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

Explanation

To find the energy required to remove an electron from the n = 2 state of a hydrogen atom, we can follow these steps:

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

### Step 2: Use the Energy Level Formula
The energy of an electron in a hydrogen atom at a specific energy level (n) can be calculated using the formula:
\[ E_n = -\frac{13.6 \, \text{eV}}{n^2} \]
where \(E_n\) is the energy at level n.

### Step 3: Calculate the Energy for n = 2
Substituting \(n = 2\) into the formula:
\[ E_2 = -\frac{13.6 \, \text{eV}}{2^2} = -\frac{13.6 \, \text{eV}}{4} = -3.4 \, \text{eV} \]

### Step 4: Determine the Energy Required for Ionization
To find the energy required to remove the electron from the n = 2 state, we need to consider that we are moving from a negative energy state to zero energy (free electron). Therefore, the energy required is the positive value of \(E_2\):
\[ \text{Energy required} = -E_2 = -(-3.4 \, \text{eV}) = 3.4 \, \text{eV} \]

### Final Answer
The energy required to remove an electron in the n = 2 state of the hydrogen atom is **3.4 eV**.

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