Emission Spectra of Atoms

Continuous vs. emission spectra

A spectrum is light spread out by wavelength, usually with a prism or a diffraction grating. A hand-held spectroscope does this and lets you see the result.

The hot filament of an incandescent bulb gives a continuous spectrum: every color from red to violet, blending smoothly with no gaps.

A thin gas excited by electricity (a neon sign, a sodium lamp) gives an emission spectrum: a few thin bright lines of specific colors on a dark background.

Gas atoms are far apart, so each atom acts on its own. The light it gives off is not a smooth blend: only certain wavelengths appear. Why? The next section explains.

Energy levels and photons

Electrons in an atom cannot have just any energy. Only certain energy levels are allowed, like the steps of a staircase: you can stand on a step, but not between steps.

When an atom is excited (by heat or electric current), an electron jumps to a higher level. It soon falls back to a lower level and the atom gives off the energy difference as a single photon:

Here $E_i$ is the starting (higher) level and $E_f$ the final (lower) level. Because only certain gaps exist, only certain photon energies appear, and each energy means one color: one spectral line.

Each element has its own set of levels, so each has its own pattern of lines. That is why the pattern works as a fingerprint.

Notice that the energies are negative. Zero is the energy of a free electron, so a bound electron has less than zero. The photon energy is still the positive gap between two levels.

Photon energy, frequency and wavelength

Light with frequency $f$ comes in photons of energy $E = hf$, where $h = 6.63 \times 10^{-34}\ \text{J·s}$. Since $c = f\lambda$, we can also write $E = hc/\lambda$.

Higher frequency means shorter wavelength and more energy per photon. Along the electromagnetic spectrum, from lowest to highest photon energy: radio waves, microwaves, infrared, visible (red to violet), ultraviolet, X-rays, gamma rays.

Atomic physicists measure energies in electron-volts: $1\ \text{eV} = 1.60 \times 10^{-19}\ \text{J}$. A handy shortcut is

Counting lines and reading spectra

With more than two levels, an atom has more possible drops. An atom with levels 1, 2 and 3 can emit photons for $3 \to 2$, $2 \to 1$ and $3 \to 1$. Three drops, three lines, each with its own energy. A two-step path ($3 \to 2$ then $2 \to 1$) gives two photons, each matching its own line.

The biggest gap gives the highest-energy photon, the shortest wavelength. The smallest gap gives the longest wavelength.

Reading a spectrum. Matching a sample's lines with the known lines of an element identifies the element. Astronomers do this for starlight and nebulae, for example with telescopes in Arizona. Helium was first noticed this way, from a line in sunlight, before it was found on Earth.

A hot, thin gas gives bright lines on a dark background (emission). A cooler gas in front of a hot, bright source absorbs photons at those same wavelengths and leaves dark lines on a continuous background (absorption). The same gaps in energy levels are involved either way.

Back to the start: a gas glows in only a few exact colors because its electrons have only certain energy levels, so photons can only carry certain energies. Astronomers match those lines to elements to read the makeup of a nebula.

Summary