Atomic Spectra

Every element, when heated or excited, glows with its own signature set of colors — a fingerprint no two elements share. Bohr explained why: electrons can only orbit at certain fixed energies, and light is emitted only when they jump between them. Push those jumps hard enough, and you get X-rays instead of visible light.

Act 1 · Bohr's Model of the Hydrogen Atom

Electrons only orbit at certain fixed energies — never in between

Bohr proposed that an electron can only occupy discrete circular orbits, each with a fixed energy En = −13.6/n² eV. The electron radiates no energy while in one of these stationary orbits. It emits or absorbs a photon of energy hf = Ei − Ef only when it jumps between two allowed orbits.

click an orbit level below to trigger a jump E (eV)
En = −13.6/n² eV · photon energy = 0 eV · λ = 

Every jump down to the same final level produces the same photon energy every time — grouping all the possible jumps into named series.

Act 2 · Hydrogen's Spectral Series

Every transition that lands on the same final level forms one named series

Jumps that end on n=1 form the Lyman series (ultraviolet). Jumps ending on n=2 form the Balmer series (mostly visible light) — the one Balmer first noticed as colored lines in hydrogen's spectrum. Higher final levels (Paschen, Brackett, Pfund) fall further into the infrared.

100 nm 2000 nm Balmer series (final level n=2)
1/λ = R(1/nf² − 1/ni²) · R = 1.097×10⁵ m⁻¹ (Rydberg constant)

A spectrometer is the instrument that actually spreads this light into its component wavelengths so we can read them off.

Act 3 · The Spectrometer

A prism or grating spreads light into its spectral lines for measurement

Light from a glowing gas passes through a narrow slit, is collimated into parallel rays, then spread by a prism or diffraction grating according to wavelength. A telescope on a rotating arm reads off the angle of each colored line, letting the wavelengths be measured precisely and compared against known spectral series.

gas discharge tube slit + collimator prism rotating telescope reads the angle of each line
Telescope angle
Sweep the telescope to pick out each colored line in turn.

Turn the process around — accelerate electrons into a metal target instead of exciting a gas — and the same energy-jump idea produces X-rays.

Act 4 · X-Rays: The Coolidge Tube

Fast electrons slammed into a metal target produce two kinds of X-rays at once

In a Coolidge tube, electrons boiled off a hot filament are accelerated by a high voltage and smashed into a metal anode. Most electrons decelerate gradually, radiating a continuous spread of X-ray wavelengths (bremsstrahlung) down to a sharp minimum wavelength set by the tube voltage. A few electrons instead knock out an inner-shell electron of the target atom, and the atom's own characteristic X-ray lines appear as the vacancy is refilled.

filament (cathode) metal anode accelerating voltage V
λmin = hc/(eV) = 0 pm
λ
Tube voltage, V50 kV
Higher voltage pushes λmin shorter and produces more penetrating X-rays.

Applications: medical imaging and cancer therapy, airport baggage screening, industrial flaw detection in metal castings, and crystallography for determining atomic structure.

In a nutshell
  • Bohr's model: electrons occupy discrete stationary orbits En = −13.6/n² eV; photons are emitted/absorbed only on transitions between orbits.
  • Spectral series: Lyman (n→1, UV), Balmer (n→2, visible), Paschen (n→3, IR) — 1/λ = R(1/nf²−1/ni²).
  • Spectrometer: slit + collimator + prism/grating + rotating telescope resolves a spectrum's wavelengths.
  • X-rays: a continuous bremsstrahlung spectrum (λmin = hc/eV) plus sharp characteristic lines from inner-shell transitions in the target atom.