What is the value of n for which time period is 8 times the time period of electron is first orbit of hydrogen atom ?

Explanation

To solve the problem, we need to find the value of \( n \) for which the time period \( T \) of an electron in the \( n^{th} \) orbit of a hydrogen atom is 8 times the time period of the electron in the first orbit (\( n = 1 \)).

### Step-by-Step Solution:

1. **Understanding the Relationship**:
The time period \( T \) of an electron in an orbit is directly proportional to the cube of the principal quantum number \( n \). This relationship can be expressed as:
\[
T \propto n^3
...