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ABCD
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Hydrogen Spectrum

Physics — Atomic Structure

What is it?

definition
memorize this!
  • Set of spectral lines emitted by a hydrogen atom when its electron transitions between energy levels.
  • Each line corresponds to a specific photon energy → unique wavelength.

Balmer Series

concept
  • Transitions where the electron falls to n = 2.
  • Lies in the visible region of the EM spectrum.
  • Famous lines: Hα (red), Hβ (cyan), Hγ (violet).
1λ=R(1n12−1n22)\frac{1}{\lambda} = R\left(\frac{1}{n_1^2} - \frac{1}{n_2^2}\right)
Rydberg formula

Other series

list
  • Lyman → n = 1 → Ultraviolet.
  • Paschen → n = 3 → Infrared.
  • Brackett → n = 4 → Far IR.
SeriesFinal nRegion
Lyman1UV
Balmer2Visible
Paschen3IR
Series at a glance

Energy of a level

important
  • Energy of the nth level is negative — electron is bound.
  • Ground state n = 1 has the lowest (most negative) energy.
En=−13.6 eVn2E_n = -\frac{13.6\,\text{eV}}{n^2}
Bohr energy of the nth level

Quick takeaway

summary
  • Higher n → higher (less negative) energy.
  • ΔE between levels gives the photon's energy and thus its color.
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