24 CHAPTER2. ORIGINSOFQUANTUMMECHANICS
(otherwiseitsmass,accordingtospecialrelativity,wouldbeinfinite),sothisresult
cannotpossiblybecorrect.
Planck’s contribution to this problemwas a masterpieceof what isknown in
physicsasphenomenology.Thefirststepofphenomenologyistostareatthedata,
inthiscasetheexperimentalcurveshowninFig. [2.1],andtrytofindsomesimple
analyticalexpressionthatfitsit.Planckfoundthat
E(f,T)=8 πhf^3
c^31
ehf/kT− 1(2.6)
woulddonicely,ifonechosetheconstanthtobe
h= 6. 626 × 10 −^34 J-s (2.7)Thesecondstepistotryto derivetheanalyticalexpressionforthedata,starting
fromsome simplephysical assumptionsaboutthesystem. Plancktookaimat the
equipartitionprinciple. Thisprincipleisonlyvalidiftheenergyassociatedwitheach
degreeoffreedomcantakeonanyvaluebetween 0 and∞,dependingonthephysical
state. Inelectromagnetism,theenergyofastandingwaveofagivenwavelengthis
proportionaltothesquareofitsamplitude,whichcancertainlybeanynumberinthe
range[0,∞]. Planck’ssuggestionwasthat,forsomeunknownreason,theoscillating
chargesinthewallscouldonlyemitorabsorbenergyinmultiplesofhf,wherefis
thefrequencyoftheoscillator. Thismeansthattheenergyofradiationoffrequency
fintheboxcouldonlyhavethepossiblevalues
En=nhf (2.8)wherenisaninteger. Thisassumption,combinedwiththerulesofstatisticalme-
chanics,isenoughtodeducethePlanckdistribution(2.6).
NotetheappearanceinPlanck’sformulaoftheconstanth,knownasPlanck’s
constant.Itisoneofthethreemostfundamentalconstantsinphysics,sharingthe
honorwithc,thespeedoflight,andG,Newton’sconstant.Alltheoreticalpredictions
of quantumphysics, to theextent that they disagreewithclassical physics, have
Planck’sconstanthappearingsomewhereintheexpression.
2.2 The Photoelectric Effect
ThesuccessofPlanck’sideaimmediatelyraisesthequestion:whyisitthatoscillators
inthewallscanonlyemitandaborbenergiesinmultiplesofhf?Thereasonforthis
wassuppliedbyAlbertEinsteinin1905,inconnectionwithhisexplanationof the
photoelectriceffect.
Itwas foundbyLenard, in1900,thatwhen lightshines oncertainmetals, the
metalsemitelectrons. Thisphenomenonisknownasthe photoelectriceffect, and