If 200 MeV of energy is released in the fission of one nucleus of `._92U^235`, The number of nuclei that must undergo fission to produce energy of 1000J in 1 sec is

Options

A. `3.125xx10^13`
B. `6.25xx10^13`
C. `12.5xx10^13`
D. `3.125xx10^14`

Answer

To solve the problem, we need to determine how many nuclei of Uranium-235 must undergo fission to produce 1000 Joules of energy in one second, given that each fission releases 200 MeV of energy.

### Step-by-Step Solution:

1. **Convert Energy from MeV to Joules**:
The energy released per fission of one Uranium-235 nucleus is given as 200 MeV. We need to convert this energy into Joules.
\[ \text{Energy per fission} = 200 \text{ MeV} \times 10^6 \text{ eV/MeV} \times 1.6 \times 10^{-19} \text{ J/eV} \]
\[ = 200 \times 10^6 \times 1.6 \times 10^{-19} \text{ J} \]
\[ = 3.2 \times 10^{-11} \text{ J} \]

2. **Calculate the Total Energy Required per Second**:
We need to produce 1000 Joules of energy in one second. This is equivalent to a power of 1000 Watts (since power is energy per time).

3. **Determine the Number of Nuclei Required**:
To find the number of fissions (nuclei) required to produce 1000 Joules, we divide the total energy required by the energy released per fission:
\[ \text{Number of nuclei} = \frac{\text{Total Energy Required}}{\text{Energy per fission}} \]
\[ = \frac{1000 \text{ J}}{3.2 \times 10^{-11} \text{ J}} \]
\[ = 3.125 \times 10^{13} \]

4. **Conclusion**:
The number of Uranium-235 nuclei that must undergo fission to produce 1000 Joules of energy in one second is approximately \(3.125 \times 10^{13}\).

### Final Answer:
The number of nuclei that must undergo fission is \(3.125 \times 10^{13}\).