Atomic Spectra

Rutherford's nuclear atom had a fatal flaw. An electron orbiting a nucleus is accelerating, and classical physics says an accelerating charge radiates energy — so it should spiral into the nucleus within a fraction of a second. Atoms plainly do not do this.

Bohr's answer was that an electron may only occupy certain allowed energy levels. In those levels it does not radiate. It can move between them, but it cannot exist anywhere in between.

The levels are conventionally given negative energies, with zero taken as the electron being completely free of the atom. So the ground state — the lowest level, the one the electron normally sits in — is the most negative, and an electron at −13.6 eV in hydrogen needs 13.6 eV supplied to escape entirely. That figure is the ionisation energy.

Levels crowd closer together as they rise, converging on zero. That crowding is directly visible in the spacing of spectral lines.

Electrons sit in defined shells, never between them. Adding protons pulls the shells inward — more nuclear charge binds the electrons more tightly, which is why every element has its own set of levels and therefore its own spectrum.

Give an atom energy — by heating it, or passing a current through a gas — and an electron jumps to a higher level. It does not stay there. Within nanoseconds it falls back, and the energy it loses is emitted as a single photon.

Because the levels are fixed, the energy difference is fixed, and so is the photon's frequency. That is why the light from an excited gas is not a continuous rainbow but a set of sharp bright lines at particular wavelengths, with darkness between them.

Each element has its own arrangement of levels, so each produces its own unique pattern of lines. The pattern is a fingerprint: helium was identified in the Sun's spectrum in 1868, nearly thirty years before anyone found it on Earth.

A larger jump gives a more energetic photon and therefore a shorter wavelength. Jumps down to the ground state in hydrogen produce ultraviolet; jumps down to the second level produce the visible red, blue-green and violet lines you see in a discharge tube.

ΔE

energy difference between levelsJ or eV

h

6.63 × 10⁻³⁴J s

f

frequencyHz

λ

wavelengthm

Run white light — which contains every wavelength — through a cool gas, and the reverse happens. An atom can absorb a photon only if its energy matches a gap between levels exactly. Photons of any other energy pass straight through.

The wavelengths that do match are removed, leaving dark lines in an otherwise continuous spectrum. Those dark lines fall at exactly the same wavelengths as the bright lines that element emits, because the same energy gaps are responsible for both.

This is how the composition of stars is known. Light from a star's hot interior is continuous; passing out through the cooler outer atmosphere, particular wavelengths are absorbed by the elements there. The dark lines in sunlight — Fraunhofer lines — identify hydrogen, helium, sodium, calcium and iron in the Sun.

It is a remarkable thing to be able to say. Nobody has ever brought back a sample of the Sun, and yet we know what it is made of, because energy levels are the same everywhere in the universe.

The existence of line spectra is evidence for two things at once, and it is worth being able to state both.

First, that energy levels in atoms are discrete. If an electron could have any energy, the differences could take any value and the spectrum would be a continuous smear. Sharp lines mean sharp levels.

Second, that light is emitted and absorbed in quanta. A single jump produces a single photon of a definite energy — the particle picture from the previous chapter, now visible in a discharge tube.

The two chapters are really one argument. The photoelectric effect showed light arrives in packets; line spectra show that the atoms it comes from have discrete levels. Together they are the foundation of quantum physics.