Consider the following energies
(1) The minimum energy needed to excite a hydrogen atom from its ground state `-E_(1)`
(2) Energy needed to ionze a hydrogen atom from ground state `=E_(2)`
(3) Energy released in `overset(235).U-"fission "=E_(3)`
(4) Energy needed to remove a neutron from a `overset(12).C_("cucleus")=E_(4)`

Options

A. `E_(1)ltE_(2)ltE_(3)ltE_(4)`
B. `E_(1)ltE_(3)ltE_(2)ltE_(4)`
C. `E_(1)ltE_(2)ltE_(4)ltE_(3)`
D. `E_(2)ltE_(1)ltE_(4)ltE_(3)`

Answer

To solve the problem, we need to compare the energies associated with different processes involving hydrogen and nuclear reactions. We will analyze each energy value and then establish their relationships.

### Step-by-Step Solution:

1. **Identify the energies:**
- **E1:** Minimum energy needed to excite a hydrogen atom from its ground state.
- **E2:** Energy needed to ionize a hydrogen atom from its ground state.
- **E3:** Energy released in the fission of Uranium-235.
- **E4:** Energy needed to remove a neutron from a carbon-12 nucleus.

2. **Find the values of each energy:**
- **E1 (Excitation energy for hydrogen):** The minimum energy required to excite a hydrogen atom from its ground state is approximately **10.2 eV**.
- **E2 (Ionization energy for hydrogen):** The energy needed to ionize a hydrogen atom from its ground state is approximately **13.6 eV**.
- **E3 (Energy released in U-235 fission):** The energy released during the fission of Uranium-235 is approximately **200 MeV** (which is equivalent to **200,000 eV**).
- **E4 (Energy to remove a neutron from carbon-12):** The energy needed to remove a neutron from the carbon-12 nucleus is approximately **92.15 MeV** (which is equivalent to **92,150 eV**).

3. **Compare the energies:**
- From our values, we can see:
- **E1 = 10.2 eV**
- **E2 = 13.6 eV**
- **E3 = 200,000 eV**
- **E4 = 92,150 eV**
- Now, we can arrange these values in increasing order:
- E1 < E2 < E4 < E3

4. **Conclusion:**
- The correct relationship among the energies is:
- **E1 < E2 < E4 < E3**
- Therefore, the correct option is **C**.