Modern Physics

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Contains: (Blackbody radiation, photoelectric effect, Compton effect)

2.1: Blackbody radiationA significant hint of the failure of classical physics arose from investigations of thermalradiation (Planck, 1900).According to Einstein (1905) electromagnetic radiation is quantized in photons.

1. Photons and Plancks quantum of action:Photons () : The energy quanta of the electromagnetic fieldPhoton energy (EPh) : It is proportional to the frequency f or the angular frequency =2 f . Usually it is givenin electron volts (eV),

PhE hf

Photon momentum ( PhP

): It is proportional to the wave number vector 2k with , isk

the wavelength

of the electromagnetic radiation),

Ph PhP k, P / k h

The vector k

points along the propagation direction of the electromagnetic radiation.

Plancks quantum of action: An universal constant,346.626 10 ,h Js

34 221.0545 10 6.5821 10 .2h Js MeV s

Particle Properties of Wave

Chapter-1


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2. Thermal radiation and the blackbody radiator:Thermal radiation, temperature radiation, the electromagnetic radiation of a body at finite temperature. Thebody also absorbs a fraction of the thermal radiation from its environment. There is a permanent exchange ofenergy between the body and its environment.

In the end, this process leads to temperature equilibrium. Blackbody radiator, a body with the reflectancezero. A blackbody absorbs any incident radiation completely.

Cavity radiator model of a blackbody radiator (Fig. 2.1): a box with a small aperture in the wall. The wallis impenetrable for radiation from inside (ideally reflecting) and has a denite temperature. The probability thata photon enters the cavity through the aperture and, after multiple reflection by the inner walls, leaves thecavity through the aperture again, is negligible (absorptance = 1). The aperture appears absolutely black.Cavity radiation, the thermal radiation leaving the aperture of a cavity radiator. The spectral distribution of theradiation energy density of the cavity radiation depends on the temperature of the cavity radiator. According to Kirchhoffs law (The absorptance is equal to the emittance), the spectral radiance Le, f of an

arbitrary thermal radiator may be reduced to that of a black body.For the radiation field in the interior of the cavity, one denes

3. Plancks radiation law:This law describes the frequency and temperature dependence of the radiant energy density of the cavityradiation:

4. Connection between radiant energy density and frequency:The dependence of the spectral radiant energy density of the cavity radiation on the angular frequency orwavelength reads as follows:

1, , . . , ,2f f

dfu T u f T u f Td


3

3 2

2 3 /

1, , , , . . ,1 f fkT

df fu T u T u f T u f Tc d ce

5 /8 1,

1hc k Thcu T

e

5. Wiens displacement law and limiting cases of Plancks formula: Wiens law: for hf >> kT

3

3

8,hfkT

ff hu f T e

c

Rayleigh-Jeans law: for hf


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2.2 Photoelectric Effect:Photoeffect- photons eject electrons from a material.

1. Properties of photoelectronsElectrons emitted, from metal when the frequency of light was sufficiently high, this phenomena is calledphotoelectric effect. And the emitted electrons are called photo-electrons.Light waves carry energy, and some of the energy absorbed by metal may somehow concentrate on individualelectrons and reappear as their kinetic energy.Photoelectric Einstein equation, describes the kinetic energy Ekin of electrons ejected from the body by theincident radiation:

The kinetic energy of the photoelectrons depends on the frequency of the incident radiation, but not on theradiation intensity (Fig. 2.3). The radiation intensity determines only the intensity of the photocurrent (Fig. 2.4).

2. Work functionWork function, WA, the minimum energy required for the ejection of an electron from a material. The workfunction typically amounts to several electron volts.

Work function WA of several elements (in eV): K 2.30, Na 2.75, Hg 4.49, Ge 5.0.For any material there isa threshold frequency for the photoeffect (red limit). Below this threshold frequency f0, no photoeffect occurs(Fig. 2.3):

0AWf

h

(Figure 2.3: Left: experimental set-up for measuring the photoelectricffect. Right: dependence of the kineticenergy of photoelectrons on the frequency f of the incident radiation.). The chemical structure and surface properties determine the work function WA, and hence the thresholdfrequency f0. The photoeffect may be explained only in the framework of the photon model of electromagneticradiation.


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When a suppression voltage is applied, the photocurrent vanishes at a threshold voltage VG, which is related tothe maximum velocity maxv of the photoelectrons by

2max/2GeV mv . The quantum of action h can be

determined by measuring the incident frequency f and the threshold voltage GV . The measurement yields alinear relation between the suppression voltage at which the photocurrent vanishes, and the frequency (Fig.2.3). The slope of the straight line yields Plancks constant, or quantum of action, /Gh e dV df .

(Figure 2.4: Photocurrent I as function of the applied voltage V for different intensities I of the incident radiation.)

2.3: Compton Effect1. Scattering of photons by electronsCompton effect, a shift of the wavelength (and hence the frequency) in the elastic scattering of photons by freeelectrons. The shift increases with the scattering angle, but does not depend on the wavelength of the incidentradiation (Fig. 2.5):

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Modern Physics