Blackbody Radiation & Planck's Law

Hot objects emit thermal radiation. Classical physics (Rayleigh-Jeans) predicted that intensity would rise without limit as wavelength decreases — the "ultraviolet catastrophe."

Planck resolved it in 1900 by proposing that energy is emitted in discrete quanta E = hf. This led to the Planck law for spectral radiance:

B(λ, T) ∝ 1 / (λ^5 (e^{hc/λkT} - 1))

Key consequences:

• Wien's displacement law: λ_max * T ≈ 2898 μm·K (peak shifts to shorter wavelengths as T rises).
• Stefan-Boltzmann law: total power radiated ∝ T^4.
• Color temperature: ~3000K orange, ~5800K (Sun) white, hotter blue-white.

This was the birth of quantum mechanics. The cosmic microwave background is a 2.7 K blackbody.

Interactive goals (explorer): Drag T and see the curve, peak, and color change. Use "Find Wien Peak" and "Show UV Catastrophe" to experience the classical failure vs quantum fix. Watch photon emission rate rise dramatically with T.

JEE/NEET focus: Derive Wien and Stefan from Planck, compute λ_max for given T, relate to stellar spectra and cavity radiation experiments.