Chapter 30, Problem 92A

To determine

The number of fusion reaction in a second.

Answer to Problem 92A

  $998400$

Explanation of Solution

Given:

Energy released in one reaction, $E=25$ MeV $=25\times {10}^6$ eV

Luminosity rate of released energy, $L=4\times {10}^{-6}$ W

Time, $t=1$ second

Calculation:

Energy released in one second $E_r=4\times {10}^{-6}\text{W}\cdot \text{s}$

Now, convert in eV

  $\begin{array}{l}1\text{ W}\cdot \text{s}=6.24\times {10}^{18}\text{ eV}\\ 4\times {10}^{-6}\text{ W}\cdot \text{s}=24.96\times {10}^{12}\text{ eV}\end{array}$

Now,

  $25\times {10}^6$ eV released energy = 1 reaction

  $24.96\times {10}^{12}$ eV released energy = $24.96\times {10}^{12}\times \frac{1}{25\times {10}^6}$ reactions

  $=998400$ reactions

Conclusion:

Hence, the number of fusion reaction in a second is 998400.