Blackbody radiation · the birth of quanta simulation

Why does a hot object glow the colour it does — and why did classical physics predict it should radiate infinite energy?

▶ Run the simulationSee the measured result

Units: m·K (Wien displacement constant b; companion σ = 5.670374419e-8 W m⁻² K⁻⁴, both exact in the 2019 SI)

How the lab tests it

Plot the Planck spectral radiance B_λ(λ,T) = (2hc²/λ⁵)/(e^{hc/λk_BT}−1) for several temperatures, alongside the classical Rayleigh–Jeans curve. Then measure the laws directly: find each curve's peak wavelength numerically (Wien), integrate ∫B dλ across many temperatures and log–log fit the exponent (Stefan–Boltzmann), and compare classical vs quantum at short wavelength.

What it checks

Wien's displacement law λ_peak·T = 2898 µm·K (constant ⇒ hotter is bluer, recovered to machine precision); the Stefan–Boltzmann law P ∝ T⁴ (fitted exponent 4.000, with σ = 5.67×10⁻⁸ W m⁻²K⁻⁴ backed out); and the ultraviolet catastrophe — Rayleigh–Jeans over-predicts Planck by ~10¹¹× at 100 nm and diverges as λ→0, while Planck's quantization of energy (E=hν, so short-wavelength modes are too costly to excite) turns the curve over and keeps it finite. The 1900 result that forced energy to come in lumps and started quantum theory