Particle Properties of Wave

Transcription

1 1 Chapter-1 Partile Properties o Wave Contains: (Blakbody radiation, photoeletri eet, Compton eet).1: Blakbody radiation A signiiant hint o the ailure o lassial physis arose rom investigations o thermalradiation (Plank, 1900). Aording to Einstein (1905) eletromagneti radiation is quantized in photons. 1. otons and Plank s quantum o ation: otons (γ) : The energy quanta o the eletromagneti ield oton energy (E ) : It is proportional to the requeny or the angular requeny ω =π. Usually it is given in eletron volts (ev), oton momentum ( E h ω P ): It is proportional to the wave number vetor k o the eletromagneti radiation), P k, P k h/ The vetor k points along the propagation diretion o the eletromagneti radiation. Plank s quantum o ation: An universal onstant, h Js, h Js MeV s. k with, is the wavelength

2 . Thermal radiation and the blakbody radiator: Thermal radiation, temperature radiation, the eletromagneti radiation o a body at inite temperature. The body also absorbs a ration o the thermal radiation rom its environment. There is a permanent exhange o energy between the body and its environment. In the end, this proess leads to temperature equilibrium. Blakbody radiator, a body with the reletane zero. A blakbody absorbs any inident radiation ompletely. Cavity radiator model o a blakbody radiator (Fig..1): a box with a small aperture in the wall. The wall is impenetrable or radiation rom inside (ideally releting) and has a deûnite temperature. The probability that a photon enters the avity through the aperture and, ater multiple reletion by the inner walls, leaves the avity through the aperture again, is negligible (absorptane α = 1). The aperture appears absolutely blak. Cavity radiation, the thermal radiation leaving the aperture o a avity radiator. The spetral distribution o the radiation energy density o the avity radiation depends on the temperature o the avity radiator. Aording to Kirhho s law (The absorptane is equal to the emittane), the spetral radiane L e, o an arbitrary thermal radiator may be redued to that o a blak body. For the radiation ield in the interior o the avity, one deûnes. Plank s radiation law: This law desribes the requeny and temperature dependene o the radiant energy density o the avity radiation: 4. Connetion between radiant energy density and requeny: The dependene o the spetral radiant energy density o the avity radiation on the angular requeny ω or wavelength λ reads as ollows: d 1 u, T u, T.. u, T, d

3 1 d u T u T u / kt T u T e 1 d,,,,.., 8 h 1 u, T 5 h/ kt e 1 5. Wien s displaement law and limiting ases o Plank s ormula: Wien s law: or h >> kt 8 h u, T e Rayleigh-Jeans law: or h << kt h kt 8 u, T kt Wien s displaement law: With inreasing temperature, the maximum o the spetral radiant energy density u (,T) is shited to higher photon energy, i.e., to higher requenies (shorter wavelengths) (Fig..) (Figure.: Radiant energy density u (, T ) or various temperatures aording to Plank s radiation law. Dashed-dotted line: Rayleigh-Jeans law.) 6. Stean-Boltzmann law: Integration o the spetral radiant energy density over all requenies yields the total radiant lux tot o a radiation emitted by an area A. The total radiant ûux tot is proportional to the ourth power o the temperature T.

4 . otoeletri Eet: otoeet- photons ejet eletrons rom a material. 1. Properties o photoeletrons Eletrons emitted, rom metal when the requeny o light was suiiently high, this phenomena is alled photoeletri eet. And the emitted eletrons are alled photo-eletrons. Light waves arry energy, and some o the energy absorbed by metal may somehow onentrate on individual eletrons and reappear as their kineti energy. otoeletri Einstein equation, desribes the kineti energy E kin o eletrons ejeted rom the body by the inident radiation: 4 The kineti energy o the photoeletrons depends on the requeny o the inident radiation, but not on the radiation intensity (Fig..). The radiation intensity determines only the intensity o the photourrent (Fig..4).. Work untion Work untion, WA, the minimum energy required or the ejetion o an eletron rom a material. The work untion typially amounts to several eletron volts. Work untion WA o several elements (in ev): K.0, Na.75, Hg 4.49, Ge 5.0.For any material there is a threshold requeny or the photoeet (red limit). Below this threshold requeny 0, no photoeet ours (Fig..): 0 W A h (Figure.: Let: experimental set-up or measuring the photoeletriet. Right: dependene o the kineti energy o photoeletrons on the requeny o the inident radiation.). The hemial struture and surae properties determine the work untion W A, and hene the threshold requeny 0. The photoeet may be explained only in the ramework o the photon model o eletromagneti radiation.

5 When a suppression voltage is applied, the photourrent vanishes at a threshold voltage V G, whih is related to the maximum veloity v max o the photoeletrons by evg mv max/. The quantum o ation h an be determined by measuring the inident requeny and the threshold voltage V G. The measurement yields a linear relation between the suppression voltage at whih the photourrent vanishes, and the requeny (Fig..). The slope o the straight line yields Plank s onstant, or quantum o ation, h e dv / d. G 5 (Figure.4: otourrent I as untion o the applied voltage V or dierent intensities I o the inident radiation.).: Compton Eet 1. Sattering o photons by eletrons Compton eet, a shit o the wavelength (and hene the requeny) in the elasti sattering o photons by ree eletrons. The shit inreases with the sattering angle, but does not depend on the wavelength o the inident radiation (Fig..5):