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 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 gamma line of the Balmer series corresponds to the transition from the n=5 energy level to the n=2 energy level. The Balmer series involves transitions to the n=2 level from higher levels (n=3, 4, 5, ...).

### Step 2: Determine the Ground State
The ground state of the hydrogen atom is represented by n=1. When the electron jumps from the gamma line (n=5) to the ground state (n=1), it will pass through the intermediate levels (n=4, n=3, and n=2).

### Step 3: Calculate the Number of Spectral Lines
The number of spectral lines produced during a transition can be calculated using the formula:
\[ \text{Number of spectral lines} = \frac{n(n-1)}{2} \]
where \( n \) is the number of energy levels involved in the transition.

In this case, since the electron is transitioning from n=5 to n=1, we consider all levels from n=2 to n=5. Thus, we have:
- n=2 (Balmer series)
- n=3
- n=4
- n=5

So, the total number of levels involved is 5 (from n=5 down to n=1).

### Step 4: Plug Values into the Formula
Now, substituting \( n = 5 \) into the formula:
\[ \text{Number of spectral lines} = \frac{5(5-1)}{2} = \frac{5 \times 4}{2} = \frac{20}{2} = 10 \]

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

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