If the energy released in the fission of the nucleus is `200 MeV`. Then the number of nuclei required per second in a power plant of `16 kW` will be.

Options

A. `0.5xx10^(14)`
B. `0.5XX10^(12)`
C. `5xx10^(12)`
D. `5xx10^(14)`

Answer

To solve the problem of finding the number of nuclei required per second in a power plant that produces 16 kW of power, given that the energy released in the fission of one nucleus is 200 MeV, we can follow these steps:

### Step 1: Convert Energy from MeV to Joules
The energy released in the fission of one nucleus is given as 200 MeV. We need to convert this energy into joules.

\[ \text{Energy (in Joules)} = 200 \, \text{MeV} \times 1.6 \times 10^{-19} \, \text{J/MeV} \]

Calculating this gives:

\[ \text{Energy} = 200 \times 1.6 \times 10^{-19} = 3.2 \times 10^{-17} \, \text{J} \]

### Step 2: Determine the Power in Watts
The power of the plant is given as 16 kW. We convert this into watts:

\[ \text{Power} = 16 \, \text{kW} = 16 \times 10^{3} \, \text{W} \]

### Step 3: Calculate Energy Required per Second
Since power is defined as energy per unit time, the energy required by the plant per second is equal to the power:

\[ \text{Energy required per second} = 16 \times 10^{3} \, \text{J/s} \]

### Step 4: Relate Energy Required to Number of Fissions
Let \( n \) be the number of fissions (or nuclei required) per second. The total energy produced by \( n \) fissions is given by:

\[ \text{Total Energy} = n \times \text{Energy per fission} \]

Setting this equal to the energy required per second:

\[ n \times 3.2 \times 10^{-17} = 16 \times 10^{3} \]

### Step 5: Solve for \( n \)
Now, we can solve for \( n \):

\[ n = \frac{16 \times 10^{3}}{3.2 \times 10^{-17}} \]

Calculating this gives:

\[ n = \frac{16 \times 10^{3}}{3.2 \times 10^{-17}} = 5 \times 10^{14} \]

### Conclusion
Thus, the number of nuclei required per second in the power plant is:

\[ \boxed{5 \times 10^{14}} \]

---