Matter Waves Louis de Broglie 1892-1987

Matter Waves Louis de Broglie was a physics graduate student when he suggested that matter had a wave nature. Recall that EMR acts as a wave in some experiments; diffraction, refraction, interference EMR also acts like a particle; photoelectric effect, momentum

Matter Waves De Broglie stated that since EMR has momentum and acts like a wave, perhaps matter, which has momentum, also acts like a wave. • He used Compton’s momentum of EMR formula, p=h/λ and equated it to the formula for momentum of matter, p=mv

De Broglie wave equation De Broglie wavelength is more significant for small masses traveling at high speeds rather than large masses traveling at low speeds

Matter Waves Matter waves have the wavelength of

Matter Waves This was not a popular idea. In fact, de Broglie’s thesis was held up until Einstein reviewed his work and agreed with it. To prove the existence of such waves is very difficult because they are so small.

Example Calculate the wavelength of a 50 kg skier moving at 16 m/s.

Solution

This means what? This wavelength (8.3 x 10-37 m) is about a billion, trillion times smaller than a hydrogen atom! This wavelength is so small that it is completely unobservable.

Examples Calculate the wavelength of an electron moving at 1.0 x 106 m/s.

Solution

What does this mean? This wavelength (7.3 x 10-10 m) is in about the same wavelength of x-rays. This is observable.

Eg) Determine the De Broglie wavelength for an alpha particle traveling at 0.015c.

Eg) An electron is accelerated by a potential difference of 220V Eg) An electron is accelerated by a potential difference of 220V. Determine the De Broglie wavelength for the electron.

Davisson-Germer Experiment • Soon after de Broglie’s idea was presented, Davisson and Germer observed evidence that beams of e¯ fired at the crystal lattice of metals diffract to produce nodes and ant- nodes. • See pages 729 and 730.

Example In the last example, the wavelength is roughly equal to the spacing between atoms in a crystal lattice. A wave going through slits equal to or smaller than the wavelength results in a wave interference pattern.

- Like these water waves

If this is extended to three dimensional grating, such as an atomic lattice, a pattern of concentric circles should be observed.

This is what is observed when a beam of electrons is passed through a salt crystal.

Technology as a Result This theory and the supporting experiments lead to the development of the electron microscope. http://www.mos.org/sln/sem/seminfo.html

2 D Scattering An incident photon with a wavelength of 4.50 x 10-11 m collides with an electron that is at rest. The photon is scattered at an angle of 62.0° and has a final momentum and energy. 62.0° λ = 4.50 x 10-11 m

What is the momentum and the velocity of the scattered electron?

Show that energy is conserved.

Assignment Read p. 726-733 Do p. 297 #2-7 in Workbook