How many lines in the spectrum will be observed when electrons returns from seventh shell to second shell.

Options

A. 13
B. 14
C. 15
D. 16

Answer

To determine how many lines will be observed in the spectrum when an electron transitions from the seventh shell (n=7) to the second shell (n=2), we can use the formula for calculating the number of spectral lines produced during a transition between two energy levels.

### Step-by-Step Solution:

1. **Identify the Energy Levels**:
- The initial energy level (n2) is 7 (the shell from which the electron is returning).
- The final energy level (n1) is 2 (the shell to which the electron is returning).

2. **Use the Formula**:
The formula to calculate the number of lines in the spectrum is given by:
\[ \text{Number of lines} = \frac{(n2 - n1)(n2 - n1 + 1)}{2} \]

3. **Substitute the Values**:
- Substitute n2 = 7 and n1 = 2 into the formula:
\[ \text{Number of lines} = \frac{(7 - 2)(7 - 2 + 1)}{2} \]

4. **Calculate the Differences**:
- Calculate \(n2 - n1\):
\[ n2 - n1 = 7 - 2 = 5 \]
- Calculate \(n2 - n1 + 1\):
\[ n2 - n1 + 1 = 5 + 1 = 6 \]

5. **Plug in the Differences**:
- Substitute these results back into the formula:
\[ \text{Number of lines} = \frac{(5)(6)}{2} \]

6. **Perform the Multiplication**:
- Multiply 5 and 6:
\[ 5 \times 6 = 30 \]

7. **Divide by 2**:
- Finally, divide by 2:
\[ \text{Number of lines} = \frac{30}{2} = 15 \]

### Final Answer:
The number of lines in the spectrum when an electron returns from the seventh shell to the second shell is **15**.