The energy released by the fission of a single uranium nucleus is 200 MeV. The number of fission of uranium nucleus per second required to produce 16 MW of power is (Assume efficiency of the reactor is 50%)

Options

A. (a) `2xx10^6`
B. (b) `2.5xx10^6`
C. (c) `5xx10^6`
D. (d) None of these

Explanation

To solve the problem, we need to determine the number of fission reactions required per second to produce a power output of 16 MW, given that the energy released by the fission of a single uranium nucleus is 200 MeV and the efficiency of the reactor is 50%.

### Step-by-Step Solution:

1. **Determine the usable energy per fission reaction:**
- The energy released by the fission of a single uranium nucleus is given as 200 MeV.
- Since the efficiency of the reactor is 50%, the usable energy from one fission reaction is:
\[ \text{Usable Energy} = 200 \text{ MeV} \times 0.5 = 100 \text{ MeV} \]

2. **Convert MeV to Joules:**
- We know that \(1 \text{ MeV} = 1.6 \times 10^{-13} \text{ Joules}\).
- Therefore, the usable energy in Joules is:
\[ \text{Usable Energy} = 100 \text{ MeV} \times 1.6 \times 10^{-13} \text{ J/MeV} = 1.6 \times 10^{-11} \text{ J} \]

3. **Calculate the total power output in Joules per second:**
- The power output is given as 16 MW, which is equivalent to:
\[ 16 \text{ MW} = 16 \times 10^6 \text{ W} = 16 \times 10^6 \text{ J/s} \]

4. **Determine the number of fission reactions per second:**
- The power output can also be expressed as the product of the number of fission reactions per second (\(N\)) and the usable energy per fission reaction:
\[ P = N \times \text{Usable Energy} \]
- Rearranging for \(N\):
\[ N = \frac{P}{\text{Usable Energy}} = \frac{16 \times 10^6 \text{ J/s}}{1.6 \times 10^{-11} \text{ J}} \]

5. **Calculate \(N\):**
- Performing the calculation:
\[ N = \frac{16 \times 10^6}{1.6 \times 10^{-11}} = 10^{18} \text{ fissions/s} \]

### Final Answer:
The number of fission reactions required per second to produce 16 MW of power is \(10^{18}\) fissions/s.