Atomic Spectra: Emission, Absorption, and Electronic Transitions

Atomic spectra arise from quantized energy transitions of electrons in atoms. When an atom absorbs energy (electrical discharge, flame, or photon), an electron can be promoted from a lower to a higher energy level. As the electron relaxes back down, the atom emits photons at discrete energies, producing line spectra that act as "fingerprints" for each element.

This topic connects quantum theory, electronic structure, and practical spectroscopy used in lab analysis and astrophysics. You should be able to describe how lines form, interpret simple spectra, and apply energy–wavelength–frequency relationships.

Key ideas

• Electrons occupy discrete energy levels. Transitions between levels involve exact energy quanta.
• Emission spectra: bright lines on a dark background (photons emitted as electrons relax).
• Absorption spectra: dark lines on a continuous spectrum (photons absorbed to promote electrons).
• Energy–light relationships: E = hν and c = λν, so E = hc/λ. Higher energy → higher frequency → shorter wavelength.
• Each element has unique transitions → unique line positions; useful for identification.

Emission vs. absorption spectra

• Emission: A hot, low-density gas emits light at specific wavelengths, giving bright lines. Example: Hydrogen discharge tube shows Balmer lines in the visible region.
• Absorption: A continuous light source passing through a cool gas yields missing wavelengths (dark lines) where atoms absorbed light to excite electrons. The pattern of missing lines matches the element’s allowed transitions.

Both reflect the same quantized energy differences. If an absorption line occurs at 656 nm (Hα), the same transition can emit at 656 nm when the electron relaxes.

Hydrogen spectrum and energy levels

The hydrogen atom is the classic case where energy levels can be modeled simply. The allowed energies (n = 1, 2, 3, …) get closer together at higher n. Series of lines correspond to electrons ending in a specific level:

• Lyman series: transitions to n = 1 (ultraviolet)
• Balmer series: transitions to n = 2 (visible and near UV)
• Paschen, Brackett, Pfund: transitions to n = 3, 4, 5 (infrared)

The Balmer lines (Hα ≈ 656 nm, Hβ ≈ 486 nm, Hγ ≈ 434 nm, Hδ ≈ 410 nm) are often seen in laboratory spectra and stellar spectra. As n increases, levels converge and the spectral lines crowd together.

Interpreting spectra qualitatively

• Line positions: Indicate the energy gaps between quantized states; shorter wavelengths mean larger energy changes.
• Line intensity: Related to transition probability and population of the upper level; more populated and more allowed transitions are brighter.
• Line broadening: Collisions, Doppler motion, and instrument resolution broaden otherwise sharp lines.

Practical uses

• Element identification: Flame tests (Na⁺ yields yellow; K⁺ lilac; Cu²⁺ green/blue) and emission spectroscopy use characteristic lines.
• Quantitative analysis: Atomic absorption spectroscopy (AAS) and inductively coupled plasma optical emission spectroscopy (ICP-OES) measure concentrations from line intensities.
• Astrophysics: Absorption lines in stellar spectra reveal composition, temperature, and motion (via Doppler shifts).

Problem walkthroughs

1. Which has higher energy: a 400 nm photon or a 700 nm photon?

• Use E = hc/λ. Smaller λ → larger E. So 400 nm photons carry more energy than 700 nm photons.

1. Why do different elements have different line patterns?

• Nuclear charge and electron–electron interactions create unique sets of energy levels; allowed transitions differ by element, so spectra are element-specific.

1. In a discharge tube, bright lines at specific wavelengths appear. What process produces these lines?

• Excited electrons relax to lower levels, emitting photons with energies equal to the level differences.

Common mistakes

• Thinking atoms emit a continuous spectrum. Continuous spectra come from hot solids or dense gases; isolated atoms produce lines.
• Mixing up emission and absorption diagrams; remember emission adds bright lines, absorption removes lines from a continuum.
• Ignoring selection rules and relative intensities; not every transition is equally likely.

Quick reference

• Emission: excited → lower level + photon (bright lines)
• Absorption: lower level + photon → excited (dark lines)
• E = hc/λ; higher E → shorter λ
• Hydrogen: Balmer series visible; Lyman UV; others IR
• Spectra identify elements and quantify amounts in samples