Cloud Chamber Lab (3D)

The lab bench

The glass chamber sits on a foam box of dry ice; warm alcohol-soaked felt strips under the lid feed the vapour. Two copper coils above and below produce a vertical field whose strength and direction are shown on the power-supply screen and by the glow of the coils. Tracks are drawn at their true height inside the sensitive layer, and the Geiger counter beside the bench counts every visible event. The scene scale is 1 unit = 10 cm.

How a diffusion cloud chamber works

Alcohol vapour diffuses from a warm top towards a plate cooled by dry ice. In a thin layer just above the plate the vapour is supersaturated: it is ready to condense but has no seeds. A fast charged particle ionises air molecules along its path, and the ions seed tiny droplets, so the track appears as a thin white cloud for a second or two before the droplets fall. The slider for the layer thickness changes the chance that a particle passes through the sensitive layer at all (shown in the side view).

Bending in a magnetic field

The Lorentz force F = q v x B is perpendicular to the velocity, so it turns the track without changing the speed: r = p / (q B), or in practical units r[m] = p[GeV/c] / (0.2998 z B[T]). Positive and negative charges turn opposite ways, a 1 MeV electron in 0.5 T has r of about 1 cm, an alpha particle (z = 2, p about 200 MeV/c) has r of tens of centimetres, and a GeV cosmic muon is almost straight. Measuring r from a photograph gives the momentum, p = 0.2998 z B r, which is how particle physics identified the positron and the muon.

Range and energy loss

Alpha particles lose energy quickly and stop in a few centimetres: the Geiger rule is R[cm] = 0.31 E^1.5 (E in MeV, 4 to 7 MeV), which gives 4.0 cm for 5.49 MeV, and their thick straight tracks end abruptly. Electrons follow the Katz-Penfold range R = 0.412 E^(1.265 - 0.0954 ln E) g/cm2 divided by the air density, and are kicked sideways by multiple Coulomb scattering with angle theta = 13.6 MeV / (beta c p) * sqrt(x / X0), which makes curly, wiggly tracks. Beta decay energies are drawn from the allowed spectrum N(T) ~ p (T + m) (Tmax - T)^2. Cosmic muons (1 to 10 GeV/c here) cross the chamber in nearly straight lines and sometimes knock out a short electron (a delta ray).

Radioactive decay is random

Decays are a Poisson process: waiting times are exponential with mean 1/activity, so counts per interval have mean equal to variance. The rate histogram shows the scatter around the expected line, which is exactly what a Geiger counter does.

What is simplified

The model is two-dimensional (tracks are projected into the plate plane), the field is uniform and perpendicular to the plate, and the visibility test is a simple depth cut. Range formulas are only valid in their stated energy ranges, straggling is ignored, and beta-spectrum Coulomb corrections are omitted. Educational model with natural-background-level activities only.

What to try

• Switch on the field with the alpha needle: the thick tracks bend only slightly; with the Sr-90 source they curl into tight spirals.
• Use the Na-22 source and reverse the field sign: positrons turn the other way from electrons.
• Look at the bottom-right graph: measured momentum from track curvature scatters around the true value because of multiple scattering.
• Shrink the sensitive layer and watch the efficiency readout drop.