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The de Broglie hypothesis The wavelength of electrons Additional questions |
The electron microscope |
 Data Glossary |
| Learning Outcomes | ||
| After studying this section, you will know about the wave nature of matter. | ||
The photoelectric effect demonstrated that light waves do, in certain experiments, behave as if they were massless particles. These particles are called PHOTONS. The apparent dual nature of light, wave properties on the one hand and the dynamic properties of moving particles on the other, was a baffling question in physics early in the 20th century. The question arose - why should particles not behave as waves?
The French theoretical physicist Louis de Broglie showed in 1924 that matter could possibly have wave properties. If this were so, a moving particle having momentum p would have a wavelength given by the expression:
where h is Planck's constant ( = 6.626x10-34 J.s-1), c the speed of light in a vacuum ( = 3.00x108 m.s-1), m the mass of the particle. The wavelength, λ, is called the DE BROGLIE WAVELENGTH
For objects moving at speeds well below the speed of light (
), the term (1 - v²/c²)½ ≅ 1. The wavelength in such cases is far too short to be measured. Experiments carried out with electrons beams soon confirmed the validity of the de Broglie hypothesis.
Davisson and Germer showed experimentally that electrons could be diffracted, and that therefore electrons behaved as waves. It should then be possible to calculate the wavelength, λ, of electrons, using de Broglie's equation λ = h/p, where h is Planck's constant, and p, the momentum of the electrons. For electrons accelerated through a potential difference of V volts, the wavelength is given by
From the above equation (), where me is the electron mass and e the electron charge, we see that the wavelength of a beam of electrons is inversely proportional to the square root of the potential difference through which the electrons have been accelerated. One can therefore vary the wavelength by altering the applied voltage.
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What experiments showed that electrons behaved as waves? (Click here for a discussion) |
In 1927-1928, that is just three years after Be broglie published his theoretical work, two separate experiments were carried out that conclusively proved that an electron beam had typical wave-like behaviour.
Electrons from an electron source were accelerated towards a positive electrode into which was drilled a small hole. The resulting narrow beam of electrons was directed towards a thin film of nickel. The lattice of nickel atoms acted as a diffraction grating, producing a typical diffraction pattern on a screen.
The wavelength of the electrons was calculated, and found to be in close agreement with that expected from the De Broglie equation.
In this experiment, a beam of electrons is directed onto the surface of a nickel crystal. Electrons are scattered, and are detected by means of a detector that can be rotated through an angle q. When the angle was 52o, the Bragg condition mλ = 2d sin q was satisfied (d is the distance tween the nickel atom, and m and integer = 1), and constructive interference produced peaks of high intensity. Again, the wavelength of the electrons was calculated, and found to be in close agreement with that expected from the De Broglie equation.
Thomson and Davisson shared the Nobel Prize for Physics in 1937.
