`A U^(235)` reactor generated power at a rate of P producting `2xx10^(18)` fussion per second. The energy released per fission is 185 MeV. The value of P is

Options

A. `59.2` MW
B. `370xx10^(18)MW`
C. `0.59 MW`
D. 370 MW

Explanation

To solve the problem, we need to calculate the power \( P \) generated by a U-235 reactor based on the given data. Here’s a step-by-step solution:

### Step 1: Identify the given values
- The number of fissions per second, \( n = 2 \times 10^{18} \) fissions/second.
- The energy released per fission, \( E = 185 \) MeV.

### Step 2: Convert energy from MeV to Joules
1. We know that \( 1 \) MeV = \( 1.6 \times 10^{-13} \) Joules.
2. Therefore, to convert \( E \) from MeV to Joules:
\[ E = 185 \, \text{MeV} \times 1.6 \times 10^{-13} \, \text{J/MeV} = 185 \times 1.6 \times 10^{-13} \, \text{J} \]
\[ E = 296 \times 10^{-13} \, \text{J} = 2.96 \times 10^{-11} \, \text{J} \]

### Step 3: Calculate the power \( P \)
1. The power generated by the reactor can be calculated using the formula:
\[ P = n \times E \]
where \( n \) is the number of fissions per second and \( E \) is the energy released per fission in Joules.
2. Substitute the values:
\[ P = (2 \times 10^{18} \, \text{fissions/second}) \times (2.96 \times 10^{-11} \, \text{J}) \]
\[ P = 5.92 \times 10^{7} \, \text{W} \]

### Step 4: Convert power from Watts to Megawatts
1. To convert Watts to Megawatts, we divide by \( 10^{6} \):
\[ P = \frac{5.92 \times 10^{7} \, \text{W}}{10^{6}} = 59.2 \, \text{MW} \]

### Final Answer
The power \( P \) generated by the U-235 reactor is \( 59.2 \, \text{MW} \).

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