Blackbody Radiation
What is light? #
This story was thought to be complete, i.e., light consisted of EM waves that obeyed Maxwell’s theory.
This turned out to not be the complete story.
Blackbody #
The ability of a body to radiate is closely related to its ability to absorb radiation
Blackbody: An ideal body that absorbs all radiation incident upon it, regardless of frequency.
Blackbody radiation #
Examined by Lord Rayleigh and James Jeans.
They considered radiation inside a cavity of temperature T(absolute) to be a series of standing EM waves.
- Density of standing waves in cavity: $G(v)dv=\frac{8\pi v^2 dv}{c^3}$
- Average energy per standing wave $\bar{ϵ}=\frac{1}{2}kT*2=kT$.
- One dimensional harmonic oscillator has 2 deg of freedom: Kinetic energy + Potential energy
Rayleigh-Jeans formula: $$u(v)dv=\frac{8\pi v^2 kT}{c^3}$$
For small ‘v’ it works but as v→∞, energy density→∞ but it should actually fall to 0.
Planck Radiation Formula #
Max Planck’s “lucky guesswork”
The oscillators in the cavity walls must have only specific energies $\epsilon _n=nhv$
- Actual average energy per standing wave: $\epsilon =\frac{hv}{e^{hv/kt}-1}$
Plank’s radiation formula: $$ u(v)dv=\frac{8\pi v^2}{c^3}\cdot \frac{hv}{e^{hv/kt}-1} $$