The ionisation energy of hydrogen atom is `13.6 eV`. Following Bohr's theory, the energy corresponding to a transition between the `3`rd and the `4`th orbit is

Options

A. `3.40 eV`
B. `1.51 eV`
C. `0.85 eV`
D. `0.66 eV`

Explanation

To find the energy corresponding to a transition between the 3rd and the 4th orbit of a hydrogen atom using Bohr's theory, we can follow these steps:

### Step-by-Step Solution

1. **Understand the Ionization Energy**: The ionization energy of a hydrogen atom is given as \( 13.6 \, \text{eV} \). This is the energy required to remove the electron from the ground state (n=1) to infinity.

2. **Energy Level Formula**: According to Bohr's theory, the energy of an electron in the nth orbit of a hydrogen atom is given by the formula:
\[ E_n = -\frac{13.6 \, \text{eV}}{n^2} \]

3. **Calculate the Energy for n=3**:
\[ E_3 = -\frac{13.6 \, \text{eV}}{3^2} = -\frac{13.6 \, \text{eV}}{9} = -1.51 \, \text{eV} \]

4. **Calculate the Energy for n=4**:
\[ E_4 = -\frac{13.6 \, \text{eV}}{4^2} = -\frac{13.6 \, \text{eV}}{16} = -0.85 \, \text{eV} \]

5. **Find the Energy Difference**: The energy corresponding to the transition from the 4th orbit to the 3rd orbit (E4 to E3) is calculated by finding the difference:
\[ \Delta E = E_4 - E_3 = (-0.85 \, \text{eV}) - (-1.51 \, \text{eV}) = -0.85 + 1.51 = 0.66 \, \text{eV} \]

6. **Conclusion**: The energy corresponding to the transition between the 3rd and the 4th orbit is \( 0.66 \, \text{eV} \).