The energy required for the ionisation of excited hydrogen atom would be (in eV)

Options

A. `lt 13.6`
B. `gt 13.6`
C. `13.6`
D. none of these

Explanation

To find the energy required for the ionization of an excited hydrogen atom, we can use the formula for the energy levels of hydrogen:

\[ E_n = -\frac{13.6 \, \text{eV}}{n^2} \]

where:
- \( E_n \) is the energy of the electron in the nth energy level,
- \( n \) is the principal quantum number,
- \( 13.6 \, \text{eV} \) is the ionization energy of hydrogen from the ground state (n=1).

### Step 1: Identify the excited state
For a hydrogen atom in an excited state, we need to determine the value of \( n \). The first excited state corresponds to \( n = 2 \) and the second excited state corresponds to \( n = 3 \).

### Step 2: Calculate the energy for \( n = 2 \)
Using the formula for \( n = 2 \):

\[ E_2 = -\frac{13.6 \, \text{eV}}{2^2} = -\frac{13.6 \, \text{eV}}{4} = -3.4 \, \text{eV} \]

### Step 3: Calculate the energy for \( n = 3 \)
Using the formula for \( n = 3 \):

\[ E_3 = -\frac{13.6 \, \text{eV}}{3^2} = -\frac{13.6 \, \text{eV}}{9} \approx -1.51 \, \text{eV} \]

### Step 4: Determine the ionization energy
The ionization energy is the energy required to remove the electron completely from the atom, which is the absolute value of the energy calculated for the excited states.

For \( n = 2 \):

\[ \text{Ionization energy from } n = 2 = |E_2| = 3.4 \, \text{eV} \]

For \( n = 3 \):

\[ \text{Ionization energy from } n = 3 = |E_3| = 1.51 \, \text{eV} \]

### Conclusion
The energy required for the ionization of an excited hydrogen atom would be less than 13.6 eV, specifically:

- For \( n = 2 \): 3.4 eV
- For \( n = 3 \): 1.51 eV

Thus, the energy required for the ionization of an excited hydrogen atom can be either 3.4 eV or 1.51 eV depending on the excited state.