200 Mev energy is released when one nucleus of `.^235U` undergoes fission. Find the number of fissions per second required for producing a power of 1 mega watt.

Options

A. `3.125xx10^14`
B. `3.125xx10^15`
C. `3.125xx10^16`
D. `3.125xx10^13`

Answer

To solve the problem of finding the number of fissions per second required to produce a power of 1 megawatt from the fission of uranium-235, we can follow these steps:

### Step 1: Understand the energy released per fission
The energy released when one nucleus of uranium-235 undergoes fission is given as 200 MeV.

### Step 2: Convert MeV to Joules
We need to convert the energy from MeV to Joules to work with the power in watts (1 watt = 1 joule/second).

1 MeV = \(1.6 \times 10^{-13}\) Joules, so:
\[ 200 \text{ MeV} = 200 \times 1.6 \times 10^{-13} \text{ Joules} = 3.2 \times 10^{-11} \text{ Joules} \]

### Step 3: Determine the power in Joules per second
The power we want to achieve is 1 megawatt, which is:
\[ 1 \text{ MW} = 1 \times 10^6 \text{ watts} = 1 \times 10^6 \text{ joules/second} \]

### Step 4: Calculate the number of fissions required per second
To find the number of fissions required per second, we divide the total power (in joules/second) by the energy released per fission (in joules):
\[ \text{Number of fissions per second} = \frac{\text{Power}}{\text{Energy per fission}} = \frac{1 \times 10^6 \text{ J/s}}{3.2 \times 10^{-11} \text{ J}} \]

### Step 5: Perform the calculation
Calculating the above expression:
\[ \text{Number of fissions per second} = \frac{1 \times 10^6}{3.2 \times 10^{-11}} = 3.125 \times 10^{16} \]

### Conclusion
The number of fissions per second required to produce a power of 1 megawatt is:
\[ \boxed{3.125 \times 10^{16}} \]