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

Answer

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

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

### Step 3: Calculate the Energy for the 3rd Orbit
To find the energy for the 3rd orbit (n=3):
\[ E_3 = -\frac{13.6 \, \text{eV}}{3^2} = -\frac{13.6 \, \text{eV}}{9} = -1.51 \, \text{eV} \]

### Step 4: Calculate the Energy for the 4th Orbit
Now, calculate the energy for the 4th orbit (n=4):
\[ E_4 = -\frac{13.6 \, \text{eV}}{4^2} = -\frac{13.6 \, \text{eV}}{16} = -0.85 \, \text{eV} \]

### Step 5: Find the Energy Transition
The energy corresponding to the transition from the 3rd orbit to the 4th orbit is given by:
\[ \Delta E = E_4 - E_3 \]
Substituting the values we calculated:
\[ \Delta E = (-0.85 \, \text{eV}) - (-1.51 \, \text{eV}) = -0.85 + 1.51 = 0.66 \, \text{eV} \]

### Final Answer
The energy corresponding to the transition between the 3rd and the 4th orbit is \( 0.66 \, \text{eV} \).

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