Compton Effect de Broglie Wavelengths The same things but backwards.

Compton Effect Light behaves as a wave when dealing with refraction but as a particle when dealing with the photoelectric effect. Einstein had proposed his photon model in 1905 with the PE effect, but it took until 1923 for the theory to gain widespread acceptance. Arthur Compton (American) used the particle model to explain x-ray scattering from graphite in 1923.

Compton Effect Compton found that energy and momentum were conserved when x-rays were scattered from a thin metal foil. Some x-rays passed straight through (lots of empty space in the atom!) Some x-rays were scattered and lost energy (and therefore frequency) and were detected with a larger wavelength at some new scattered angle.

Compton Effect In an experiment by Compton, an x-ray would collide with an electron at rest (assumed), which causes the electron to recoil at one angle and the x-ray at another like a billiard ball collision. Energy conservation yields: hƒ = hƒ’ + Ek, where the incident photon energy is hƒ, the scattered photon energy is hƒ’ and the electron’s recoil kinetic energy is Ek. Mom of incident photon = mom of scattered photon + mom of recoil electron

Compton Effect A new formula has to be developed for photon momentum as photons have no rest mass, so p = mv can NOT be used. Combining p = mv and E = mc2; yields E = pc As E = hc/λ then we can also obtain p = h/ λ

Compton Effect The momentum of photons can be applied for space travel with solar sails. The solar sail would have to be designed to give the largest momentum change (and largest impulse as a result) to propel a craft. (It would have to be shiny and not black).

Compton Effect Example Find the energy and momentum of a 48.7 nm photon.

De Broglie Wavelength In 1924, Louis de Broglie suggested that as light waves could exhibit particle-like behaviour then matter particles should exhibit wave-like behaviour! De Broglie suggested that the same relationship found by Compton could be used to find the wavelength of a particle of matter moving with a velocity v: p = h/λ λ = h/p λ = h/mv

De Broglie Wavelength Confirmation of this proposal was accomplished in 1927 by Davisson and Germer (diffraction pattern of electrons with crystals) and independently in the same year by GP Thomson (interference pattern of electrons). A scanning electron microscope (SEM) uses the wave nature of electrons to reveal highly detailed images of small objects

De Broglie Wavelength

De Broglie Wavelength The de Broglie wavelength is only measurable for very small objects (like electrons) moving at non-relativistic speeds. (A baseball thrown at 99 mph has a de Broglie wavelength but is too small to even detect). The de Broglie wavelength plays a significant part in the atom as electron’s wavelengths must be incorporated into the atomic model. Standing wave theory predicts that stable orbits only occur when the path travelled by electrons, in orbit, produce constructive interference like sound waves do in a hollow tube.

De Broglie Wavelength Example What is the de Broglie wavelength of an electron accelerated by 100. V? Note: Atom is 10-10 m = 1 Angstrom = 1Å

De Broglie Wavelength Example Calculate the de Broglie wavelength of a 12.0 kg object moving at 15.0 m/s and show that the result is so small to be immeasurable.