De Broglies original idea

De Broglie had suggested that the wavelength of these matter waves, could be evaluated from the same relationship which exists between the wavelength of light and the energy of a photon. As we know, and will further discuss in Section 13.2, a photon has energy E = hf, and momentum p = hf/c = h/A; similarly, matter waves of a particle of momentum p should have a wavelength A = h/p. The propagation of these matter waves, according to de Broglie, governs the motion of the particle, with the consequence that under the right conditions particles such as electrons should exhibit 'wave phenomena' such as interference and diffraction!

The de Broglie wavelength of even the tiniest particles in the household world is so short that their wave characteristics are impossible to demonstrate. For example, let us calculate the wavelength of the matter wave of a mosquito of mass 1/100 of a gram moving with a speed of 10 ms-1:

Louis de Broglie (1892-1987)

l = h = 6-63¥ 10"34 = 6.63 ¥ 10"30m p 10-5 x 10

which is 20 orders of magnitude smaller than the diameter of an atom.

In the case of electrons, however, the wavelength of the matter wave is similar to that of X-rays, which is of the order of the separation of atomic planes in a crystal. A beam of electrons should therefore undergo diffraction in the same way as a beam of X-rays.

De Broglie presented his ideas in a doctoral thesis to the University of Paris in November 1924. The examining committee were highly impressed by the originality of his ideas, but did not really believe in the reality of the proposed waves. When asked whether their existence could be experimentally verified, De Broglie replied that this should be possible in diffraction experiments of electrons by crystals. Neither he nor the examiners were aware of the fact that such evidence already existed, but had not been recognised. For example, in a paper by C.J. Davisson (1881-1958) and C.H. Kunsman on 'the scattering of electrons by nickel' published in 1921, examination of experimental figures with hindsight clearly shows a peak due to diffraction. The first official recognition of electron waves came in 1927, in a paper by Davisson and Lester H. Germer (1896-1971) entitled 'Diffraction of Electrons by a Crystal of Nickel'.

In 1928, George Paget Thompson (1892-1979), working at Cambridge, was able to secure diffraction patterns by passing narrow beams of electrons through thin sheets of matter. The electrons, when they reached a photographic plate, created a pattern of concentric rings very similar to the patterns made by X-rays. Matter waves interfere in the same way as light waves. Figure 12.2 shows the resulting patterns of X-rays (left) and

Light (X-rays) Electrons

Figure 12.2 Diffraction patterns.

Light (X-rays) Electrons

Figure 12.2 Diffraction patterns.

electrons (right) passing through the same thin sheet of aluminium foil.

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