The ionisation potential of hydrogen atom is `13.6` volt. The energy required to remove an electron in the `n = 2` state of the hydrogen atom is

Options

A. 27.2 eV
B. 13.6 eV
C. 6.8 eV
D. 3.4 eV

Answer

To find the energy required to remove an electron from the n = 2 state of a hydrogen atom, we can use the formula for the energy levels of the hydrogen atom:

### Step-by-Step Solution:

1. **Understand the Ionization Potential**:
The ionization potential of hydrogen is given as 13.6 eV. This is the energy required to remove an electron from the ground state (n = 1) of the hydrogen atom.

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

3. **Substitute n = 2**:
We need to find the energy for the n = 2 state. Substitute \( n = 2 \) into the formula:
\[ E_2 = -\frac{13.6 \, \text{eV}}{2^2} = -\frac{13.6 \, \text{eV}}{4} \]

4. **Calculate the Energy**:
Now calculate the value:
\[ E_2 = -\frac{13.6}{4} = -3.4 \, \text{eV} \]

5. **Interpret the Result**:
The negative sign indicates that the electron is bound to the atom. To remove the electron from this state, we need to provide energy equal to the absolute value of this energy:
\[ \text{Energy required} = 3.4 \, \text{eV} \]

6. **Final Answer**:
Therefore, the energy required to remove an electron from the n = 2 state of the hydrogen atom is 3.4 eV.