Analyze experimental evidence about black body radiation, including Wien's displacement law related to Planck's contribution to a changed model of light.
Formula: (\lambda_{max} = \frac{b}{T})_
Black Body Radiation
Definition: An ideal object that absorbs all radiation within its vicinity.
At thermal equilibrium, it emits radiation equal to what it absorbs.
Example: A large box with a small hole acts as a near-perfect black body.
Experiment: Wien and Lummer measured radiation from a black-body-like oven.
Classical Theory of Electromagnetic Radiation
Rayleigh-Jeans Law
Intensity of black body radiation is directly proportional to frequency.
Assumes radiation is continuous and not discrete.
Predicts continuous radiation emission, which violates the Law of Conservation of Energy.
Ultraviolet Catastrophe
Classical model predicts infinite energy emission, which is incorrect.
Validity declines for frequencies above (10^{17}) Hz.
Resolution by Planck
Proposed energy is quantized, not continuous.
Energy of light: (E = nhf), where (h) is Planck's constant and (f) is frequency.
Energy emitted by black bodies is finite.
Wien's Displacement Law
Builds upon Planck's theory.
Black-body radiation peaks at different wavelengths for different temperatures:
Formula: (\lambda_{max} = \frac{b}{T})
(b) is Wien's constant: (2.898 \times 10^{-3}) m K_
Applications of Wien’s Law
Stellar Emission: Stars' emission depends on surface temperature.
Mammals: Emit infrared radiation at body temperature (~300 K).
Fire: Radiation peaks around 2000 nm due to temperature (~1500 K).