In a uranium reactor whose thermal power is `P=100 MW`, if the average number of neutrons liberated in each nuclear spitting is `2.5`. Each splitting is assumed to release an energy `E=200 MeV`. The number of neutrons generated per unit time is-

Options

A. `4xx10^(18)s^(-1)`
B. `8xx10^(19)s^(-1)`
C. `8xx10^(19)s^(-1)`
D. `(125)/(16)xx10^(18)s^(-1)`

Explanation

To solve the problem, we need to find the number of neutrons generated per unit time in a uranium reactor, given the thermal power, the average number of neutrons released per fission, and the energy released per fission.

### Step-by-Step Solution:

1. **Convert Power to Watts**:
The thermal power of the reactor is given as \( P = 100 \, \text{MW} \).
\[ P = 100 \, \text{MW} = 100 \times 10^6 \, \text{W} = 10^8 \, \text{W} \]

2. **Convert Energy Released per Fission to Joules**:
The energy released per fission is given as \( E = 200 \, \text{MeV} \).
To convert MeV to Joules, we use the conversion factor \( 1 \, \text{MeV} = 1.6 \times 10^{-13} \, \text{J} \).
\[ E = 200 \, \text{MeV} = 200 \times 1.6 \times 10^{-13} \, \text{J} = 3.2 \times 10^{-11} \, \text{J} \]

3. **Calculate the Number of Fissions per Second**:
The number of fissions occurring per second can be calculated using the formula:
\[ \text{Number of fissions} = \frac{\text{Power}}{\text{Energy per fission}} = \frac{10^8 \, \text{W}}{3.2 \times 10^{-11} \, \text{J}} \]
\[ \text{Number of fissions} = 3.125 \times 10^{18} \, \text{fissions/s} \]

4. **Calculate the Number of Neutrons Generated per Second**:
Given that each fission releases an average of \( 2.5 \) neutrons, the total number of neutrons generated per second is:
\[ \text{Number of neutrons} = 2.5 \times \text{Number of fissions} \]
\[ \text{Number of neutrons} = 2.5 \times 3.125 \times 10^{18} \]
\[ \text{Number of neutrons} = 7.8125 \times 10^{18} \, \text{neutrons/s} \]

5. **Final Result**:
Therefore, the number of neutrons generated per unit time is approximately:
\[ \text{Number of neutrons} \approx 7.81 \times 10^{18} \, \text{neutrons/s} \]