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Chapter 40

Introduction to Quantum Physics (Cont.)

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Outline

The Compton effect Compton’s scattering experiment and

results Compton shift equation and its

derivation Wave properties of particle

De Broglie wavelength for material particles and matter waves

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The Compton effect In 1923, Compton’s

experiment of x-ray scattering from electrons provided the direct experimental proof for Einstein’s concept of Photons.

Einstein’s concept of phonons Phonon energy: E = hf Phonon momentum p: = E/c =

hf/c = h/. Compton’s apparatus to study

scattering of x-rays from electrons

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Results of Compton’s scattering experiment

Experimental intensity-versus-wavelength plots for four scattering angles .

The graphs for the three nonzero angles show two peaks, one at 0 and one at ’ > 0.

The shifted peak at ’ is caused by the scattering of x-rays from free electrons.

Compton shift equation: Compton’s prediction for the shift in wavelength

’ - 0 = (h/mec)(1 – cos ). h/mec = 0.00243 nm

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Derivation of the Compton Shift Equation

Assuming that The photon is treated as

a particle having energy E = hf = hc/ and momentum p = h/.

A photon collides elastically with a free electron initially at rest – both the total energy and total momentum of the phonon-electron pair are conserved.

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The wave properties of particles

In 1923, French physicist Louis de Broglie postulated that because photons have both wave and particle characteristics, perhaps all forms of matter have both properties (Louis de Broglie won the Nobel Prize in 1929).

De Broglie suggested that material particles of momentum p and energy E have a characteristic wavelength and frequency f given by

= h/p – The de Broglie wavelength of a material particle and f = E/h.

Note: p = mv for v << c and p = mv for any speed v, where = (1-v2/c2)-1/2.

The particle and wave dual nature of matter and the matter waves.

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Example 40.8 The wavelength of an electron

Calculate the de Broglie wavelength for an electron (m = 9.11 x 10-31 kg) moving at 1.00 x 107 m/s.

As a comparison, find the de Broglie wavelength of a stone of mass 50 g thrown with a speed of 40 m/s.

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The Davisson-Germer experiment and the electron microscope

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Homework

P. 1315, Ch. 40, Problems: #22, 33, 34.