In a collection of H-atoms, all the electrons jump from n=5 to ground level finally ( directly of indirectly) ,without emitting any line in Balmer series. The number of possible different radiations is :

Options

A. (a) 10
B. (b) 8
C. (c) 7
D. (d) 6

Answer

To solve the problem of determining the number of possible different radiations emitted by hydrogen atoms when electrons transition from n=5 to ground level (n=1) without emitting any lines in the Balmer series, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Energy Levels**:
- The hydrogen atom has discrete energy levels denoted by quantum numbers (n=1, 2, 3, 4, 5, ...).
- The ground state is n=1, and the excited state we are considering is n=5.

2. **Identify the Series**:
- Transitions to n=1 correspond to the Lyman series.
- Transitions to n=2 correspond to the Balmer series.
- Transitions to n=3 correspond to the Paschen series.
- Transitions to n=4 correspond to the Brackett series.
- Transitions to n=5 correspond to the Pfund series.

3. **Determine Allowed Transitions**:
- The electrons can transition from n=5 to n=1 directly or through intermediate levels (n=4, n=3, n=2).
- However, since we are instructed that no lines in the Balmer series (n=2) can be emitted, we must avoid any transitions that involve n=2.

4. **List Possible Transitions**:
- Direct transition: n=5 to n=1.
- Indirect transitions:
- n=5 → n=4 → n=1
- n=5 → n=3 → n=1
- n=5 → n=4 → n=3 → n=1

5. **Count the Unique Transitions**:
- From n=5 to n=1: 1 transition.
- From n=5 to n=4 to n=1: 1 transition.
- From n=5 to n=3 to n=1: 1 transition.
- From n=5 to n=4 to n=3 to n=1: 1 transition.
- Total unique transitions: 4.

6. **Conclusion**:
- The total number of possible different radiations emitted by the hydrogen atoms when electrons transition from n=5 to ground level without emitting any lines in the Balmer series is **4**.

### Final Answer:
The number of possible different radiations is **4**.