Emission Spectra

When atoms are energized — by heat, electricity, or light — their electrons jump to higher energy levels. These excited electrons quickly fall back down to lower energy levels, and as they do, they release energy in the form of photons. Because electrons can only exist at specific, quantized energy levels within an atom, the photons they emit have only specific energies, and therefore only specific frequencies (colors) of light. The result is an emission spectrum: a set of sharp, bright lines against a dark background, unique to each element like a fingerprint. This is fundamentally different from a continuous spectrum (like white light from the Sun's surface), which contains all visible wavelengths blended together. An emission spectrum is discrete — only certain wavelengths appear. For hydrogen, these lines were first systematically catalogued by Johann Balmer in 1885, who found a mathematical pattern in the visible lines. Niels Bohr later explained this pattern in 1913 using his model of quantized electron orbits, making emission spectra one of the earliest triumphs of quantum theory. Emission spectra are not just laboratory curiosities. Astronomers use them to identify the chemical composition of stars and nebulae billions of light-years away. Medical imaging, neon lighting, lasers, and even fireworks all depend on controlled emission of photons from excited atoms. Understanding emission spectra means understanding the quantum architecture of matter itself.

Key takeaways
  • Quantized Energy Levels
  • Excitation: Moving Electrons Upward
  • Spontaneous Emission: The Photon is Released
  • Series of Lines in Hydrogen
  • The Spectrum as a Chemical Fingerprint

Quantized Energy Levels

Electrons in an atom do not orbit the nucleus at arbitrary distances. They occupy discrete energy levels, often labeled n = 1, 2, 3, … where n = 1 is the ground state (lowest energy). In the Bohr model of hydrogen, the energy of level n is given by E_n = −13.6 eV / n². The negative sign indicates that energy must be added to free the electron from the nucleus. Each element has its own unique set of energy levels determined by its nuclear charge and electron configuration.

Excitation: Moving Electrons Upward

An atom is excited when an electron absorbs energy — from a collision with another particle, from an electrical discharge, or from an absorbed photon — and jumps from a lower level (n_i) to a higher level (n_f > n_i). Think of it like pushing a ball up a staircase: the ball can only rest on specific steps, not between them. The atom is now in an unstable, excited state and will not stay there for long — typically around 10⁻⁸ seconds before the electron falls back down.

Spontaneous Emission: The Photon is Released

When the electron drops from a higher energy level n_upper back down to a lower level n_lower, it releases a photon whose energy exactly equals the difference between the two levels: E_photon = E_upper − E_lower. Since E = hf (Planck's relation), this fixes the frequency — and therefore the wavelength — of the emitted photon with great precision. Every downward transition between a specific pair of energy levels always produces a photon of exactly the same wavelength, creating a sharp spectral line.

Series of Lines in Hydrogen

For hydrogen, downward transitions to n = 1 produce ultraviolet photons (the Lyman series), transitions to n = 2 produce visible photons (the Balmer series — the familiar red, cyan, violet lines), and transitions to n = 3 produce infrared photons (the Paschen series). The Balmer series lines have wavelengths in the range 410 nm to 656 nm, all within the visible spectrum. Each series forms because a whole family of higher levels can all dump their electrons into the same lower level, each giving a different photon energy.

The Spectrum as a Chemical Fingerprint

Because every element has a unique set of energy levels, every element produces a unique emission spectrum. Sodium's characteristic yellow doublet at 589 nm makes streetlights glow yellow. Neon's complex red-orange spectrum gives neon signs their glow. By dispersing light through a prism or diffraction grating and measuring line positions precisely, scientists can identify elements in stars, detect trace pollutants in air, and even measure the recession speed of galaxies via Doppler shifts of known spectral lines.

The Key Equation

1λ=RH(1nlower2−1nupper2)\frac{1}{\lambda} = R_H \left( \frac{1}{n_{\text{lower}}^2} - \frac{1}{n_{\text{upper}}^2} \right)
  • \lambda — Wavelength of emitted photon (m): The wavelength of the light emitted; determines the color (for visible light) or region of the electromagnetic spectrum.
  • R_H — Rydberg constant (m⁻¹): A fundamental constant equal to 1.097 × 10⁷ m⁻¹, derived from the electron mass, charge, and Planck's constant.
  • n_{\text{lower}} — Lower principal quantum number (dimensionless): The quantum number of the energy level the electron falls INTO. For Balmer series, n_lower = 2.
  • n_{\text{upper}} — Upper principal quantum number (dimensionless): The quantum number of the energy level the electron falls FROM. Must be greater than n_lower.

Worked Example

Problem. Calculate the wavelength of light emitted when a hydrogen electron falls from n = 4 to n = 2 (a Balmer series transition). In which part of the visible spectrum does this line appear?

λ=486 nm (blue-green, Hβ line)\lambda = 486 \text{ nm (blue-green, H}\beta\text{ line)}

Answer. The emitted photon has a wavelength of approximately 486 nm, appearing as a blue-green (cyan) line in the visible spectrum.

Figure
Diagram
Hydrogen Emission: Balmer Series Transitionsn=1−13.6 eVn=2−3.40 eVn=3−1.51 eVn=4−0.85 eVn=5−0.54 eV656nmH-α486nmH-β434nmH-γEmission SpectrumBalmer Series (visible)656486434410400nm700nmArrows show downwardelectron transitionsending at n = 2
Origins · 1 minNiels Bohr and how this was discovered
NB
Niels Bohr
1885–1962 · Danish

Bohr proposed the first quantum model of the hydrogen atom in 1913, postulating that electrons orbit the nucleus only at discrete energy levels and that emission of light occurs when an electron transitions from a higher to a lower level. His formula correctly predicted the wavelengths of all known hydrogen spectral lines and introduced the concept of quantized angular momentum, earning him the Nobel Prize in Physics in 1922. Bohr was also a talented footballer (soccer player) in his youth — his brother Harald won a silver medal in football at the 1908 Olympics. The Bohr family was one of Denmark's most famous intellectual and sporting dynasties.

  • Absorption Spectra — Absorption spectra are the complementary phenomenon: electrons jumping upward by absorbing photons of the same specific wavelengths that emission spectra release, producing dark lines at identical positions.
  • Bohr Model of the Atom — The Bohr model provides the theoretical framework — quantized orbits and energy levels — that directly explains why emission spectra consist of discrete lines rather than a continuous spread.
  • Photons and Energy Quantization — Each spectral line corresponds to a photon whose energy E = hf is exactly equal to the energy difference between two atomic levels; understanding photons is prerequisite to understanding emission.
  • The Rydberg Formula — The Rydberg formula is the mathematical tool used to calculate precise wavelengths of all hydrogen emission lines across the Lyman, Balmer, Paschen, and higher series.