Question

Paschen series in spectrum of hydrogen atom lies in :

• A. infrared region
• B. ultraviolet region
• C. visible region
• D. partly in ultraviolet region and partly in visible region

Hint:

Order of spectral series for Hydrogen atom:
Lyman $\rightarrow$ UV
Balmer $\rightarrow$ Visible
Paschen, Brackett, Pfund $\rightarrow$ Infrared

Answer 1

The Correct Option is A

Concept:
• The spectral series of hydrogen atom transitions are categorized based on lower orbit quantum number $n_1$.

• Lyman series ($n_1 = 1$) lies in the Ultraviolet (UV) region.

• Balmer series ($n_1 = 2$) lies in the Visible region.

• Paschen ($n_1 = 3$), Brackett ($n_1 = 4$), and Pfund ($n_1 = 5$) series lie in the Infrared (IR) region.

Step 1: Identify transition quantum numbers
For Paschen series, electron transitions occur from outer orbits $n_2 = 4, 5, 6, \dots$ down to lower orbit $n_1 = 3$.

Step 2: Calculate wavelength range
Using Rydberg formula $\frac{1}{\lambda} = R\left(\frac{1}{3^2} - \frac{1}{n_2^2}\right)$:
For shortest wavelength ($n_2 = \infty$): $\lambda_{min} = \frac{9}{R} \approx 820\text{ nm}$.
For longest wavelength ($n_2 = 4$): $\lambda_{max} = \frac{144}{7R} \approx 1875\text{ nm}$.
Since visible spectrum ranges from $400\text{ nm}$ to $700\text{ nm}$, wavelengths above $700\text{ nm}$ belong to the Infrared region.

Step 3: Conclusion
Paschen series lies entirely in the infrared region, corresponding to option (A).