In Bohr's model of hydrogen atom, the period of revolution of an electron in the 1st orbit to that in the 2nd orbit are in the ratio

Options

A. `1 : 2`
B. `2 : 1`
C. `1 : 4`
D. `1 : 8`

Explanation

To find the ratio of the period of revolution of an electron in the first orbit to that in the second orbit according to Bohr's model of the hydrogen atom, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept**: According to Bohr's model, the period of revolution (T) of an electron in an orbit is directly proportional to the cube of the principal quantum number (n) of that orbit. This can be expressed as:
\[ T \propto n^3 \]

2. **Identify the Orbits**: We need to find the periods for the first orbit (n=1) and the second orbit (n=2).

3. **Write the Expression for Periods**:
- For the first orbit (n=1):
\[ T_1 \propto 1^3 = 1 \]
- For the second orbit (n=2):
\[ T_2 \propto 2^3 = 8 \]

4. **Set Up the Ratio**: Now, we can set up the ratio of the periods:
\[ \frac{T_1}{T_2} = \frac{1}{8} \]

5. **Express the Ratio in Standard Form**: The ratio can be expressed as:
\[ T_1 : T_2 = 1 : 8 \]

### Final Answer:
The ratio of the period of revolution of an electron in the first orbit to that in the second orbit is:
\[ 1 : 8 \]