The period of revolution of an electron in the ground state of hydrogen atom is T. The period of revolution of the electron in the first excited state is

Options

A. 2T
B. 4T
C. 6T
D. 8T

Answer

To find the period of revolution of the electron in the first excited state of the hydrogen atom, we can follow these steps:

### Step 1: Understand the relationship between time period and quantum numbers
The time period \( T \) of an electron in a hydrogen atom is related to the principal quantum number \( n \). The formula for the time period \( T \) is proportional to \( n^3 \):
\[ T \propto n^3 \]

### Step 2: Define the periods for the ground state and first excited state
In the ground state, the principal quantum number \( n \) is 1, and we denote the time period as \( T \):
\[ T = k \cdot 1^3 = k \]
where \( k \) is a constant.

In the first excited state, the principal quantum number \( n \) is 2. Therefore, the time period \( T' \) for the first excited state is:
\[ T' = k \cdot 2^3 = k \cdot 8 \]

### Step 3: Relate the two periods
Since we have established that \( T = k \), we can express \( T' \) in terms of \( T \):
\[ T' = 8T \]

### Conclusion
Thus, the period of revolution of the electron in the first excited state is:
\[ T' = 8T \]