Question

A uranium reactor develops thermal energy at a rate of 300 MW. Calculate the amount of ${235}_U$ being consumed every second. Average energy released per fission is 200 MeV.

Answer 1

We have,

The thermal energy of Uranium is $300MW$

Now, Let the number of atoms disintegrate per second is 'n'.

So,

Total energy emitted per second is:

$power=n\times 200\times {10}^6\times 1.6\times 1.6\times {10}^{-19}J$

$300\times {10}^6=n\times 200\times {10}^6\times 1.6\times 1.6\times {10}^{-19}J$

Where $1.6\times {10}^{-19}$ is the charge of electron

$n=\frac{3}{2\times 1.6}\times {10}^{19}$

$=\frac{3}{3.2}\times {10}^{19}$

$6\times {10}^{23}$ atoms present in the Urenium 238g

$\frac{238\times 3\times {10}^{19}}{6\times {10}^{23}\times 3.2}$

$3.7\times {10}^{-4}g$