Atomic spectra
Nothing movesHydrogen through a grating spectrometer: each line is an electron falling between two levels, and a graph of them gives the Rydberg constant.
Nuclear & quantum — Radioactive decay, the absorption of radiation, photons, and energy levels in the atom.
Experiments already set up on it
Measuring the Rydberg constant
The headline: 1/λ against (1/n₁² − 1/n₂²) is straight, with gradient R.
- The photon carries exactly the gap between two levels
- Which is the Rydberg formula: 1/λ = R(1/n₁² − 1/n₂²)
- So the gradient of that graph is R, and 1/n² is why the lines crowd together
Which lines can you see?
Only the Balmer series lands in the visible — the others are either side.
- Falling to n = 1 releases far more energy, so those lines are ultraviolet
- Falling to n = 3 releases less, so those are infrared
- Which is why hydrogen looks pink and not like a rainbow
The orders of the grating
A second order is further out — and sometimes there is not one at all.
- nλ = d sin θ, so each order comes further round
- Past sin θ = 1 that order does not exist, and there is nothing to measure
- A finer grating spreads the spectrum more, and runs out of orders sooner
What you can measure
Each of these can be recorded over time, aggregated over a run, or read at the moment something happens — through an instrument that carries its own uncertainty.
- Wavelengthλ (nm)
- 1/λinvlam (1/m)
- 1/n₁² − 1/n₂²term
- Angle from the gratingθ (°)
- Photon energyE (eV)
- Falls to leveln₁
- Falls from leveln₂
- Energy of the upper levelE_u (eV)
- Visible to the eyevis
What you can change
Any of these can be the thing you vary, and every combination of the ones you choose is run as its own trial.
- Falls from leveln₂
- GratingN (1/mm)
- Ordern
The equations behind it
What atomic spectra is built on. Every one of these is in the lab's formula reference too, where it copies straight into a write-up.
The nucleus
- Nuclide notation — A is the nucleon number, Z the proton number.
- Mass–energy equivalence
- Energy from a mass defect
- Nuclear radius — R₀ ≈ 1.2 fm.
- Binding energy per nucleon — The curve peaks at iron-56, which is why both fusion and fission release energy.
Quantum physics
- Energy of a photon
- Photoelectric equation — Φ is the work function.
- Work function and threshold frequency
- Stopping voltage
- de Broglie wavelength
- Energy levels of hydrogen
- Heisenberg uncertainty, position and momentum
- Heisenberg uncertainty, energy and time
- The electronvolt
Also in Nuclear & quantum
Radioactive decay
A source counted with a Geiger tube, decay by decay, with the √N scatter of real counting statistics and a background that does not decay.
Absorption of radiation
Alpha, beta and gamma through absorbers of your choosing: only one of the three is absorbed exponentially, and the counter still does not subtract the background.
Photoelectric effect
Light on a metal plate and a retarding voltage turned up until the current stops: the stopping voltage is found rather than calculated, and brightness changes nothing about it.
Muon decay & time dilation
Cosmic-ray muons counted at any altitude you like: far more arrive than a muon’s lifetime allows, and only a slow-running clock accounts for it.
Electron diffraction
Electrons accelerated through a voltage and diffracted by graphite: the rings move as 1/√V, which is de Broglie’s λ = h/p made visible.
Rutherford scattering
Alpha particles onto a thin foil, counted at an angle: the 1/sin⁴(θ/2) law is what a point nucleus gives, and a head-on alpha says how small it is.