A certain electronic transtion from an excited state to the ground state of the hydrogen atom in one or more steps gives rise to four lines in the ultra violet region of the spectrum how many lines does this transition produce in the infra red region ?

Options

A. 1
B. 3
C. 2
D. 4

Answer

To solve the problem of how many lines are produced in the infrared region from a transition that gives rise to four lines in the ultraviolet region of the hydrogen atom, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Series**:
The four lines in the ultraviolet region correspond to the Lyman series, which involves transitions to the ground state (n=1) from higher energy levels (n=2, n=3, n=4, n=5).

2. **Determine the Transitions**:
The transitions that produce the four lines in the ultraviolet region are:
- n=2 to n=1
- n=3 to n=1
- n=4 to n=1
- n=5 to n=1

3. **Identify the Infrared Series**:
The infrared region corresponds to the Paschen series, which involves transitions to n=3 from higher energy levels (n=4, n=5, n=6, etc.).

4. **Calculate the Possible Transitions for Infrared**:
For the Paschen series, the possible transitions from n=4 and n=5 to n=3 are:
- n=4 to n=3
- n=5 to n=3
- n=5 to n=4 (this is not counted in the infrared series as it does not transition to n=3)

5. **Count the Lines**:
The transitions that produce lines in the infrared region from the excited states (n=4 and n=5) to n=3 are:
- n=4 to n=3 → 1 line
- n=5 to n=3 → 1 line
- n=5 to n=4 → 1 line (not counted)

Therefore, the total number of lines produced in the infrared region is:
- n=5 to n=4 (not counted)
- n=5 to n=3 → 1 line
- n=4 to n=3 → 1 line

Total = 2 lines.

6. **Final Answer**:
The total number of lines produced in the infrared region is **3 lines**.

### Summary:
The answer to the question is that the electronic transition from an excited state to the ground state of the hydrogen atom produces **3 lines** in the infrared region.