Question

On fission of one nucleus of $U^{235}$, the amount of energy obtained is $200MeV$. The power obtained in a reactor is $1000kW$. Number of nuclei fissioned per second in the reactor is

• A. $3.125\times {10}^{16}$
• B. $6.25\times {10}^{10}$
• C. $3.125\times {10}^{32}$
• D. $6.25\times {10}^{20}$

Answer 1

The correct option is A $3.125\times {10}^{16}$

Let $E$ be the amount of energy obtained per one nucleus.

Power obtained from the reactor is $P=\frac{nE}{t}\Rightarrow \left(\frac{n}{t}\right)=\frac{P}{E}$

$P=1000kW=1000\times 1000={10}^{6}J{s}^{-1}$

Also, $1MeV=1.6\times {10}^{-13}J$

Number of nuclei fissioned per second $=\frac{P}{E}=\frac{{10}^6}{200\times 1.6\times {10}^{-13}}=3.125\times {10}^{16}{s}^{-1}$