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