Question

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

Answer 1

Given:
Rate of development of thermal energy = 300 MW
Average energy released per fission = 200 MeV
Let N be the number of atoms disintegrating per second.
Then, the total energy emitted per second will be
N$\times$200$\times$10⁶$\times$1.6$\times$10^$-19$ = Power
N$\times$200$\times$10⁶$\times$1.6$\times$10^$-19$ = 300$\times$10⁶
$\Rightarrow N=\frac{3}{2\times 1.6}\times {10}^{19}=\frac{3}{3.2}\times {10}^{19}$ atoms
6.023 × 10²³ atoms = 238 gm of U²³⁵
$\frac{3}{3.2}\times {10}^{19}\mathrm{atoms}\mathrm{will}\mathrm{present}\mathrm{in}\frac{238\times 3\times {10}^{19}}{6\times {10}^{23}\times 3.2}=3.7\mathrm{mg}$