COMPTON
Δλ = λ_C(1−cosθ) — and the recoil electron’s E²−p² is still m², to the bit.
Use the simulation above to change the variables and play through the guided stages. The explanation below describes the default starting values; the simulation updates its explanation as you experiment.
Setup
A photon strikes an electron at rest. The wave story says the scattered light keeps its color at every angle. Compton’s 1923 photographic plates said otherwise — and with that, the photon earned its momentum.
The formula
The wavelength grows by lambda-C times one minus cosine theta — and lambda-C is not fitted here: it is hc over the electron rest energy, built from exact h and c plus the CODATA mass, matching the tabulated Compton wavelength to ten digits. The shift never asks what E₀ was; only the angle matters.
The ledger
Energy and both momentum components close simultaneously — the triangle on the right is the momentum invoice, drawn to scale. And the massenergy invariant is reused mid-collision: the recoil electron’s E squared minus p squared is still exactly m squared. It got kicked; it did not stop being an electron.
Sweeping the angle
The sweep runs theta from zero to one-eighty. At zero there is no recoil, so the electron recoil angle is not defined and is displayed as a dash. At one-eighty the wavelength shift reaches exactly two Compton wavelengths.
Audit
Audited: E₁ by the wavelength road and E₁ by the direct energy formula agree at four parts in ten to the sixteen over the whole plane; the recoil electron’s energy computed by conservation and by the invariant is bitwise identical at the defaults; the invariant residual is exactly zero there and within four parts in ten to the fifteen everywhere; and the theta-zero and theta-one-eighty branches are bit-exact identities.