Chapter 31, Problem 22P

To determine

The initial mass to undergo fission to supply the electrical needs of such a house for a year.

Answer to Problem 22P

The initial mass to undergo fission to supply the electrical needs of such a house for a year is $3.7\times {10}^{-7}\text{ kg}$ .

Explanation of Solution

Given:

The power consumption by fission of ${}_{92}^{235}\text{U}$ is 900 W.

Calculation:

Use the factor level method to obtain the mass in kg.

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 $3.7\times {10}^{-7}\text{ kg}$