What is the maximum number of emission lines are obtained when the excited electron of a H atom in n = 5 drops to the ground state?

Options

A. 12
B. 15
C. 21
D. 10

Explanation

To find the maximum number of emission lines obtained when an excited electron of a hydrogen atom in the n = 5 level drops to the ground state (n = 1), we can use a formula that relates to the number of possible transitions between energy levels.

### Step-by-Step Solution:

1. **Identify the Initial and Final Energy Levels**:
- The excited state is n = 5.
- The ground state is n = 1.

2. **Understand the Concept of Emission Lines**:
- When an electron transitions from a higher energy level to a lower one, it emits a photon, resulting in an emission line.
- The maximum number of emission lines corresponds to the number of unique transitions that can occur as the electron drops from n = 5 to n = 1.

3. **Use the Formula for Maximum Emission Lines**:
- The formula to calculate the maximum number of emission lines when an electron drops from level n to the ground state is given by:
\[ \text{Maximum Emission Lines} = \frac{n(n-1)}{2} \]
- Here, n is the principal quantum number of the excited state.

4. **Substitute the Value of n**:
- For n = 5:
\[ \text{Maximum Emission Lines} = \frac{5(5-1)}{2} = \frac{5 \times 4}{2} \]

5. **Calculate the Result**:
- Simplifying the equation:
\[ = \frac{20}{2} = 10 \]

6. **Conclusion**:
- Therefore, the maximum number of emission lines obtained when the excited electron drops from n = 5 to n = 1 is **10**.

### Final Answer:
The maximum number of emission lines is **10**.