Question

When ${}_{92}{U}^{235}$ undergoes fission about $0.1\%$ of the original mass is converted into energy. Then the amount of ${}_{92}{U}^{235}$ should undergo fission per day in a nuclear reactor, so that it provides $200$ mega watt electric power, is :

• A. $9.6\times {10}^{-2}kg$
• B. $4.8\times {10}^{-2}kg$
• C. $19.2\times {10}^{-2}kg$
• D. $1.2\times {10}^{-2}kg$

Answer 1

The correct option is C $19.2\times {10}^{-2}kg$

$m=$ total mass of Uranium required per second

$\Delta m=\frac{M}{1000}$ for direct energy conversion.

Energy/second $=200\times {10}^{6}J/s$

Power = Energy conversion per second

$\Rightarrow 200\times {10}^6=0.001M{c}^2$

$\Rightarrow M=\frac{200\times {10}^6}{0.001\times c^2}=0.222\times {10}^{-5}$

So mass required in whole day $M=0.222\times {10}^{-5}\times 24\times 60\times 60$

Mass Per day $=19.2\times {10}^{-2}Kg$