Spectral Lines
Rydberg: 1/λ = R(1/n₁² − 1/n₂²) — selector for Lyman, Balmer, Paschen, Brackett, Pfund.
Key Notes
Atoms emit and absorb light only at DISCRETE wavelengths (spectral lines) — direct evidence of quantised energy levels.
Each line corresponds to a transition between two specific levels: hf = E_i − E_f.
Hydrogen line series (named by final state n_f): Lyman (n_f=1, UV), Balmer (n_f=2, visible), Paschen (n_f=3, IR), Brackett (n_f=4, IR), Pfund (n_f=5, IR).
Lyman-α (n=2 → 1): 121.6 nm (UV). Balmer-α (n=3 → 2): 656.3 nm (red, Hα).
Series limit: shortest wavelength in a series — corresponds to n_i = ∞. λ_lim(Lyman) = 91.2 nm. λ_lim(Balmer) = 364.6 nm.
Emission spectrum (hot atoms emit lines) vs absorption spectrum (cool atoms in front of bright continuum — dark lines).
Fraunhofer lines in the solar spectrum are absorption lines from cooler gas in the Sun's atmosphere.
Formulas
Rydberg formula
R = 1.097 × 10⁷ m⁻¹ for hydrogen. Valid for n_i > n_f.
Series limit (n_i = ∞)
Shortest λ in series; e.g., Lyman limit = 1/R = 91.2 nm.
Number of lines from level n
Combinations of pairs of levels with smaller numbers.
Important Points
Each chemical element has a UNIQUE spectral fingerprint — basis of spectroscopy.
Helium was first discovered in the SUN by Janssen (1868) via an unidentified emission line in the solar spectrum (later named 'He').
Absorption lines = transitions upward; emission lines = transitions downward. Same wavelengths in both.
Doppler effect shifts spectral lines — used in measuring stellar velocities and exoplanet detection (radial-velocity method).
Hydrogen Balmer series (n=2 lower) is the only series mostly in visible: 656 nm (Hα red), 486 nm (Hβ blue-green), 434 nm (Hγ violet).
Limit of a series corresponds to ionisation from that lower level.
Spectral Lines notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 12 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.