Energy levels and line spectra
Every element's fingerprint
- A neon sign glows red; a sodium street lamp glows orange.
- Each element gives out its own unique set of colours.
- That fingerprint comes from the atom's energy levels.
Energy levels
- An atom's electrons can only sit at certain discrete energy levels — never in between.
- Levels are written negative, with $0$ for a just-free electron; the lowest is the ground state.
Electrons in an atom can only occupy certain ____ energy levels.
The levels are discrete (quantised) — an electron cannot have an energy in between them.
Atomic energy levels are written as negative, with 0 for a just-free electron.
The most tightly bound (ground) state is the most negative; energy rises toward 0 as the electron is freed.
Emission spectrum
- An electron dropping from $E_2$ to $E_1$ emits one photon: $hf = E_2 - E_1$.
- Discrete levels → only certain photon energies → sharp bright lines on a dark background.
When an electron drops from level $E_2$ to $E_1$, the emitted photon has energy:
$hf = E_2 - E_1$ — a positive amount, since $E_2$ is the higher (less negative) level.
An electron drops from $-1.5\ \text{eV}$ to $-3.4\ \text{eV}$. What is the energy of the emitted photon?
$hf = E_2 - E_1 = (-1.5) - (-3.4) = 1.9\ \text{eV}$.
An emission spectrum looks like:
Discrete transitions give discrete wavelengths — bright lines. (Dark lines on bright is an absorption spectrum.)
Absorption spectrum
- White light through a cool gas loses the photons that match an upward jump.
- The result is dark lines on a bright background, at the same wavelengths as the emission lines.
A gas absorbs light at the same wavelengths at which it emits.
The same energy gaps work both ways — so absorption lines sit exactly where the emission lines are.
You've got it
- electrons occupy discrete energy levels (negative, 0 = free)
- emission: $hf = E_2 - E_1$ → bright lines; absorption → dark lines at the same wavelengths
- the line pattern is a unique fingerprint of the element