Energy released in the fission of a single `._92 U^235` nucleus is `200 MeV`. The fission rate of a `._92 U^235` fuelled reactor operating at a power level of `5 W` is.

Options

A. `1.56 xx 10^(+10) s^-1`
B. `1.56 xx 10^(+11) s^-1`
C. `1.56 xx 10^(+16) s^-1`
D. `1.56 xx 10^(+17) s^-1`

Explanation

To find the fission rate of a `._92 U^235` fuelled reactor operating at a power level of `5 W`, we can follow these steps:

### Step 1: Understand the given values
- Energy released in the fission of a single `._92 U^235` nucleus = `200 MeV`
- Power level of the reactor = `5 W`

### Step 2: Convert energy from MeV to Joules
1 MeV (mega electron volt) is equivalent to \(1.6 \times 10^{-13}\) Joules. Therefore, we need to convert `200 MeV` to Joules:
\[ \text{Energy in Joules} = 200 \, \text{MeV} \times 1.6 \times 10^{-13} \, \text{J/MeV} \]
\[ = 200 \times 1.6 \times 10^{-13} \, \text{J} = 3.2 \times 10^{-11} \, \text{J} \]

### Step 3: Calculate the fission rate
The fission rate can be calculated using the formula:
\[ \text{Fission rate} = \frac{\text{Power}}{\text{Energy per fission}} \]
Substituting the values we have:
\[ \text{Fission rate} = \frac{5 \, \text{W}}{3.2 \times 10^{-11} \, \text{J}} \]
Since \(1 \, \text{W} = 1 \, \text{J/s}\), we can rewrite the equation as:
\[ \text{Fission rate} = \frac{5 \, \text{J/s}}{3.2 \times 10^{-11} \, \text{J}} \approx 1.5625 \times 10^{11} \, \text{fissions/s} \]

### Step 4: Round off the answer
Rounding to two decimal places:
\[ \text{Fission rate} \approx 1.56 \times 10^{11} \, \text{fissions/s} \]

### Final Answer
The fission rate of the `._92 U^235` fuelled reactor operating at a power level of `5 W` is approximately \(1.56 \times 10^{11} \, \text{fissions/s}\).

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