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 sample of hydrogen atoms, we can use the formula for calculating the number of spectral lines produced during electronic transitions.

### Step-by-Step Solution:

1. **Identify the quantum levels**:
- The initial energy level (n2) is 5 (where the electron is jumping from).
- The final energy level (n1) is 1 (where the electron is jumping to).

2. **Use the formula for spectral lines**:
The formula to calculate the total number of spectral lines when an electron transitions between two energy levels is given by:
\[ \text{Number of spectral lines} = \frac{(n2 - n1)(n2 - n1 + 1)}{2} \]

3. **Substitute the values into the formula**:
- Here, \( n2 = 5 \) and \( n1 = 1 \).
- Calculate \( n2 - n1 \):
\[ n2 - n1 = 5 - 1 = 4 \]
- Now substitute into the formula:
\[ \text{Number of spectral lines} = \frac{(4)(4 + 1)}{2} \]

4. **Perform the calculations**:
- Calculate \( 4 + 1 \):
\[ 4 + 1 = 5 \]
- Now substitute back into the equation:
\[ \text{Number of spectral lines} = \frac{(4)(5)}{2} \]
- Multiply:
\[ 4 \times 5 = 20 \]
- Divide by 2:
\[ \frac{20}{2} = 10 \]

5. **Conclusion**:
- The total number of spectral lines obtained when the electron jumps from n = 5 to n = 1 is **10**.