The period of revolution of the electron in the third orbit in a hydrogen atom is `4.132 xx 10^(-15) s`. Hence find the period in the 5th Bohr orbit.

Answer

To find the period of revolution of the electron in the 5th Bohr orbit of a hydrogen atom, we can use the relationship between the periods of revolution in different orbits.

### Step-by-Step Solution:

1. **Understanding the Relationship**: The period of revolution (T) of an electron in the nth orbit of a hydrogen atom is proportional to the square of the principal quantum number (n). Mathematically, this can be expressed as:
\[ T_n \propto n^2 \]
This means that:
\[ \frac{T_n}{T_m} = \frac{n^2}{m^2} \]
where \(T_n\) is the period in the nth orbit and \(T_m\) is the period in the mth orbit.

2. **Given Data**: We know that the period of revolution in the 3rd orbit (T3) is given as:
\[ T_3 = 4.132 \times 10^{-15} \text{ s} \]

3. **Finding the Ratio of Periods**: We want to find the period in the 5th orbit (T5). Using the relationship derived above:
\[ \frac{T_5}{T_3} = \frac{5^2}{3^2} = \frac{25}{9} \]

4. **Calculating T5**: Rearranging the equation gives:
\[ T_5 = T_3 \times \frac{25}{9} \]
Now substituting the value of \(T_3\):
\[ T_5 = 4.132 \times 10^{-15} \times \frac{25}{9} \]

5. **Performing the Calculation**:
\[ T_5 = 4.132 \times 10^{-15} \times 2.7778 \approx 11.47 \times 10^{-15} \text{ s} \]

6. **Final Answer**: Thus, the period of revolution of the electron in the 5th Bohr orbit is approximately:
\[ T_5 \approx 11.47 \times 10^{-15} \text{ s} \]