For a nuclear reactor , 48 KJ of energy is produced per minute. If the energy released per fission is `3.2 xx 10^(-11)` j, then the number of fission which would be taking place in a reactor per second is :

Options

A. `5 xx 10^(14)`
B. `2 xx 10^(14)`
C. `5.2 xx 10^(13)`
D. `2.5 xx 10^(13)`

Explanation

To solve the problem, we need to determine the number of fissions occurring in a nuclear reactor per second, given the energy produced and the energy released per fission.

### Step-by-Step Solution:

1. **Convert Energy Produced Per Minute to Joules Per Second**:
- The energy produced by the reactor is given as 48 kJ per minute.
- Convert kilojoules to joules:
\[ 48 \text{ kJ} = 48 \times 10^3 \text{ J} = 48000 \text{ J} \]
- Since this is per minute, we need to convert it to per second:
\[ \text{Energy produced per second} = \frac{48000 \text{ J}}{60 \text{ s}} = 800 \text{ J/s} = 0.8 \times 10^3 \text{ J/s} \]

2. **Identify Energy Released Per Fission**:
- The energy released per fission is given as \(3.2 \times 10^{-11} \text{ J}\).

3. **Calculate the Number of Fissions Per Second**:
- The number of fissions per second can be calculated using the formula:
\[ \text{Number of fissions per second} = \frac{\text{Energy produced per second}}{\text{Energy released per fission}} \]
- Substituting the values we have:
\[ \text{Number of fissions per second} = \frac{0.8 \times 10^3 \text{ J/s}}{3.2 \times 10^{-11} \text{ J}} \]

4. **Perform the Calculation**:
- First, simplify the division:
\[ = \frac{0.8 \times 10^3}{3.2 \times 10^{-11}} = \frac{0.8}{3.2} \times 10^{3 + 11} \]
- Calculate \(\frac{0.8}{3.2} = 0.25\):
\[ = 0.25 \times 10^{14} = 2.5 \times 10^{13} \]

5. **Final Answer**:
- Therefore, the number of fissions taking place in the reactor per second is:
\[ \boxed{2.5 \times 10^{13}} \]