The series corresponding to minimum wavelength transition in H-atom :-

Options

A. Balmer
B. Lyman
C. Paschan
D. Bracket

Answer

To determine the series corresponding to the minimum wavelength transition in a hydrogen atom, we can follow these steps:

### Step 1: Understand the Series in Hydrogen Atom
In the hydrogen atom, there are several spectral series based on electron transitions:
- **Lyman series**: Transitions to n=1
- **Balmer series**: Transitions to n=2
- **Paschen series**: Transitions to n=3
- **Brackett series**: Transitions to n=4
- **Pfund series**: Transitions to n=5

### Step 2: Identify the Formula for Wavelength
The formula to calculate the wavelength of the emitted or absorbed light during an electron transition is given by the Rydberg formula:
\[ \frac{1}{\lambda} = R \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right) \]
where:
- \( R \) is the Rydberg constant,
- \( n_1 \) is the lower energy level,
- \( n_2 \) is the higher energy level.

### Step 3: Determine Minimum Wavelength Condition
To find the minimum wavelength, we need to consider the transition where \( n_1 = 1 \) (the lowest energy level) and \( n_2 \) approaches infinity (the highest energy level). This corresponds to the Lyman series.

### Step 4: Calculate Minimum Wavelength for Lyman Series
For the Lyman series:
- Set \( n_1 = 1 \)
- Set \( n_2 = \infty \)

Substituting these values into the formula:
\[ \frac{1}{\lambda_{\text{min}}} = R \left( \frac{1}{1^2} - \frac{1}{\infty^2} \right) \]
This simplifies to:
\[ \frac{1}{\lambda_{\text{min}}} = R \left( 1 - 0 \right) = R \]
Thus, the minimum wavelength for the Lyman series is:
\[ \lambda_{\text{min}} = \frac{1}{R} \]

### Step 5: Compare with Other Series
For other series:
- **Balmer series**: \( n_1 = 2 \), \( n_2 = \infty \)
\[ \frac{1}{\lambda_{\text{min}}} = R \left( \frac{1}{2^2} - 0 \right) = \frac{R}{4} \implies \lambda_{\text{min}} = \frac{4}{R} \]
- **Paschen series**: \( n_1 = 3 \), \( n_2 = \infty \)
\[ \frac{1}{\lambda_{\text{min}}} = R \left( \frac{1}{3^2} - 0 \right) = \frac{R}{9} \implies \lambda_{\text{min}} = \frac{9}{R} \]

### Conclusion
The Lyman series has the shortest wavelength (minimum wavelength) transition in the hydrogen atom, as it corresponds to the transition from the highest energy level to the lowest (n=1).

### Final Answer
**The series corresponding to the minimum wavelength transition in the hydrogen atom is the Lyman series.**

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