If 13.6 eV energy is required to ionise the hydrogen atom, then energy required to remove an electron from `n=3` is :

Options

A. 9 eV
B. 6.8 eV
C. 3.4 eV
D. 1.5 eV

Answer

To find the energy required to remove an electron from the n=3 level of a hydrogen atom, we can use the formula for the energy levels of the hydrogen atom. The energy required to ionize a hydrogen atom from the ground state (n=1) is given as 13.6 eV.

### Step-by-Step Solution:

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

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

3. **Perform the Calculation**:
Now, calculate \( E_3 \):
\[ E_3 = -\frac{13.6}{9} \approx -1.511 \, \text{eV} \]

4. **Determine the Energy Required to Remove the Electron**:
The energy required to remove the electron from the n=3 level (which is equivalent to ionization from that level) is the positive value of \( E_3 \):
\[ \text{Energy required} = 1.511 \, \text{eV} \approx 1.5 \, \text{eV} \]

5. **Select the Correct Option**:
From the options provided, the closest value is:
- 1.5 eV

### Final Answer:
The energy required to remove an electron from \( n=3 \) is approximately **1.5 eV**.

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