If `13.6 eV` energy is required to ionized the hydrogen atom then the energy required to ionize the hydrogen atom , then the energy required to remove an electron from `n = 2 ` is

Options

A. `10.2 eV`
B. `0 eV`
C. `3.4 eV`
D. `6.8 eV`

Explanation

To find the energy required to remove an electron from the n = 2 level of a hydrogen atom, we can use the formula for the energy of an electron in a hydrogen atom, which is given by:

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

where \( E_n \) is the energy of the electron at the principal quantum number \( n \).

### Step-by-Step Solution:

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

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

3. **Calculate \( 2^2 \)**: Calculate the square of 2:
\[ 2^2 = 4 \]

4. **Plug in the value**: Substitute \( 4 \) back into the equation:
\[ E_2 = -\frac{13.6 \, \text{eV}}{4} \]

5. **Perform the division**: Now, divide \( 13.6 \) by \( 4 \):
\[ E_2 = -3.4 \, \text{eV} \]

6. **Interpret the result**: The negative sign indicates that this is the energy required to remove the electron from the n = 2 level to the point where it is free (ionization). Therefore, the energy required to remove the electron from n = 2 is:
\[ \text{Energy required} = 3.4 \, \text{eV} \]

### Final Answer:
The energy required to remove an electron from \( n = 2 \) is **3.4 eV**.

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