Hydrogen atoms are excited from ground state to the principal quantum number 5. Number of spectral lines observed will be

Options

A. 5
B. 4
C. 10
D. 8

Answer

To find the number of spectral lines observed when hydrogen atoms are excited from the ground state (n=1) to the principal quantum number n=5, we can use the formula for the number of spectral lines generated during transitions between energy levels.

### Step-by-Step Solution:

1. **Understanding the Energy Levels**:
- The hydrogen atom has discrete energy levels represented by principal quantum numbers (n=1, n=2, n=3, n=4, n=5).
- When an electron is excited from the ground state (n=1) to n=5, it can transition back to any of the lower energy levels (n=1, n=2, n=3, n=4).

2. **Calculating Possible Transitions**:
- The number of spectral lines corresponds to the number of unique transitions between energy levels.
- The formula to calculate the number of transitions (spectral lines) from a given principal quantum number \( n \) is:
\[ \text{Number of spectral lines} = \frac{n(n-1)}{2} \]
- Here, \( n \) is the highest principal quantum number, which in this case is 5.

3. **Applying the Formula**:
- Substitute \( n = 5 \) into the formula:
\[ \text{Number of spectral lines} = \frac{5(5-1)}{2} = \frac{5 \times 4}{2} = \frac{20}{2} = 10 \]

4. **Conclusion**:
- Therefore, the total number of spectral lines observed when hydrogen atoms transition from n=5 to lower energy levels is **10**.

### Final Answer:
The number of spectral lines observed will be **10**.

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