Number of visible lines when an electron returns from 5th orbit to ground state in H spectrum :

Options

A. 5
B. 4
C. 3
D. 10

Answer

To determine the number of visible lines when an electron returns from the 5th orbit to the ground state in the hydrogen spectrum, we can follow these steps:

### Step 1: Understand the Energy Levels
In a hydrogen atom, the energy levels are quantized and are represented by the principal quantum number \( n \). The levels are as follows:
- Ground state: \( n = 1 \)
- First excited state: \( n = 2 \)
- Second excited state: \( n = 3 \)
- Third excited state: \( n = 4 \)
- Fourth excited state: \( n = 5 \)

### Step 2: Identify the Series
When an electron transitions between energy levels, it emits or absorbs light. The transitions from higher energy levels to lower ones can be categorized into series:
- Lyman series: Transitions to \( n = 1 \) (ultraviolet region)
- Balmer series: Transitions to \( n = 2 \) (visible region)
- Paschen series: Transitions to \( n = 3 \) (infrared region)

Since we are interested in the visible lines, we will focus on the Balmer series.

### Step 3: Determine Possible Transitions
When an electron drops from the 5th orbit (\( n = 5 \)) to the ground state (\( n = 1 \)), it can go through several intermediate states. The possible transitions from \( n = 5 \) to lower energy levels are:
1. \( n = 5 \) to \( n = 4 \)
2. \( n = 5 \) to \( n = 3 \)
3. \( n = 5 \) to \( n = 2 \)

From \( n = 4 \), \( n = 3 \), and \( n = 2 \), the electron can further transition down to the ground state \( n = 1 \):
- From \( n = 4 \) to \( n = 1 \) (Lyman series)
- From \( n = 3 \) to \( n = 1 \) (Lyman series)
- From \( n = 2 \) to \( n = 1 \) (Lyman series)

### Step 4: Identify Visible Lines
However, for visible lines, we only consider transitions that end at \( n = 2 \):
- \( n = 5 \) to \( n = 2 \)
- \( n = 4 \) to \( n = 2 \)
- \( n = 3 \) to \( n = 2 \)

These transitions correspond to the Balmer series, which produces visible light.

### Step 5: Count the Visible Lines
The transitions that result in visible lines from \( n = 5 \) to \( n = 2 \) involve:
1. \( n = 5 \) to \( n = 2 \)
2. \( n = 4 \) to \( n = 2 \)
3. \( n = 3 \) to \( n = 2 \)

Thus, there are a total of **3 visible lines** when the electron returns from the 5th orbit to the ground state.

### Final Answer
The number of visible lines when an electron returns from the 5th orbit to the ground state in the hydrogen spectrum is **3**.

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