When electron jumps from n = 4 to n = 1 orbit, we get

Options

A. Third line of Lyman series
B. second line of Balmer series
C. second line of Paschen series
D. an absorption line of Balmer series

Answer

To solve the question of what happens when an electron jumps from the n = 4 orbit to the n = 1 orbit, we can follow these steps:

### Step 1: Understand the Energy Levels
The energy levels of an electron in a hydrogen atom are quantized and are given by the formula:
\[ E_n = -\frac{13.6 \, \text{eV}}{n^2} \]
where \( n \) is the principal quantum number (energy level).

### Step 2: Calculate the Energy of the Initial and Final States
1. For \( n = 4 \):
\[ E_4 = -\frac{13.6 \, \text{eV}}{4^2} = -\frac{13.6 \, \text{eV}}{16} = -0.85 \, \text{eV} \]

2. For \( n = 1 \):
\[ E_1 = -\frac{13.6 \, \text{eV}}{1^2} = -13.6 \, \text{eV} \]

### Step 3: Calculate the Energy Released
When the electron jumps from a higher energy level to a lower one, energy is released in the form of a photon. The energy of the photon can be calculated as:
\[ E_{\text{photon}} = E_{\text{final}} - E_{\text{initial}} \]
Substituting the values:
\[ E_{\text{photon}} = E_1 - E_4 = (-13.6 \, \text{eV}) - (-0.85 \, \text{eV}) = -13.6 + 0.85 = -12.75 \, \text{eV} \]

### Step 4: Identify the Series
The transition from \( n = 4 \) to \( n = 1 \) corresponds to the Lyman series, which involves transitions to the first energy level (n=1). The Lyman series includes transitions from higher levels (n ≥ 2) to n = 1.

### Step 5: Determine the Specific Line
In the Lyman series, the transition from \( n = 4 \) to \( n = 1 \) is specifically the third line of the Lyman series.

### Conclusion
Thus, when an electron jumps from \( n = 4 \) to \( n = 1 \), we get the third line of the Lyman series.

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