If 200 MeV energy is released per fission of `._(92)U^(235)` How many fissions must occur per second to produce a power of 1m W?

Answer

To solve the problem, we need to determine how many fissions of Uranium-235 (U-235) must occur per second to produce a power output of 1 milliwatt (mW).

### Step-by-Step Solution:

1. **Understand the Power Requirement**:
- Given power \( P = 1 \, \text{mW} = 1 \times 10^{-3} \, \text{W} \).

2. **Energy Released per Fission**:
- The energy released per fission of U-235 is given as \( E = 200 \, \text{MeV} \).
- Convert MeV to Joules:
\[ 1 \, \text{MeV} = 1.6 \times 10^{-13} \, \text{J} \]
Therefore,
\[ E = 200 \, \text{MeV} = 200 \times 1.6 \times 10^{-13} \, \text{J} = 3.2 \times 10^{-11} \, \text{J} \]

3. **Calculate the Number of Fissions per Second**:
- The power produced by \( n \) fissions per second is given by:
\[ P = n \times E \]
- Rearranging for \( n \):
\[ n = \frac{P}{E} \]
- Substitute the values:
\[ n = \frac{1 \times 10^{-3} \, \text{W}}{3.2 \times 10^{-11} \, \text{J}} = \frac{1 \times 10^{-3}}{3.2 \times 10^{-11}} \approx 3.125 \times 10^{7} \]

4. **Final Result**:
- Therefore, the number of fissions that must occur per second to produce a power of 1 mW is approximately:
\[ n \approx 3.125 \times 10^{7} \, \text{fissions/second} \]

### Summary of Steps:
1. Convert power from mW to W.
2. Convert energy from MeV to Joules.
3. Use the formula \( n = \frac{P}{E} \) to find the number of fissions per second.