Question

given that fuel grade uranium contains 4% fissile material (235U) that the fissile material is completely utilised that 200MeV (1eV=1.6× 10^-19 J) of thermal energy is released during fission of a single 235U nucleus and that the thermal to electrical conversion of efficiency is 33% the annual requirement of fuel grade uranium for round the clock operation of a 1000MW nuclear power plant would be

Answer 1

Let's denote $M$ as fuel grade uranium.

We know the mass of 235U is $0.04M$. We need to calculate how many U-235 nucleus are inside of this mass.

$N = \frac{0.04M}{235} N_A = \frac{0.04M}{235}\cdot 6.02 \cdot 10^{23}= 1.025\cdot 10^{20} M$

These nucleus will produce

$E= 1.025 \cdot 10^{20} M \cdot 200 \; MeV = 1.025 \cdot 10^{20} \cdot 200 \cdot 10^{6} \cdot 1.6 \cdot 10^{-19} \cdot M \; \;J =$

$= 328 \cdot 10^7 M \; \; J$

This energy should be equal to $\epsilon \mathcal{E} t = 0.33 \cdot1000\; MW \cdot 1 \; year= 330 \cdot 10^6 \cdot 31\; 556\; 926 \; J \approx 1.043 \cdot 10^{16} \; J$

So,

$327 \cdot 10^7 M = 1.043 \cdot 10^{16}$

$M = 3.2 \cdot 10^{6} \; g = 3.2 \cdot 10^{3} \; kg.$