The energy released during the fission of 1kg of `U^(235)` is a `E_1` and that product during the fusion of 1 kg of hydrogen is `E_2` . If energy released per fission of Uranium - 235 is 200 MeV and that per fusion of hydrogen is 24.7 MeV , then the ratio `E_2/E_1` is

Options

A. 2
B. 7
C. 10
D. 20

Answer

To solve the problem, we need to find the ratio of the energy released during the fusion of 1 kg of hydrogen (E2) to the energy released during the fission of 1 kg of uranium-235 (E1).

### Step-by-Step Solution:

1. **Determine the number of fission reactions (N1) for Uranium-235:**
- The mass of Uranium-235 is given as 1 kg, which is equal to 1000 grams.
- The mass number of Uranium-235 is 235 g/mol.
- The number of fission reactions (N1) can be calculated using the formula:
\[ N1 = \frac{\text{mass of U-235}}{\text{mass number of U-235}} = \frac{1000 \text{ g}}{235 \text{ g/mol}} \approx 4.26 \text{ moles} \]

2. **Determine the number of fusion reactions (N2) for Hydrogen:**
- The fusion of hydrogen involves the fusion of 2 hydrogen nuclei (H) to form 1 helium nucleus (He-4).
- The mass of hydrogen involved in one fusion reaction is approximately 4 grams (2 g for each H atom).
- Therefore, the number of fusion reactions (N2) can be calculated as:
\[ N2 = \frac{\text{mass of H}}{\text{mass for one fusion}} = \frac{1000 \text{ g}}{4 \text{ g}} = 250 \text{ reactions} \]

3. **Calculate the total energy released for each reaction:**
- The energy released per fission of Uranium-235 is given as 200 MeV.
- The total energy released during fission (E1) is:
\[ E1 = N1 \times \text{energy per fission} = 4.26 \times 200 \text{ MeV} = 852 \text{ MeV} \]
- The energy released per fusion of hydrogen is given as 24.7 MeV.
- The total energy released during fusion (E2) is:
\[ E2 = N2 \times \text{energy per fusion} = 250 \times 24.7 \text{ MeV} = 6175 \text{ MeV} \]

4. **Calculate the ratio E2/E1:**
- Now, we can find the ratio of the energies:
\[ \frac{E2}{E1} = \frac{6175 \text{ MeV}}{852 \text{ MeV}} \approx 7.26 \]
- Thus, the ratio \( \frac{E2}{E1} \) is approximately 7.

### Conclusion:
The ratio \( \frac{E2}{E1} \) is approximately 7.