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Chapter 40

Introduction to Quantum Physics

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Outline

Blackbody radiation and Planck’s Hypothesis

The photoelectron effect

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Blackbody

Black body: A black body is an ideal system that absorbs all radiation incident on it.

Black body radiation: The electromagnetic radiation emitted by the black body is called black-body radiation.

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Black-body radiation Two experimental findings:

1. The total power of the emitted radiation increases with temperature. Stefan’s law: P = AeT4. : Stefan-Boltzmann constant = 5.670 x

10-8 W/m2·K4; e: the emissivity of the surface.

Stefan’s law for a black body: I = T4.

2. The peak of the wavelength distribution shifts to shorter wavelength as the temperature increases. Wien’s displacement law: maxT = 2.898 x 10-3 m·K.

The intensity on the y-axis is the intensity per wavelength.

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Early attempts of explanation using classical ideas

Rayleigh-Jeans law: I(, T) = 2ckBT/ 4. At long wavelengths, the Rayleigh-

Jeans law is in reasonable agreement with experimental data, but at short wavelengths major disagreement is apparent.

Ultraviolet catastrophe: the energy emitted by any black body will become infinite in the limit of zero wavelength according to classical theory – a mismatch of theory and experiment.

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Planck’s theory of black-body radiation

German Physicist Max Planck

Planck’s two assumptions concerning the nature of the atomic oscillators: The energy of an oscillator can have

only certain discrete values En: En = nhf. n: a positive integer, a quantum number

that describes an allowed state of a system; f: frequency of oscillation; h: Planck’s constant.

Energy is quantized. Quantum state. The oscillators emit or absorb energy

when making a transition from one quantum state to another. The entire energy difference in the transition is emitted or absorbed as a single quantum of radiation.

Energy-level diagram

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An energy-level diagram

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Planck’s theoretical expression for I(, T)

12

, /5

2

Tkhc Be

hcTI

h: Planck’s constant (a fundamental constant of nature). h = 6.626 x 10-34 J·s

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The photoelectric effect

Photoelectric effect: Light incident on certain metallic surfaces causes electrons to be emitted from those surfaces.

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Features of the photoelectric effect

1. Dependence of photoelectron kinetic energy on light intensity

Experimental result: The maximum kinetic energy of photoelectrons is independent of light intensity.

2. Time interval between incidence of light and ejection of photoelectrons

Experimental result: Electrons are emitted from the surface of the metal almost instantaneously, even at very low light intensities.

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Features of the photoelectric effect (Cont.)

3. Dependence of ejection of electrons on light frequency

Experimental result: No electrons are emitted if the incident light frequency falls below some cutoff frequency fc, of which the value depends on the material.

4. Dependence of photoelectron kinetic energy on light frequency

Experimental result: The maximum kinetic energy of the photoelectrons increases with increasing frequency.

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Einstein’s explanation of the photoelectric effect Photons: Einstein assumed that light (or

any other electromagnetic wave) of frequency f can be considered a stream of quanta, regardless of the source of the radiation. These quanta are called photons. Energy of each photon: E = hf.

Einstein’s model of photoelectric effect: A photon of the incident light gives all its energy hf to a single electron in the metal. The energy transfer is accomplished via a one

photon-one electron event.

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The maximum kinetic energy of photoelectrons

Kmax = hf - : the work function of the metal.

The work function represents the minimum energy with which an electron is bound in the metal.

Einstein’s model predicts a linear relationship between Kmax and the light frequency f, which is confirmed by experimental observation.

Cutoff frequency fc and cutoff wavelength c: fc = /h and c = hc/.

Stopping potential Kmax = e Vs.

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An application of photoelectric effect – the photomultiplier tubes

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Homework

Ch. 40, P. 1314, Problems: #2, 4, 14.