Question

If $200 \, MeV$ energy is released in the fission of a single nucleus of ${ }_{92} U ^{235}$ . How many fissions must occur per second to produce a power of $1 \, kW$ ?

• A. $3.125 \, \times \, 10^{13}$
• B. $6.250\times \, 10^{13}$
• C. $1.525 \, \times 10^{13}$
• D. None of these

Answer 1

Answer: (A)

We know that $1\, kW = \, 1 \, \times \, 10^{3} \, Js^{- 1}$
Also, $1.6 \, \times \, 10^{- 9} \, J \, = \, 1 \, eV$
$\therefore 200 \, MeV= \, 200 \, \times \, 1.6 \, \times \, 10^{- 19} \, \times \, 10^{6} \, J$
Number of fissions = $\frac{\text{Power}}{\text{Energy released}}$
$=\frac{10^{3}}{200 \, \times \, 1.6 \, \times 10^{- 13}}= \, 3.125 \, \times \, 10^{13}$