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 electrons return from the seventh shell to the second shell, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Quantum Levels**:
- The initial shell (N2) is the seventh shell, so N2 = 7.
- The final shell (N1) is the second shell, so N1 = 2.

2. **Use the Formula for Spectral Lines**:
- The formula to calculate the number of spectral lines when electrons transition between energy levels is given by:
\[ \text{Number of spectral lines} = \frac{(N2 - N1)(N2 - N1 + 1)}{2} \]

3. **Substitute the Values**:
- Plugging in the values we have:
\[ \text{Number of spectral lines} = \frac{(7 - 2)(7 - 2 + 1)}{2} \]

4. **Calculate the Differences**:
- Calculate \(N2 - N1\):
\[ 7 - 2 = 5 \]
- Calculate \(N2 - N1 + 1\):
\[ 7 - 2 + 1 = 6 \]

5. **Calculate the Total**:
- Now substitute these results back into the formula:
\[ \text{Number of spectral lines} = \frac{(5)(6)}{2} \]
- Calculate the product:
\[ 5 \times 6 = 30 \]
- Divide by 2:
\[ \frac{30}{2} = 15 \]

6. **Conclusion**:
- Therefore, the total number of spectral lines observed when electrons return from the seventh shell to the second shell is **15**.

### Final Answer:
**15 lines in the spectrum will be observed.**