Consider the following energies :-
1. minimum energy needed to excite a hydrogen atom
2. energy needed to ionize a hydrogen atom
3. energy released in `.^(235)U` fission
4. energy released to remove a neutron from a `.^(12)C` nucleus
Rank them in order of increasing value.

Options

A. A.`1,2,3,4`
B. B.`1,3,2,4`
C. C.`1,2,4,3`
D. D.`2,1,4,3`

Answer

To rank the energies in order of increasing value, we need to first identify the numerical values associated with each energy type mentioned in the question. Here’s a step-by-step breakdown:

### Step 1: Identify the energies
1. **Minimum energy needed to excite a hydrogen atom (E1)**: This is approximately **10.2 eV**.
2. **Energy needed to ionize a hydrogen atom (E2)**: This is approximately **13.6 eV**.
3. **Energy released in the fission of Uranium-235 (E3)**: This is approximately **200 MeV** (which is equal to 200,000,000 eV).
4. **Energy released to remove a neutron from a Carbon-12 nucleus (E4)**: This is approximately **92.5 MeV** (which is equal to 92,500,000 eV).

### Step 2: Convert all energies to the same unit
To compare the energies easily, we can convert all values to electron volts (eV):
- E1 = 10.2 eV
- E2 = 13.6 eV
- E3 = 200 MeV = 200,000,000 eV
- E4 = 92.5 MeV = 92,500,000 eV

### Step 3: Rank the energies
Now that we have all the energies in eV, we can rank them in increasing order:
1. **E1**: 10.2 eV (minimum energy needed to excite a hydrogen atom)
2. **E2**: 13.6 eV (energy needed to ionize a hydrogen atom)
3. **E4**: 92,500,000 eV (energy released to remove a neutron from a Carbon-12 nucleus)
4. **E3**: 200,000,000 eV (energy released in the fission of Uranium-235)

### Final Ranking
Thus, the order of increasing energy values is:
**E1 < E2 < E4 < E3**

### Conclusion
The final ranking of the energies in order of increasing value is:
1. Minimum energy needed to excite a hydrogen atom (10.2 eV)
2. Energy needed to ionize a hydrogen atom (13.6 eV)
3. Energy released to remove a neutron from a Carbon-12 nucleus (92.5 MeV)
4. Energy released in Uranium-235 fission (200 MeV)