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.
Nuclear & quantum — Radioactive decay, the absorption of radiation, photons, and energy levels in the atom.
Experiments already set up on it
Gamma through aluminium
The headline: ln R against thickness is straight, with gradient −μ.
- I = I₀e^{−μx}, so ln I against x is straight with gradient −μ
- The half-value thickness is ln2/μ
- The background must come off before the log is taken
Why lead?
The same gamma through lead: a few millimetres do what centimetres of aluminium did.
- μ depends on the material, and on its density most of all
- Comparing half-value thicknesses is comparing shielding
An alpha has a range
Not a curve — a cliff. A few centimetres of air stop it completely.
- An alpha loses energy steadily and then stops: it has a definite range
- So the count does not fall exponentially, and μ means nothing for it
- Past the range the counter reads the background, not zero
Beta through aluminium
Roughly exponential — and then it stops too, at about four millimetres.
- Beta is in between: nearly exponential over most of its path
- But it has a range as well, so the log plot breaks away at the end
- Which is why beta is described by a range and gamma by a coefficient
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.
- Timet (s)
- Counts so farN
- Count rateR (1/s)
- Counting time so fart_c (s)
- Fraction getting throughT
- Mass thicknessrx (g/cm^2)
- Attenuation coefficientmu (1/mm)
- Half-value thicknessxh (mm)
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.
- Decays reaching the absorberA (1/s)
- Thicknessx (mm)
- Efficiency of the tubeε
- Background rateR_b (1/s)
- Count fort_g (s)
The equations behind it
What absorption of radiation 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.
Radioactive decay
- Number of nuclei remaining
- Activity
- Activity with time
- Half-life
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.
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.
Atomic spectra
Hydrogen through a grating spectrometer: each line is an electron falling between two levels, and a graph of them gives the Rydberg constant.
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.