Question

The energy released per fission of ${}^{235}_{92}\mathrm{U}$ is $200\,\text{MeV}$. The fission rate of ${}^{235}_{92}\mathrm{U}$ required to produce $2\,\text{W}$ power is

• A. $1.25\times10^{26}$ per second
• B. $2.56\times10^{26}$ per second
• C. $1.25\times10^{13}$ per second
• D. $6.25\times10^{10}$ per second

Hint:

To find reaction rate from power, always convert energy per event into joules and use \[ \text{Rate}=\frac{\text{Power}}{\text{Energy per event}}. \]

Answer 1

The Correct Option is D

Step 1: Convert energy per fission from MeV to joules. \[ 1\,\text{MeV} = 1.6\times10^{-13}\,\text{J} \] \[ E_{\text{fission}} = 200\times1.6\times10^{-13} = 3.2\times10^{-11}\,\text{J} \]
Step 2: Power is energy released per second. Given power: \[ P = 2\,\text{W} = 2\,\text{J s}^{-1} \]
Step 3: Fission rate $N$ required: \[ N = \frac{P}{E_{\text{fission}}} = \frac{2}{3.2\times10^{-11}} = 6.25\times10^{10}\ \text{per second} \]