Chapter 31, Problem 21P

To determine

The mass required to produce the same amount of energy as in burning coal.

Answer to Problem 21P

The mass required to produce the same amount of energy as in burning coal is $3.7\times {10}^{-7}\text{ kg}$ .

Explanation of Solution

Given:

The energy released by 1 kg of coal is $3\times {10}^7\text{ kg}$ .

The energy by fission of ${}_{92}^{235}\text{U}$ is 200 MeV.

Formula used:

The expression is given by,

  $\mathrm{n}=\frac{\mathrm{Q}}{{\mathrm{Q}}_1}$

Calculation:

Substitute the values in the above equation.

  $\begin{array}{c}\mathrm{n}=\frac{\mathrm{Q}}{{\mathrm{Q}}_1}\\ =\frac{3\times {10}^7\text{ kg}}{200\times 1.6\times {10}^{-19}}\\ =9.375\times {10}^{17}\text{ atoms}\end{array}$

The mass is calculated as,

  $\begin{array}{c}\mathrm{m}=238\times {10}^{-3}\times \frac{9.375\times {10}^{17}}{6.023\times {10}^{23}}\text{ kg}\\ =3.7\times {10}^{-7}\text{ kg}\end{array}$

Thus, the mass required to produce the same amount of energy as in burning coal is $3.7\times {10}^{-7}\text{ kg}$ .