All Labs

Blackbody Radiation Lab

Investigate how hot objects emit radiation across all wavelengths. Adjust temperature to see the glowing object change color, watch the spectral curve shift according to Planck's quantum law, and compare it with the classical Rayleigh-Jeans prediction that famously diverges at short wavelengths.

Guided Experiment: Wien's Displacement Law

If you double the temperature of a blackbody, what do you predict will happen to the peak wavelength of emitted radiation?

Write your hypothesis in the Lab Report panel, then click Next.

Controls

Temperature5,778 K
300 K15,000 K
Emissivity1.00

Results

Approximate blackbody color at 5,778 K
λmax⁡=bT=2.898×10−35778≈501.6 nm\lambda_{\max} = \frac{b}{T} = \frac{2.898 \times 10^{-3}}{5778} \approx 501.6\text{ nm}
Peak Wavelength
501.6 nm
Visible
Total Power
6.320e+7 W/m²
Temperature
5,778 K
Emissivity
1.00
Stefan-Boltzmann Law
P=εσT4=6.320e+7W/m2P = \varepsilon \sigma T^4 = 6.320e+7 W/m²

Spectral Radiance vs Wavelength

Planck (quantum)Wien's peak

Data Table

(0 rows)
#TrialTemperature(K)Peak Wavelength(nm)Total Power(W/m²)Emissivity
0 / 500
0 / 500
0 / 500

Reference Guide

Planck's Law

Max Planck resolved the ultraviolet catastrophe in 1900 by proposing that electromagnetic energy is emitted in discrete quanta. The spectral radiance of a blackbody depends on both wavelength and temperature.

B(λ,T)=2hc2λ5⋅1ehc/λkBT−1B(\lambda, T) = \frac{2hc^2}{\lambda^5} \cdot \frac{1}{e^{hc/\lambda k_B T} - 1}

Where h = 6.626 × 10⁻⁵⁴ J·s (Planck constant), c = 3 × 10⁸ m/s, and k₂ = 1.381 × 10⁻²³ J/K (Boltzmann constant). The curve peaks, then falls to zero at short wavelengths — the quantum correction that classical physics missed.

Wien's Displacement Law

The peak wavelength of blackbody emission shifts inversely with temperature. Hotter objects emit at shorter (bluer) wavelengths.

λmax⁡=bT,b=2.898×10−3 m\cdotK\lambda_{\max} = \frac{b}{T}, \quad b = 2.898 \times 10^{-3} \text{ m\cdot K}

The Sun's surface at 5778 K peaks near 502 nm (visible green). A room-temperature object (300 K) peaks near 9660 nm, deep in the infrared — invisible to the eye but detectable with thermal cameras.

Stefan-Boltzmann Law

The total power radiated per unit area by a blackbody scales dramatically with temperature — a T⁴ relationship. Doubling temperature increases radiated power by a factor of 16.

P=εσT4,σ=5.670×10−8 W m−2K−4P = \varepsilon \sigma T^4, \quad \sigma = 5.670 \times 10^{-8} \text{ W m}^{-2} \text{K}^{-4}

Emissivity ε = 1 for an ideal blackbody. Real materials have ε < 1. This law explains why stars much hotter than the Sun emit vastly more energy per unit area, and is fundamental to climate science and stellar astrophysics.

The Ultraviolet Catastrophe

Classical physics predicted that a blackbody should radiate infinite energy at short wavelengths — the Rayleigh-Jeans law. This failure, called the ultraviolet catastrophe, showed that classical mechanics was incomplete.

BRJ(λ,T)=2ckBTλ4→∞ as λ→0B_{\text{RJ}}(\lambda, T) = \frac{2ck_BT}{\lambda^4} \to \infty \text{ as } \lambda \to 0

Toggle "Show Rayleigh-Jeans curve" in the lab to see this divergence. The classical curve matches Planck's only at long wavelengths, then shoots upward at the short end, while Planck's quantum formula correctly predicts a peak followed by a drop to zero.