Question

In which region of the electromagnetic spectrum does the Lyman series of hydrogen lie?

• A. Infrared
• B. Visible
• C. X-rays
• D. Ultraviolet

Hint:

Lyman lines end on the ground state \( n=1 \) and are the highest-energy hydrogen transitions, so they lie in the ultraviolet.

Answer 1

The Correct Option is D

Step 1: Identify the Lyman series.
The Lyman series consists of the spectral lines emitted when an electron in a hydrogen atom falls from a higher level \( (n = 2,3,4,\dots) \) to the ground level \( n = 1 \).

Step 2: Use the Rydberg formula.
\[ \frac{1}{\lambda} = R\left(\frac{1}{1^2} - \frac{1}{n^2}\right),\quad R = 1.097\times10^{7}\ \text{m}^{-1}. \]

Step 3: Estimate the wavelength range.
The series limit (\( n\to\infty \)) gives \[ \lambda_{min} = \frac{1}{R} \approx 91\ \text{nm}, \] and the longest line (\( n=2 \)) gives about \( 122 \) nm. Both values are well below the visible band (400–700 nm).

Step 4: Match to the spectrum.
Wavelengths of roughly 91–122 nm fall in the ultraviolet region.

Step 5: Reject the others.
Infrared (Paschen, Brackett) and visible (Balmer) correspond to transitions ending on \( n=3 \) and \( n=2 \) respectively; X-rays require far shorter wavelengths. Hence option (iv) Ultraviolet is correct.
\[\boxed{\text{Ultraviolet}}\]