12 eV energy is given to electron in third orbit of H-atom, then final energy of electron when it ionise from third orbit, is

Options

A. 5.25 eV
B. 10.49 eV
C. 12 eV
D. 11.15 eV

Explanation

To solve the problem step by step, we need to determine the final energy of an electron in the third orbit of a hydrogen atom after it has been given an additional energy of 12 eV and then ionized.

### Step 1: Calculate the energy of the electron in the third orbit.
The formula for the total energy of an electron in the nth orbit of a hydrogen atom is given by:

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

For the third orbit (n = 3):

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

### Step 2: Calculate the total energy after adding 12 eV.
The total energy after adding the 12 eV to the energy of the electron in the third orbit is:

\[ E_{\text{total}} = E_3 + 12 \, \text{eV} = -1.51 \, \text{eV} + 12 \, \text{eV} = 10.49 \, \text{eV} \]

### Step 3: Determine the ionization energy.
The ionization energy for a hydrogen atom is the energy required to remove the electron completely from the atom, which is equal to the absolute value of the total energy in the ground state (n = 1). For hydrogen, this value is:

\[ E_{\text{ionization}} = 13.6 \, \text{eV} \]

### Step 4: Calculate the final energy after ionization.
When the electron is ionized, it will have energy equal to the total energy minus the ionization energy:

\[ E_{\text{final}} = E_{\text{total}} - E_{\text{ionization}} = 10.49 \, \text{eV} - 13.6 \, \text{eV} \]

Since the electron is ionized, the final energy will be:

\[ E_{\text{final}} = 10.49 \, \text{eV} - 13.6 \, \text{eV} = -3.11 \, \text{eV} \]

However, since we are interested in the energy of the electron after ionization, the final energy will be 0 eV (the electron is free).

### Final Answer:
The final energy of the electron after ionization is **0 eV**.