Atomic Spectra

Step 1: Using the Rydberg formula for wavelength.
The wavelength of the photon emitted during an electronic transition is given by the Rydberg formula: where: : Rydberg constant, : Final orbit number, : Initial orbit number ( ).

Step 2: For the transition from the 3rd orbit ( ) to the 2nd orbit ( ).
The wavelength is given as . Substituting into the Rydberg formula: Simplify the terms:

Step 3: For the transition from the 4th orbit ( ) to the 3rd orbit ( ).
The wavelength for this transition, say , is: Simplify the terms:

Step 4: Relating to .
Divide the two equations: Simplify: Thus:

Step 5: Conclusion.
The wavelength of the electron when it jumps from the 4th orbit to the 3rd orbit is:

Ratio of Wavelengths: Lyman Limit to Paschen Limit

Step 1: Energy of Series Limit

The series limit corresponds to transitions to a fixed lower level from .
Energy of a photon emitted during a transition in hydrogen is: For the **series limit**, , so:

Step 2: Lyman and Paschen Series Limits

- For **Lyman series**: - For **Paschen series**:

Step 3: Relationship with Wavelength

Since , wavelength is inversely proportional to energy: Therefore, the ratio of wavelengths is:

✅ Final Answer: