Quanta to Quarks Focus Area 2

Wait…Electrons are waves? In explaining the photoelectric effect, Einstein introduced a model of electromagnetic radiation that had both wave and particle properties. In 1924, Louis de Broglie proposed that this was true of all matter, and not just electromagnetic radiation. That is, objects traditionally thought of as particles also have a wave nature. In 1922 he proposed that any mass that was moving had a wavelength associated with it. According to de Broglie, if a particle had momentum mv, it had an associated matter wave with wavelength, λ.

A bit about de Broglie

De Broglie’s Equation Questions

De Broglie…You mad! De Broglie’s proposals had almost no impact on the scientific community at first. His mathematics were checked and found to be totally correct. His hypothesis was totally consistent with the Quantum Theory, and with the Bohr model. The physicists of the day, including Plank, Einstein, Rutherford and Bohr were all very interested by his work, but it was just a neat mathematical exercise, without any evidence based in experiment or observation. Usually, scientists observe a phenomenon and then try to explain it by theory. de Broglie was putting theory first, without any facts to explain!

The (Hor)Crux of the Matter de Broglie described an experiment that could be conducted to show that matter had wave properties. He suggested that electrons were the particles most likely to exhibit observable wave properties because they were the lightest particle known, so their momentum would be very small. Therefore, electrons would have a relatively large wavelength. The wavelength of the particle is important because De Broglie’s proposed experiment used the wave property of diffraction.

Diffraction…remember me? Waves are diffracted when they are transmitted through several evenly spaced gaps or reflected off several evenly spaced surfaces. (Waves are also diffracted when light passes a sharp edge.) Each gap or reflective surface behaves as a point source of light. The light emitted from each point interferes with light from the other sources to produce an interference pattern.

Diffraction occurs when the width of the point sources of light are comparable to the wavelength of the light. Atoms in many crystals are separated by a similar distance to the wavelength of electrons that de Broglie expected. Therefore, de Broglie proposed that if a beam of electrons were reflected off a crystal, an interference pattern would be detected.

Ha Ha I was right Davisson and Germer used a modified cathode ray tube to test de Broglie’s hypothesis. A beam of electrons travelling through a vacuum was allowed to strike a crystal of nickel, specially prepared so that electrons would reflect from parts of it. Different parts of the beam could then overlap their pathways as they travelled into a detection device which could measure the intensity of the beam. Result? An interference pattern was detected! This proved that electrons have wave properties, and confirmed the de Broglie hypothesis.

Bohr and de Broglie Bohr understood that electrons were only found at certain distances from the nucleus, but was unable to explain why. By realizing that electrons have a wave nature, De Broglie was able to explain why electrons were found orbiting at these specific radii, and not others.

De Broglie reasoned that electrons could only exist in certain orbits because electrons formed standing waves when the radius of orbit was an integer number of wavelengths. In these orbits an electron would constructively interfere with itself and remain in a stable orbit indefinitely. If an electron were to orbit at one of the forbidden radii it would not form a standing wave and would destructively interfere with itself.

Contributions of Heisenberg and Pauli See Surfing and KISS booklets