The total number of spectral lines obtained when an electron jumps, from n = 5 to n =1 in a sample of hydrogen atoms.

Options

A. 4
B. 6
C. 12
D. 10

Answer

To find the total number of spectral lines obtained when an electron jumps from n = 5 to n = 1 in a hydrogen atom, 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 (n1) is 1.
- The final energy level (n2) is 5.

2. **Use the Formula**:
The formula to calculate the number of spectral lines (R) is:
\[ R = (n_2 - n_1) \times (n_2 - n_1 + 1) / 2 \]

3. **Substitute the Values**:
Substitute n1 = 1 and n2 = 5 into the formula:
\[ R = (5 - 1) \times (5 - 1 + 1) / 2 \]

4. **Calculate the Differences**:
- Calculate \( n_2 - n_1 \):
\[ 5 - 1 = 4 \]
- Calculate \( n_2 - n_1 + 1 \):
\[ 5 - 1 + 1 = 5 \]

5. **Multiply the Results**:
Now, multiply the two results:
\[ R = 4 \times 5 / 2 \]

6. **Simplify the Expression**:
- Calculate \( 4 \times 5 = 20 \)
- Divide by 2:
\[ R = 20 / 2 = 10 \]

7. **Conclusion**:
The total number of spectral lines obtained when an electron jumps from n = 5 to n = 1 in a sample of hydrogen atoms is **10**.

### Final Answer:
The total number of spectral lines is **10**.