Blackbody Radiation and Wien's Law

Every object with a temperature above absolute zero emits electromagnetic radiation. A "blackbody" is an idealized object that absorbs all radiation and emits a characteristic spectrum that depends only on its temperature. The shape of this spectrum — the Planck curve — was the problem that launched quantum mechanics.

Wien's displacement law

The peak wavelength of the Planck curve shifts to shorter wavelengths as temperature increases:

$\lambda_{\max} = \dfrac{b}{T} = \dfrac{2.898 \times 10^{-3}}{T}\text{ m}$

• 3000 K: $\lambda_{\max} = 966$ nm (near-infrared — glows dull red)
• 5000 K: $\lambda_{\max} = 580$ nm (yellow-green — like the sun)
• 5778 K (sun): $\lambda_{\max} = 501$ nm (green, but appears white because of broad spectrum)
• 7000 K: $\lambda_{\max} = 414$ nm (violet — appears blue-white)

This explains why hot objects change color: dull red → orange → yellow → white → blue-white as temperature increases.

Stefan-Boltzmann law

The total power radiated per unit area increases dramatically with temperature:

$P = \sigma T^{4}$

where $\sigma = 5.67 \times 10^{-8}$ W/m²K⁴. Doubling the temperature increases radiated power by $2^{4} = 16$ times.

The ultraviolet catastrophe and Planck's solution

Classical physics (Rayleigh-Jeans law) predicted that a blackbody should emit infinite energy at short wavelengths — the "ultraviolet catastrophe." In 1900, Max Planck resolved this by proposing that light energy is emitted in discrete quanta of energy $E = hf$. This was the birth of quantum mechanics.

Try it in the visualization

Adjust the temperature slider and watch the Planck curve shift and grow. Higher temperatures push the peak leftward (shorter wavelength) and dramatically increase the total area under the curve (total power). The color swatch shows the approximate perceived color of the glowing object.