Atoms & Modern Physics
Drag a temperature slider from human body heat to a blue supergiant. Watch Planck's curve shift, see why classical physics predicted an ultraviolet catastrophe, and understand Wien's law and Stefan-Boltzmann in real time.
temperature slider ghumao · object ka colour + Planck curve dono live shift hote hain · UV catastrophe toggle karo
5 minutes · +4 right, −1 wrong (real NEET marking) · one global leaderboard.
Wien's displacement law states λ_max × T = 2.898 × 10⁻³ m·K, where λ_max is the wavelength of peak emission and T is the absolute temperature in kelvin. As temperature rises, the peak shifts toward shorter wavelengths — which is why hotter stars appear blue and cooler stars appear red.
The Stefan-Boltzmann law says the total radiated power per unit area of a blackbody is P = σT⁴, where σ is the Stefan-Boltzmann constant (5.67 × 10⁻⁸ W m⁻² K⁻⁴). Doubling the temperature increases the radiated power by a factor of 16, since the relationship is to the fourth power.
Classical physics (Rayleigh-Jeans law) predicted that a blackbody should emit infinite energy at short wavelengths, including the ultraviolet region. Real blackbodies do nothing of the sort — they show a finite peak and then drop off. The mismatch between theory and experiment was called the ultraviolet catastrophe.
In 1900, Max Planck proposed that energy is exchanged in discrete packets called quanta, where E = nhν. This restriction made the high-frequency modes statistically rare, so the predicted intensity dropped off at short wavelengths and matched experiment exactly. The idea launched quantum mechanics.
Wien's law gives λ_max × T = constant, so if T doubles then λ_max is halved. The peak emission wavelength shifts to half its original value. This is a frequent NEET question and the answer is always 'halved' for a doubling of absolute temperature.
If the absolute temperature of a blackbody is doubled, the wavelength of maximum emission becomes: