Hydrogen atom is exited from ground state to another state with principal quantum number equal to `4` Then the number of spectral line in the emission spectra will be

Options

A. 2
B. 3
C. 5
D. 6

Answer

To determine the number of spectral lines in the emission spectrum of a hydrogen atom that has been excited from the ground state to a state with a principal quantum number of 4, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Initial and Final States**:
- The hydrogen atom is initially in the ground state (n=1) and is excited to the state with principal quantum number n=4.

2. **Possible Transitions**:
- From n=4, the atom can transition to lower energy levels (n=3, n=2, and n=1).
- The possible transitions are:
- From n=4 to n=3
- From n=4 to n=2
- From n=4 to n=1
- From n=3 to n=2
- From n=3 to n=1
- From n=2 to n=1

3. **Count the Transitions**:
- We can count the transitions:
- From n=4: 3 transitions (to n=3, n=2, n=1)
- From n=3: 2 transitions (to n=2, n=1)
- From n=2: 1 transition (to n=1)
- Total transitions = 3 + 2 + 1 = 6.

4. **Use the Formula**:
- Alternatively, we can use the formula for the number of spectral lines in the emission spectrum:
\[ \text{Number of spectral lines} = \frac{n(n-1)}{2} \]
- Here, \( n = 4 \):
\[ \text{Number of spectral lines} = \frac{4(4-1)}{2} = \frac{4 \times 3}{2} = 6 \]

5. **Conclusion**:
- Therefore, the total number of spectral lines in the emission spectrum when the hydrogen atom transitions from n=4 to lower energy levels is **6**.

### Final Answer:
The number of spectral lines in the emission spectra is **6**.