Walk it through, one step at a time — the live panel on the right brings every idea to life: alpha particles ricochet off a tiny nucleus, electrons leap between quantized orbits, photons fly out as coloured lines, and an X-ray tube glows. Use ▶ to play, or scroll.
1 — The nuclear atom
In 1911 Rutherford fired fast, positive alpha particles at gold foil only a few atoms thick. He expected them all to pass nearly straight through Thomson's soft "plum-pudding" atom.
- Most pass straight — the atom is mostly empty space.
- A few deflect, ~1 in 8000 bounces back — there is a tiny, dense, positive nucleus they hit head-on.
The nuclear atomnucleus ≈ 10⁻¹⁴ m · atom ≈ 10⁻¹⁰ m
nearly all the mass and all the positive charge sits in the nucleus
Exam point: Rutherford gave us the nuclear atom, but a classical orbiting electron would radiate energy and spiral in within nanoseconds — that flaw forced Bohr's new idea.
2 — The Bohr model
Bohr rescued the nuclear atom with a bold rule: the electron is allowed only certain special orbits. While it stays in one, it does not radiate — so it never spirals in.
Bohr's quantum conditionm v r = n ℏ = n h/2π (n = 1, 2, 3, …)
radius: rₙ = n² × 0.529 Å — orbits grow as n²
- Stationary states — stable orbits where the electron circles without emitting light.
- Quantum number n — labels the orbit; only whole numbers are allowed (a staircase, not a ramp).
Why "quantized"? The electron's energy can only take a fixed set of values — like steps you can stand on, never the space between.
3 — Energy levels of hydrogen
Each allowed orbit has a fixed energy. The energies are negative because the electron is bound — you must add energy to pull it free.
Hydrogen energy levelsEₙ = −13.6 / n² eV
E₁ = −13.6 eV · E₂ = −3.40 eV · E₃ = −1.51 eV · E∞ = 0
- Ground state (n = 1) — lowest, most stable, E₁ = −13.6 eV.
- Excited states (n ≥ 2) — higher rungs; the electron jumps here when given energy.
- Ionisation energy — 13.6 eV lifts the electron from n = 1 all the way to n = ∞ (free).
4 — Emission of light
When an excited electron falls from a higher level to a lower one, the atom emits a photon carrying exactly the energy difference. That is where the bright colours in a glowing gas come from.
Emissionh f = E_initial − E_final = ΔE
λ = h c / ΔE (bigger drop → shorter wavelength, bluer light)
worked — the red Balmer line (Hα)
n = 3 → n = 2 in hydrogen?
ΔE = −1.51 − (−3.40) = 1.89 eV
λ = 1240 / 1.89 = 656 nm (red)
Real life: a neon sign, a sodium street lamp's orange glow and a firework's colour are all electrons dropping down energy ladders.
5 — Absorption of light
The reverse of emission. A photon whose energy matches a gap is absorbed, lifting the electron upward. A photon of any other energy sails straight past — the atom is fussy.
AbsorptionE_photon = E_final − E_initial = ΔE
only photons with the exact gap energy are absorbed
- Resonance — absorption happens only at the same energies emission would give.
- Dark lines — cool gas absorbs those colours from white light, leaving black gaps.
Fraunhofer lines: dark lines in the Sun's spectrum reveal which gases sit in its cooler outer layers — spectroscopy reads the stars.
6 — The hydrogen line spectrum
Because only certain jumps are allowed, hydrogen emits only certain colours — a set of sharp lines, not a continuous rainbow. The lines group into families named after their final level.
| Series | Falls to | Region |
|---|
| Lyman | n = 1 | Ultraviolet |
| Balmer | n = 2 | Visible (the ones we see) |
| Paschen | n = 3 | Infrared |
Fingerprint: every element has its own unique line pattern — that is how chemists and astronomers identify what something is made of.
7 — The Rydberg formula
The wavelengths of all hydrogen lines fall out of a single formula, decades before Bohr explained why it worked.
Rydberg formula1/λ = R (1/n₁² − 1/n₂²), n₂ > n₁
R = 1.097 × 10⁷ m⁻¹ (Rydberg constant)
worked — Balmer (n₁ = 2, n₂ = 3)
1/λ = 1.097×10⁷ (1/4 − 1/9) = 1.097×10⁷ × 0.1389
1/λ = 1.524×10⁶ → λ = 656 nm (the red Hα line)
Series limit: letting n₂ → ∞ gives the shortest wavelength of each series — the high-energy edge of the barcode.
8 — Production of X-rays
X-rays are very short-wavelength, high-energy photons. In an X-ray tube, electrons are boiled off a hot filament, accelerated through a huge voltage, and smashed into a metal target.
Two ways X-rays formcontinuous (Bremsstrahlung): electron slows in the target → photon
characteristic: inner-shell vacancy is refilled → sharp X-ray line
shortest wavelength: λ_min = h c / (e V)
- Continuous spectrum — a smooth range from braking electrons, cut off at λ_min set by the tube voltage.
- Characteristic lines — sharp peaks unique to the target metal (the same level-jump idea, deep inside the atom).
Uses: medical imaging of bones, dentistry, airport scanners, and crystal X-ray diffraction.
9 — Recap · lasers & applications
Every idea here is one electron moving between quantized energy levels. Lasers push that idea further with stimulated emission: an incoming photon triggers an excited atom to emit a clone — same energy, direction and phase — giving an intense, single-colour, coherent beam.
Laser essentialspopulation inversion + stimulated emission → coherent, monochromatic beam
"LASER" = Light Amplification by Stimulated Emission of Radiation
- Rutherford: a tiny dense positive nucleus in mostly empty space.
- Bohr: electrons orbit only in quantized stationary states; m v r = n ℏ.
- Eₙ = −13.6/n² eV — a ladder, deepest at the ground state.
- Emission: electron drops, photon out, h f = ΔE; absorption is the reverse.
- Hydrogen lines group as Lyman (UV), Balmer (visible), Paschen (IR).
- Rydberg: 1/λ = R(1/n₁² − 1/n₂²) predicts every line.
- X-ray tube: fast electrons → continuous + characteristic X-rays.
- Lasers: population inversion + stimulated emission → coherent light.