5.61 Fall 2007 page 1 Lecture #3 The DEMISE of CLASSICAL PHYSICS (cont’d) (a) Blackbody radiation – When heated all objects emit light! Classically: (1) (2) Radiation from a blackbody is the result of electrons oscillating with frequency ν Oscillating charged particle ⇔ antennae The electrons can oscillate (& radiate) equally well at any frequency ⇒ Rayleigh-Jeans Law for spectral density ρ(ν), where intensity of emitted light in frequency range from ν to ν + dν is I(ν) ~ ρ(ν)dν ( ) d ρ = ρ ν ,T dν = where 8π kT 2 ν dν ∝ ν 2 3 c dρ(ν,T) = density of radiative energy in frequency range from ν to ν + dν at temperature T k = Boltzmann’s constant [= R/NA (gas constant per molecule)] c = speed of light RayleighJeans Law ρ(ν ) () ρ ν ∝ ν 2 ⇒ divergence at high freq. ⇒ lots of emission in UV, x-ray regions! “UV catastrophe” – not observed in exp’t T3 T2 T1 Exp’t ν T1 < T2 < T3 5.61 Fall 2007 Planck (~1900) (1) page 2 Lecture #3 First “quantum” ideas ⇒ The energy of the oscillator ∝ frequency E∝ν (2) The energy ∝ an integral multiple of ν (the # of oscillators n) E ∝ nν or E = nhν constant hν becomes a “quantum” of energy Planck used statistical mechanics (5.62) to derive the expression for black body radiation ⎞ 8π hν 3 ⎛ 1 d ρ = ρ ν ,T dν = dν c3 ⎜⎝ ehν kT − 1⎟⎠ ( ) ∼ ν3 ρ(ν ) ⎛ ⎞ 1 ⎜⎝ ehν kT − 1⎟⎠ ν Fitting exp’t to model ⇒ h = 6.626 x 10-34 J-sec Planck’s constant 5.61 Fall 2007 (b) page 3 Lecture #3 Photoelectric effect UV light Exp’t: eK.E. = _mv2 metal Classically expect: K.E. K.E. ν I Exp’t: Opposite! K.E. K.E. I linear ν0 ν threshold Einstein (1905) proposed: (1) Light is made up of energy “packets: “photons” (2) The energy of a photon is proportional to the light frequency E = hν h ≡ Planck’s constant 5.61 Fall 2007 Lecture #3 page 4 New model of photoelectric effect: K.E. of e- E energy of photon = hν 0 φ = work function of metal K.E. = hν – φ = hν – hν0 = h(ν – ν0) ∴ K.E. ∴ K.E. = h(ν – ν0) ν0 = φ/ h ν Comparing to exp’t, value of “h” matches the one found by Planck! This was an extraordinary result ! Summary: (1) (2) (3) (4) Structure of atom can’t be explained classically Discrete atomic spectra and Rydberg’s formula can’t be explained Blackbody radiation can be “explained” by quantifying energy of oscillators E = hν Photoelectric effect can be “explained” by quantifying energy of light E = hν