Question

Assuming that about $200MeV$ of energy is released per fission of ${}_{92}{U}^{235}$ nuclei, the mass of $U^{235}$ consumed per day in a fission reactor of power $1MW$ will be approximately

• A. ${10}^{-2}g$
• B. $1g$
• C. $100g$
• D. $10,000g$

Answer 1

The correct option is B $1g$

Energy released per disintegration $=200MeV=$ $200\times (1.6\times {10}^{-13})J=3.2\times {10}^{-11}J$
Total Energy required $=1MW=$ ${10}^{6}J/s$
No. of integrations required $=N=$ $\frac{{10}^6}{3.2\times {10}^{-11}}=3.125\times {10}^{16}$
Moles (n) $=\frac{N}{N_A}=5.188\times 10-8moles/s$
Mass consumption $=nM=$ $1.22\times {10}^{-5}gms/s$
Total consumption in a day $=1.22\times {10}^{-5}gm/s\times (24\times 3600)=1.053gms$