac{\text{N}\text{.reaction}}{\text{s}}\right)$

Rearrange the above equation.

  $\begin{array}{l}\mathrm{P}=\frac{\text{Energy}}{\text{Reaction}}\left(\frac{\text{N}\text{.reaction}}{\text{s}}\right)\\ \frac{\text{N}\text{.reaction}}{\text{s}}=\frac{\mathrm{P}\left(\text{Reaction}\right)}{\text{Energy}}\end{array}$

Calculation:

Substitute the values in the above equation.

  $\begin{array}{c}\frac{\text{N}\text{.reaction}}{\text{s}}=\frac{200\times {10}^{-6}}{200\times {10}^{-6}\left(1.60\times {10}^{-19}\right)}\\ =6\times {10}^{18}\text{ reactions per second}\end{array}$

Thus, the number of fissions is $6\times {10}^{18}\text{ reactions per second}$ .