An electron in the hydrogen atom absorbs energy and jumps to the 4th orbit. It jumps back to the ground state in steps e.g., from 4th to 3rd orbit, then from 3rd to 2nd orbit and finally to the ground state etc.
Total number of lines obtained in the spectrum would be

Options

A. 3
B. 6
C. 9
D. 12

Explanation

To determine the total number of spectral lines obtained when an electron in a hydrogen atom jumps from the 4th orbit back to the ground state in steps, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Initial and Final States**:
- The electron starts at the 4th orbit (n = 4) and will return to the ground state (n = 1) in steps.

2. **Understand the Transition Steps**:
- The electron will transition from:
- 4th orbit (n = 4) to 3rd orbit (n = 3)
- 3rd orbit (n = 3) to 2nd orbit (n = 2)
- 2nd orbit (n = 2) to ground state (n = 1)

3. **Determine the Total Number of Transitions**:
- The electron can transition between orbits in multiple ways. Each transition corresponds to a spectral line.
- The total number of transitions can be calculated using the formula for the number of lines in a spectrum:
\[ \text{Number of lines} = \frac{n(n-1)}{2} \]
- Here, \( n \) is the highest energy level from which the electron is transitioning (in this case, n = 4).

4. **Substituting the Value into the Formula**:
- Substitute \( n = 4 \) into the formula:
\[ \text{Number of lines} = \frac{4(4-1)}{2} = \frac{4 \times 3}{2} = \frac{12}{2} = 6 \]

5. **Conclusion**:
- The total number of spectral lines obtained when the electron transitions from the 4th orbit to the ground state in steps is **6**.

### Final Answer:
The total number of lines obtained in the spectrum is **6**.