Question

What is the power output of ${}_{92}{U}^{235}$ reactor if it takes $30$ days to use $2kg$ of fuel, and if each fission gives $185MeV$ of usable energy

• A. $50.48MW$
• B. $46.58MW$
• C. $58.46MW$
• D. $36.58MW$

Answer 1

Answer: (C)

$58.46MW$

Given : $m=2000$ g $t=30\times 86400=2592000$ s

Output power $P_o=185\times {10}^6\times 1.6\times {10}^{-19}=2.96\times {10}^{-11}$ J

Number of Uranium atom in 2 kg ${}_{92}{U}^{235}$ $N=\frac{m{N}_A}{M}$ atoms

$\therefore$ $N=\frac{2000\times 6.023\times {10}^{23}}{235}=5.12\times {10}^{24}$ atoms

Rate of fission reactions $R=\frac{5.12\times {10}^{24}}{2592000}=1.975\times {10}^{18}$ per sec

Total power output $P=P_o\times R=2.96\times {10}^{-11}\times 1.975\times {10}^{18}=58.46$ MW