Hydrogen atoms are excited on n=4 state. In the spectrum of emitted radiation, number of lines in the ultraviolet and visible regions are respectively-

Options

A. `3 : 1`
B. `1 : 3`
C. `2 : 3`
D. `3 : 2`

Answer

To solve the problem of determining the number of spectral lines emitted by hydrogen atoms excited to the n=4 state in the ultraviolet and visible regions, we can follow these steps:

### Step 1: Understand the Series
The hydrogen spectrum consists of different series based on the principal quantum number (n):
- **Lyman series** (Ultraviolet region): Transitions to n=1
- **Balmer series** (Visible region): Transitions to n=2
- **Paschen series** (Infrared region): Transitions to n=3

### Step 2: Calculate Lines in the Ultraviolet Region
For the ultraviolet region, we will consider the Lyman series. The number of spectral lines can be calculated using the formula:
\[ \text{Number of lines} = n_2 - r \]
where \( n_2 \) is the excited state (n=4) and \( r \) is the final state (for Lyman series, \( r=1 \)).

Substituting the values:
\[ \text{Number of lines in UV} = 4 - 1 = 3 \]

### Step 3: Calculate Lines in the Visible Region
For the visible region, we will consider the Balmer series. Using the same formula:
\[ \text{Number of lines} = n_2 - r \]
where \( n_2 \) is still 4 and \( r \) for the Balmer series is 2.

Substituting the values:
\[ \text{Number of lines in Visible} = 4 - 2 = 2 \]

### Step 4: Conclusion
The number of spectral lines in the ultraviolet region is 3, and in the visible region, it is 2. Therefore, the answer is:
- Ultraviolet lines: 3
- Visible lines: 2

### Final Answer
The number of lines in the ultraviolet and visible regions are respectively **3 and 2**.

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