The ionization potential of H atoms is 13.6 V. The energy difference between n = 2 and n = 3 levels is nearest to

Answer

To find the energy difference between the n = 2 and n = 3 levels of a hydrogen atom, we can use the formula for the energy levels of hydrogen:

1. **Energy Level Formula**: The energy of an electron in the nth level of a hydrogen atom is given by the formula:
\[ E_n = -\frac{13.6 \text{ eV}}{n^2} \]

2. **Calculate Energy for n = 2**:
- For n = 2:
\[ E_2 = -\frac{13.6 \text{ eV}}{2^2} = -\frac{13.6 \text{ eV}}{4} = -3.4 \text{ eV} \]

3. **Calculate Energy for n = 3**:
- For n = 3:
\[ E_3 = -\frac{13.6 \text{ eV}}{3^2} = -\frac{13.6 \text{ eV}}{9} \approx -1.51 \text{ eV} \]

4. **Calculate Energy Difference**:
- The energy difference between the n = 2 and n = 3 levels is given by:
\[ \Delta E = E_3 - E_2 \]
- Substituting the values we calculated:
\[ \Delta E = -1.51 \text{ eV} - (-3.4 \text{ eV}) = -1.51 \text{ eV} + 3.4 \text{ eV} = 1.89 \text{ eV} \]

5. **Final Result**:
- The energy difference between the n = 2 and n = 3 levels is approximately **1.89 eV**, which is nearest to **2 eV**.