Emission spectra and models of the atom

Light carries energy in packets

Visible light is part of the electromagnetic spectrum, with wavelengths from about 400 nm (violet) to 700 nm (red). Light behaves as a wave, with $c = f\lambda$, but it also arrives in packets of energy called photons. The energy of one photon is proportional to its frequency:

$$E = hf = \frac{hc}{\lambda}$$

where h = 6.626 × 10⁻³⁴ J s (Planck's constant), c = 3.00 × 10⁸ m s⁻¹ and λ is in metres. Shorter wavelength means higher energy: a violet photon carries almost twice the energy of a red one.

How atoms emit light

An atom with all its electrons in the lowest available levels is in its ground state. Heat or an electric discharge can give an electron enough energy to jump to a higher level: the atom is now in an excited state. Excited states are unstable. Within about a hundred-millionth of a second the electron falls back to a lower level and the energy difference is released as a single photon.

Because the energy levels in an atom have fixed values, the gaps between them have fixed values too. So an element emits only certain wavelengths. Passing the light through a prism or diffraction grating spreads it into an emission line spectrum: a few bright coloured lines on a dark background. Every element's line spectrum is different, like a fingerprint. A hot solid such as a light bulb filament gives a continuous spectrum instead, containing every colour.

The reverse also happens. When white light passes through a cool gas, atoms absorb exactly the photons that match their energy gaps, leaving dark lines in a continuous spectrum: an absorption spectrum. In 1868 astronomers saw an unknown yellow line in the Sun's spectrum; the element responsible was named helium after the Greek word for the Sun, 27 years before it was found on Earth.

Flame tests

A Bunsen flame is hot enough to excite the outer electrons of some metal ions, so each gives a characteristic colour. Not every metal does: magnesium, for example, has energy gaps that correspond to ultraviolet light, so a magnesium salt leaves the flame unchanged to your eye.

The Bohr model

In 1913 Niels Bohr proposed that the electron in a hydrogen atom moves in circular orbits of fixed radius and fixed energy, labelled n = 1, 2, 3 ... An electron in an allowed orbit does not radiate energy. It absorbs or emits a photon only when it jumps between orbits, and the photon's energy equals the difference between them. Bohr calculated the energies of hydrogen's orbits and predicted the wavelengths of its spectral lines with remarkable accuracy.

Strengths: it explained why spectra are lines, gave the right wavelengths for hydrogen, and introduced quantised energy levels, which survive in all later models.

Limitations: it only worked for hydrogen and other one-electron ions; it could not explain the spectra of atoms with two or more electrons, why some lines are brighter than others, or why some lines split into closely spaced pairs; and it gave no reason why an orbiting electron should not radiate and spiral into the nucleus.

The Schrödinger model

In the 1920s Louis de Broglie suggested that electrons behave as waves, and in 1926 Erwin Schrödinger wrote an equation describing an electron as a standing wave around the nucleus. Its solutions are orbitals: three-dimensional regions in which there is a high probability of finding the electron. The model does not give the electron an exact path. Heisenberg's uncertainty principle says that is impossible anyway: you cannot know an electron's position and momentum precisely at the same time.

The solutions come out naturally in families that match the s, p, d and f subshells, with exactly the shapes and numbers of orbitals in lesson 1D. That is why the Schrödinger model, now called the quantum mechanical model, explains the spectra of all elements and the structure of the periodic table.