15 eV is given to `e^(-)` in `4^("th")` orbit then find it's final energy when it comes out of H-atom

Options

A. 14.14 eV
B. 13.6 eV
C. 12.08 eV
D. 15.85

Explanation

To solve the problem step by step, we need to find the final energy of an electron when it comes out of a hydrogen atom after being given 15 eV in the fourth orbit.

### Step 1: Determine the energy of the electron in the fourth orbit.
The energy of an electron in a hydrogen atom in the nth orbit is given by the formula:

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

For the fourth orbit (n = 4):

\[ E_4 = -\frac{13.6 \, \text{eV}}{4^2} = -\frac{13.6 \, \text{eV}}{16} = -0.85 \, \text{eV} \]

### Step 2: Calculate the ionization energy from the fourth orbit.
The ionization energy is the energy required to remove the electron from the fourth orbit to infinity (where the energy is 0 eV). The ionization energy from the fourth orbit is the absolute value of the energy of the fourth orbit:

\[ \text{Ionization Energy} = -E_4 = 0.85 \, \text{eV} \]

### Step 3: Calculate the total energy of the electron after receiving 15 eV.
The electron initially has 15 eV of energy. When it is in the fourth orbit, its total energy is:

\[ \text{Total Energy} = \text{Initial Energy} - \text{Ionization Energy} \]

Substituting the values:

\[ \text{Total Energy} = 15 \, \text{eV} - 0.85 \, \text{eV} = 14.15 \, \text{eV} \]

### Step 4: Conclusion
The final energy of the electron when it comes out of the hydrogen atom is:

\[ \text{Final Energy} = 14.15 \, \text{eV} \]