What are the maximum number of emission lines when the excited electron of a H atom in n = 4 drops to the ground state ?

Answer

To determine the maximum number of emission lines when an excited electron of a hydrogen atom in the n = 4 energy level drops to the ground state (n = 1), we can follow these steps:

### Step 1: Understand the Energy Levels
The hydrogen atom has discrete energy levels denoted by the principal quantum number \( n \). When an electron transitions from a higher energy level to a lower one, it emits energy in the form of light, resulting in emission lines.

### Step 2: Identify the Initial and Final States
In this case, the electron starts at \( n = 4 \) and can drop to \( n = 1 \) (ground state). The possible transitions can be from \( n = 4 \) to \( n = 3 \), \( n = 2 \), and \( n = 1 \).

### Step 3: Calculate the Number of Possible Transitions
The number of possible transitions from a higher energy level \( n \) to lower energy levels can be calculated using the formula:
\[ \text{Number of transitions} = \frac{n(n-1)}{2} \]
Where \( n \) is the principal quantum number of the initial state.

### Step 4: Substitute the Value of n
For \( n = 4 \):
\[ \text{Number of transitions} = \frac{4(4-1)}{2} = \frac{4 \times 3}{2} = \frac{12}{2} = 6 \]

### Step 5: Conclusion
Thus, the maximum number of emission lines when the excited electron of a hydrogen atom in \( n = 4 \) drops to the ground state is 6.

### Final Answer
The maximum number of emission lines is **6**.

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