The failure of the classical mechanics

Transcription

1 h failur of th classical mchanics W rviw som xprimntal vidncs showing that svral concpts of classical mchanics cannot b applid. - h blac-body radiation. - Atomic and molcular spctra. - h particl-li charactr of EMR. - h photolctric ffct his will nabl us to rformulat th natur of lctromagntic radiation in trms of quantum mchanics: th photon.

2 h blac-body radiation A hot objct mits lctromagntic radiation of varying frquncis dpnding of th natur of th objct and its tmpratur. lac-body = thortical objct that absorbs and mits all radiation frquncis. As th tmpratur incrass, th pa wavlngth mittd by th blac body dcrass. As tmpratur incrass, th total nrgy mittd incrass.

3 h Rayligh-Jans law Rayligh and Jans considrd a collction of classical lctromagntic oscillators of all possibl frquncis. h radiation nrgy distribution (or dnsity), de, btwn and d at a tmpratur is givn by: 8 de d with 4 = dnsity of stats (J/m 4 ), = oltzmann s constant ( J/K), hnc de is xprssd in J/m 3 (an nrgy pr volum). From this, on could asily calculat th total radiation nrgy: E ot de dλ d incrass dcrass dcrass incrass! Ultraviolt catastroph

4 Planc s law Planc proposd that th nrgy of ach lctromagntic oscillator is limitd to non-arbitrary discrt valus (quantization of nrgy): E = nh n =, 1, 2, whr h = Planc s constant ( J s). On this basis, h drivd th Planc distribution: 8 de = d with = 5 / λ 1 Rproducs th xprimntal curvs for all wavlngths and rsmbls th Rayligh-Jans law apart from th all-important xponntial factor in th dnominator. / For short wavlngths: 1 and fastr than 5 thrfor as (or n ) For long wavlngths: 1 / 1 1 and sris xpansion givs:... 1 Classical mchanics: all oscillators shar qually in th nrgy supplid by th walls (vn highst frquncis). Quantum mchanics: oscillators ar xcitd only if thy can acquir an nrgy of at last h (too larg at high frquncis).

5 Win s displacmnt law W obsrvd that th pa wavlngth mittd, max, dcrass as tmpratur incrass. h rlation btwn max and is nown as Win s displacmnt law. Naturally, it is dducd from th condition: d/d = : dρ dλ 8 λ 7 / / 1 2 λ / 1 λ 1 1 / 5 If w dfin: x x, thn: 5 λ x 1 Numrically: x = (dimnsionlss). λ max x mk Or: λ max mk

6 h Stfan-oltzmann law W obsrvd that as tmpratur incrass, th total nrgy mittd incrass. h rlation btwn th total nrgy mittd pr unit surfac pr unit tim (th powr radiatd) and is nown as th Stfan-oltzmann law. o dfin this law, w simply hav to intgrat th nrgy dnsity ovr all wavlngths: / 5 1 λ dλ 8 dλ ρ P() h intgration is asir to prform if w convrt to : 2 d c d c Hnc: x / h dx x 8 1 d c h 8 d ρ P() h last intgral happns to b 4 /15: c () P whr = Stfan-oltzmann constant ( Js -1 m -2 K -4 )

7 Exampls of application h tmpratur of a Pahoho lava flow can b stimatd by obsrving its colour. h rsult agrs nicly with th masurd tmpraturs of lava flows at about 1 to 12 C. Mammals at roughly 3K mit pa radiation at 1 μm, in th far infrard. his is thrfor th rang of infrard wavlngths that pit vipr snas and passiv IR camras must sns. h univrsal microwav bacground radiation, originating from th ig ang, pas in powr at = 1 mm, and fits th Planc curv for a blac-body of = 2.728K to grat prcision. h solar spctrum shows max at about 5 nm, corrsponding to a surfac tmpratur of 6K. his wavlngth is (not by accidnt) fairly in th middl of th most snsitiv part of land animal visual spctrum acuity.

8 Atomic and molcular spctra Most complling vidnc for quantization of nrgy coms from spctroscopy = dtction + analysis of EMR absorbd, mittd, or scattrd by a substanc. A typical atomic spctrum: A typical molcular spctrum: Obvious fatur: radiation is mittd or absorbd at a sris of discrt frquncis. Only undrstood if th nrgy of th atoms (molculs) is also confind to discrt valus. If th nrgy is dcrasd by E, th nrgy is carrid away as radiation of frquncy, and an mission lin, a sharply dfind pa, appars in th spctrum. h atom (or molcul) undrgos a spctroscopic transition, a chang of stat, whn th ohr frquncy condition is fulfilld: E = h

9 h particl-li charactr of EMR Quantization of nrgis h, 2h, 3h, suggsts that EMR consists of 1, 2, 3, particls of nrgy h, calld photons. As xampl, lt s calculat th numbr of photons mittd by a 1 W yllow lamp, 56 nm, in 1 scond: - Each photon has an nrgy of h. - otal # of photons to produc an nrgy E is E/h. - Powr is dfind by an nrgy ovr a tim: P = E/ t. - Hnc: N E P t P t h h c / - Solving with numrical inputs yilds: N = It would ta narly 4 minuts to produc 1 mol of ths photons.

10 h photolctric ffct h photolctric ffct is th jction of lctrons from mtals whn xposd to UV radiation. Exprimntal obsrvations: 1) No lctrons ar jcts, rgardlss of EMR intnsity blow a -thrshold,, charactristic of th mtal. 2) Kintic nrgy of mittd lctrons incrass linarly with but indpndnt of EMR intnsity. 3) Evn at vry low intnsity, lctrons ar jctd immdiatly if >. From classical mchanics: I E 2, hnc intic nrgy of lctrons is indpndnt. No frquncy thrshold. Obsrvations suggst a collision with a particl-li projctil carrying nough nrgy to jct th lctron form th mtal. Consrvation of nrgy rquirs: 1 m v 2 h 2 is charactristic of th mtal, calld its wor function, that is, th nrgy rquird to rmov an lctron to infinity.