In the hydrogen atom, the electrons are excited to the 5th energy level. The number of lines that may appear in the spectrum will be

Options

A. 4
B. 8
C. 10
D. 12

Explanation

To determine the number of spectral lines that may appear when the electrons in a hydrogen atom are excited to the 5th energy level, we can use the formula for calculating the number of spectral lines produced during transitions between energy levels.

### Step-by-Step Solution:

1. **Identify the Energy Level (n)**:
The electrons are excited to the 5th energy level, so we have \( n = 5 \).

2. **Use the Formula for Spectral Lines**:
The formula to calculate the number of spectral lines is given by:
\[ \text{Number of lines} = \frac{n(n-1)}{2} \]
where \( n \) is the principal quantum number of the excited state.

3. **Substitute the Value of n**:
Substitute \( n = 5 \) into the formula:
\[ \text{Number of lines} = \frac{5(5-1)}{2} \]

4. **Calculate the Expression**:
First, calculate \( 5 - 1 \):
\[ 5 - 1 = 4 \]
Now, multiply:
\[ 5 \times 4 = 20 \]
Finally, divide by 2:
\[ \frac{20}{2} = 10 \]

5. **Conclusion**:
Therefore, the number of spectral lines that may appear in the spectrum when electrons are excited to the 5th energy level is **10**.

### Final Answer:
The number of lines that may appear in the spectrum is **10**.