Energy of the electron in `nth` orbit of hydrogen atom is given by `E_(n) =-(13.6)/(n^(2))eV`. The amount of energy needed to transfer electron from first orbit to third orbit is

Options

A. 10.2 J
B. 12.09 J
C. 12.09 eV
D. 13.6 eV

Answer

To find the amount of energy needed to transfer an electron from the first orbit to the third orbit in a hydrogen atom, we can follow these steps:

### Step 1: Write the formula for energy in the nth orbit
The energy of the electron in the nth orbit of a hydrogen atom is given by the formula:
\[ E_n = -\frac{13.6}{n^2} \text{ eV} \]

### Step 2: Calculate the energy of the first orbit (n=1)
Substituting \( n = 1 \) into the formula:
\[ E_1 = -\frac{13.6}{1^2} = -13.6 \text{ eV} \]

### Step 3: Calculate the energy of the third orbit (n=3)
Substituting \( n = 3 \) into the formula:
\[ E_3 = -\frac{13.6}{3^2} = -\frac{13.6}{9} \approx -1.51 \text{ eV} \]

### Step 4: Calculate the energy required to transfer from the first orbit to the third orbit
The energy required to move the electron from the first orbit to the third orbit is given by the difference in energy between these two states:
\[ \Delta E = E_3 - E_1 \]
Substituting the values we calculated:
\[ \Delta E = (-1.51) - (-13.6) = -1.51 + 13.6 = 12.09 \text{ eV} \]

### Conclusion
The amount of energy needed to transfer the electron from the first orbit to the third orbit is approximately:
\[ \Delta E \approx 12.09 \text{ eV} \]