Absorption Spectra

When white light passes through a cool gas, something remarkable happens: the emerging light is missing very specific colors. These missing colors appear as dark lines against the continuous rainbow spectrum — and they are not random. Every element has its own unique set of missing lines, acting like a fingerprint. This pattern is called an absorption spectrum, and it arises because atoms can only absorb light at the exact energies that match transitions between their quantized energy levels. The mechanism is electron excitation. An atom's electrons occupy discrete energy levels — they cannot exist between these levels, only on them. When a photon strikes an atom, the electron will absorb it only if the photon's energy exactly equals the gap between the electron's current level and a higher one. If the energy doesn't match precisely, the photon passes straight through. When a match occurs, the electron jumps up to the higher level, removing that wavelength of light from the beam. The result is a dark absorption line at that precise wavelength. Absorption spectra have enormous practical importance. Astronomers use them to determine the composition of stars: sunlight filtered through the solar atmosphere produces hundreds of dark Fraunhofer lines, each identifying a specific element present in the sun's outer layers. The technique extends across chemistry, medicine, and environmental science — essentially any situation where you want to identify what a substance is made of without touching it.

Key takeaways
  • Quantized Energy Levels
  • Photon Energy Must Match Exactly
  • The Electron Jumps to a Higher Level
  • Photon is Re-emitted in a Random Direction
  • A Spectrum of Dark Lines

Quantized Energy Levels

Electrons in an atom are bound by the electric force of the nucleus and can only exist at specific, discrete energy levels. For hydrogen, these are given by Eₙ = −13.6 eV / n², where n = 1, 2, 3, … is the principal quantum number. The ground state (n = 1) has the lowest energy at −13.6 eV, and higher levels are less negative (less tightly bound).

Photon Energy Must Match Exactly

A photon carries energy E = hf, where h is Planck's constant and f is the photon's frequency. For an electron to absorb the photon and jump from level n₁ to a higher level n₂, the photon energy must exactly equal the energy gap: hf = E_{n₂} − E_{n₁}. Even a tiny mismatch means no absorption — this is the key quantum selectivity that makes spectra element-specific.

The Electron Jumps to a Higher Level

Upon absorbing the photon, the electron is promoted ('excited') to the higher energy level. This is a real physical change in the electron's state. The atom is now in an excited state. Note that this photon has been completely removed from the original beam of light, creating a dark band at that wavelength.

Photon is Re-emitted in a Random Direction

The excited state is unstable. After a very short time (typically ~10⁻⁸ s), the electron falls back to its original or another lower level, releasing a photon of the same energy. Crucially, this re-emitted photon goes in a random direction — not necessarily forward along the original beam. So from the perspective of the transmitted beam, that wavelength is depleted, producing the dark absorption line.

A Spectrum of Dark Lines

Because each element has a unique set of allowed energy levels, it can only absorb photons of specific wavelengths. Hydrogen absorbs at 410 nm, 434 nm, 486 nm, and 656 nm in the visible range (the Balmer series, transitions down to n = 2). No other element has this exact pattern, making absorption spectra a reliable tool for elemental identification.

The Key Equation

ΔE=hf=hcλ=En2−En1\Delta E = hf = \frac{hc}{\lambda} = E_{n_2} - E_{n_1}
  • \Delta E — Energy gap (J or eV): The difference in energy between two electron energy levels; the exact energy a photon must have to trigger absorption.
  • h — Planck's constant (J·s): Fundamental constant of quantum mechanics: h = 6.626 × 10⁻³⁴ J·s.
  • f — Photon frequency (Hz): The number of oscillations per second of the electromagnetic wave associated with the photon.
  • c — Speed of light (m/s): Speed of electromagnetic radiation in a vacuum: c = 3.00 × 10⁸ m/s.
  • \lambda — Wavelength (m): The distance between successive wave crests; determines the color of visible light.
  • E_{n_2},\, E_{n_1} — Energy levels (J or eV): Energies of the higher (n₂) and lower (n₁) electron states. For hydrogen: Eₙ = −13.6/n² eV.

Worked Example

Problem. A hydrogen atom is in its ground state (n = 1, E₁ = −13.6 eV). A photon is absorbed and the electron jumps to the n = 3 level (E₃ = −1.51 eV). (a) Calculate the energy of the photon absorbed. (b) Find the wavelength of this photon and state whether it is visible.

λ=hcΔE=(6.626×10−34)(3.00×108)1.937×10−18≈1.026×10−7 m=102.6 nm\lambda = \frac{hc}{\Delta E} = \frac{(6.626\times10^{-34})(3.00\times10^8)}{1.937\times10^{-18}} \approx 1.026\times10^{-7}\text{ m} = 102.6\text{ nm}

Answer. The photon has energy 12.09 eV and wavelength 102.6 nm (ultraviolet — not visible).

Figure
Diagram
Absorption Spectrum: FormationIncident white lightTransmitted light (absorption spectrum)cool gase⁻ excitedphoton inre-emitted (random dir.)Hydrogen Energy Levels & Transitionsn=1−13.6 eVn=2−3.4 eVn=3−1.51 eVn=4−0.85 eVn=5−0.54 eV656 nm(red)486 nm(blue)410 nm(violet)Balmer series: transitions TO n=2 produce visible absorption lines
Origins · 1 minJoseph von Fraunhofer and how this was discovered
JV
Joseph von Fraunhofer
1787–1826 · German

Fraunhofer systematically catalogued the dark lines in the solar spectrum in 1814, mapping over 570 absorption lines and labeling the strongest ones A through K (many of these labels are still used today). His precise measurements, made using diffraction gratings he helped perfect, established the field of spectroscopy and provided the data that later physicists used to decode atomic structure. Fraunhofer was orphaned at age 11 and became an apprentice glassmaker. He only began his formal scientific education after a building collapse that trapped him — the rescuers happened to include the Elector of Bavaria, who was so impressed by the boy that he funded Fraunhofer's education.

  • Emission Spectra — Emission spectra are the complement of absorption spectra: excited electrons falling to lower levels release photons at exactly the same wavelengths that absorption spectra remove, making the two concepts inseparable.
  • Atomic Energy Levels — Absorption can only occur because electron energies are quantized. Understanding discrete energy levels is the essential foundation for explaining why only specific wavelengths are absorbed.
  • Photoelectric Effect — Both the photoelectric effect and absorption spectra rely on the same quantum principle: photons carry discrete packets of energy E = hf, and matter interacts with light one photon at a time.
  • The Bohr Model — Bohr's 1913 model was the first to quantitatively predict the wavelengths of hydrogen's spectral lines using quantized orbits, directly explaining the pattern of absorption lines.