Number of spectral lines in Balmer series when an electron retrurn from `7 ^(th )` orbit to` 1 ^(st)` orbit of hydrogen atom are

Options

A. 5
B. 6
C. 21
D. 15

Answer

To determine the number of spectral lines in the Balmer series when an electron transitions from the 7th orbit to the 1st orbit of a hydrogen atom, we can follow these steps:

### Step 1: Understand the Balmer Series
The Balmer series consists of spectral lines that result from electron transitions from higher energy levels (n ≥ 3) to the second energy level (n = 2) of the hydrogen atom.

**Hint:** Remember that in the Balmer series, the lower energy level (n1) is always 2.

### Step 2: Identify the Initial and Final Energy Levels
In this case, the electron is transitioning from the 7th orbit (n2 = 7) to the 1st orbit (n1 = 1). However, since we are interested in the Balmer series, we will only consider transitions that end at n = 2.

**Hint:** For the Balmer series, n1 is fixed at 2, regardless of the initial level.

### Step 3: Calculate the Number of Possible Transitions
The number of spectral lines (transitions) can be calculated using the formula:
\[ \text{Number of transitions} = n2 - n1 \]
Where:
- \( n2 \) is the initial energy level (7 in this case).
- \( n1 \) is the final energy level (2 for the Balmer series).

Substituting the values:
\[ \text{Number of transitions} = 7 - 2 = 5 \]

**Hint:** The formula gives the number of transitions possible from the higher level to the lower level.

### Step 4: List the Possible Transitions
The possible transitions from the 7th orbit to the 2nd orbit are:
1. From n = 7 to n = 2
2. From n = 6 to n = 2
3. From n = 5 to n = 2
4. From n = 4 to n = 2
5. From n = 3 to n = 2

**Hint:** Each transition corresponds to a spectral line in the Balmer series.

### Conclusion
Thus, the total number of spectral lines in the Balmer series when an electron returns from the 7th orbit to the 1st orbit of the hydrogen atom is **5**.

**Final Answer:** 5 (Option A)