Question

If the minimum wavelength of Lyman series is 911 Å, the minimum wavelength of Paschen series will be

• A. 8200 Å
• B. 7300 Å
• C. 5500 Å
• D. 4600 Å

Hint:

Remember the general pattern that the wavelength in the Paschen series is longer than in the Lyman series due to the difference in energy levels.

Answer 1

The Correct Option is B

Step 1: Relationship between series.
The Lyman series corresponds to transitions to the first energy level (n = 1), while the Paschen series corresponds to transitions to the third energy level (n = 3). The wavelength of the spectral lines is related to the energy difference between levels by the Rydberg formula: \[ \frac{1}{\lambda} = R_H \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right) \] where \( R_H \) is the Rydberg constant.
Step 2: Finding the ratio of wavelengths.
Given that the minimum wavelength in the Lyman series corresponds to the transition from n = 2 to n = 1, the wavelength in the Paschen series for the transition from n = 4 to n = 3 will be:
\[ \frac{\lambda_{\text{Paschen}}}{\lambda_{\text{Lyman}}} = \frac{3^2}{2^2} = \frac{9}{4} \] Thus: \[ \lambda_{\text{Paschen}} = \lambda_{\text{Lyman}} \times \frac{9}{4} = 911 \times \frac{9}{4} = 7300 \, \text{Å} \] Thus, the correct answer is
(B) 7300 Å.