Number of spectral line produced when electron jumps from gamma line region of Balmer series to ground state in hydrogen atom.

Options

A. 15
B. 10
C. 20
D. 5

Explanation

To determine the number of spectral lines produced when an electron jumps from the gamma line region of the Balmer series to the ground state in a hydrogen atom, we can follow these steps:

### Step 1: Identify the Initial and Final Energy Levels
- The Balmer series corresponds to electronic transitions where the final energy level (n1) is 2. The gamma line is the third line in the Balmer series, which corresponds to an initial energy level (n2) of 5.
- Therefore, we have:
- Initial state (n2) = 5 (gamma line)
- Final state (n1) = 1 (ground state)

### Step 2: Use the Formula for Spectral Lines
- The formula to calculate the number of spectral lines produced when an electron transitions from a higher energy level (n2) to a lower energy level (n1) is given by:
\[ \text{Number of spectral lines} = \frac{(n2 - n1)(n2 - n1 + 1)}{2} \]

### Step 3: Substitute the Values into the Formula
- Substitute n2 = 5 and n1 = 1 into the formula:
\[ \text{Number of spectral lines} = \frac{(5 - 1)(5 - 1 + 1)}{2} \]
\[ = \frac{(4)(5)}{2} \]

### Step 4: Calculate the Result
- Now, calculate the value:
\[ = \frac{20}{2} = 10 \]

### Conclusion
- The total number of spectral lines produced when the electron jumps from the gamma line region of the Balmer series to the ground state in a hydrogen atom is **10**.