In a sample of `H-` atom electrons make transition from `5^(th)` excited state to ground state, producing all possible types of photons, then number of lines in infrared region are

Options

A. 4
B. 5
C. 6
D. 3

Explanation

To solve the problem, we need to determine the number of spectral lines produced when electrons in a hydrogen atom transition from the 5th excited state to the ground state, specifically focusing on the transitions that result in photons in the infrared region.

### Step-by-Step Solution:

1. **Identify the Excited State:**
The 5th excited state corresponds to the principal quantum number \( n = 6 \) (since the ground state is \( n = 1 \), the first excited state is \( n = 2 \), and so forth).

2. **Determine Possible Transitions:**
From \( n = 6 \), electrons can transition to lower energy levels (ground state and excited states). The possible transitions are:
- From \( n = 6 \) to \( n = 1 \) (Lyman series, UV region)
- From \( n = 6 \) to \( n = 2 \) (Balmer series, visible region)
- From \( n = 6 \) to \( n = 3 \) (Paschen series, infrared region)
- From \( n = 6 \) to \( n = 4 \) (Brackett series, infrared region)
- From \( n = 6 \) to \( n = 5 \) (Pfund series, infrared region)

3. **List the Transitions for Each Series:**
- **Lyman Series (UV):** \( 6 \to 1 \)
- **Balmer Series (Visible):** \( 6 \to 2 \)
- **Paschen Series (Infrared):** \( 6 \to 3 \)
- **Brackett Series (Infrared):** \( 6 \to 4 \)
- **Pfund Series (Infrared):** \( 6 \to 5 \)

4. **Count the Infrared Transitions:**
The transitions that produce photons in the infrared region are:
- \( 6 \to 3 \)
- \( 6 \to 4 \)
- \( 6 \to 5 \)

Additionally, we can also consider transitions from lower excited states:
- From \( n = 5 \): \( 5 \to 3 \), \( 5 \to 4 \), \( 5 \to 2 \) (not in infrared)
- From \( n = 4 \): \( 4 \to 3 \) (not in infrared)

Therefore, the relevant transitions in the infrared region are:
- \( 6 \to 3 \)
- \( 6 \to 4 \)
- \( 6 \to 5 \)
- \( 5 \to 4 \)
- \( 5 \to 3 \)
- \( 4 \to 3 \)

5. **Total Count of Infrared Lines:**
The total number of transitions that produce lines in the infrared region is:
- \( 6 \to 3 \)
- \( 6 \to 4 \)
- \( 6 \to 5 \)
- \( 5 \to 4 \)
- \( 5 \to 3 \)
- \( 4 \to 3 \)

This gives us a total of **6 transitions** that result in infrared lines.

### Final Answer:
The number of lines in the infrared region is **6**.