Question

In a reactor, $2kg$ of ${}_{92}{U}^{235}$ fuel is fully used up in 30 days. The energy released per fission is $200MeV$. Given that the Avogadro number, $N=6.023\times 10^{26}$ per kilo mole and $1eV=1.6\times 10^{-19}J$. The power output of the reactor is close to :

• A. $125MW$
• B. $60MW$
• C. $35MW$
• D. 54 MW

Answer 1

Answer: (B)

Number of uranium atoms in $2kg$
$=\frac{2\times 6.023\times 10^{26}}{235}$
energy from one atom is $200\times 10^6$ e.v. hence total energy from $2kg$ uranium
$=\frac{2\times 6.023\times 10^{26}}{235}\times 200\times 10^6\times 1.6\times 10^{-19}J$
$2kg$ uranium is used in 30 days hence this energy is recieved in 30 days hence energy recived per second or power is
Power $=\frac{2\times 6.023\times 10^{26}\times 200\times 10^6\times 1.6\times 10^{-19}}{235\times 30\times 24\times 3600}$
Power $=63.2\times 10^6$ watt or 63.2 Mega Watt