Light has momentum, too!

The Compton Effect Discovered in 1923 by Arthur Compton Pointed x-rays at metal atoms X-rays are high frequency, high energy photons X-rays knocked electrons from the metal A low energy photon emitted after the collision

Compton treated this like an elastic collision The incoming photon (x-ray) strikes the electron The electron emits a low energy photon Electron and photon scatter in opposite directions From the path and speed of the electron, Compton could calculate the momentum of the scattered photon: p = h/λ Like the energy of a photon, the momentum depends only on its frequency (or wavelength.

What is happening? The incoming x-ray is a very high energy photon The x-ray has more energy than is needed to eject the electron from the metal. The ejected electron gets rid of the extra energy in the form of a lower energy photon.

What is learned from this? We know that electrons have momentum because they have mass Photons have momentum too, even though they have no mass! Photons seem to behave much like particles when they interact (collide?) with electrons.

The deBroglie Wavelength Louis deBroglie turned quantum physics upside down when he asked: if light waves can behave like particles, can particles behave like light waves? Taking Compton’s formula: p = h/λ The wavelength of a particle is given by: λ = h/p Remember, momentum is given by p = mv

What does this mean? h = 6.6 x J s h is an extremely small number, so λ is very small unless m or v is very small. For everyday objects like baseballs and ham sandwiches, the wavelength is unnoticeable. For electrons and protons, the wavelength is noticeable, especially if they have a low speed.

Ok, now what does that mean? If a small particle has a wavelength, then it can do everything that waves do, such as: Diffract (bend around corners) Interfere with other small particles Young’s experiment has been done with electrons. The result: interference pattern on screen. Some electrons cancel, others constructively interfere.

Applications of Matter-Waves Optical microscopes are limited by the wavelength of the light they use. The best microscopes possible can only see down to the micrometer. A free electron has a much smaller wavelength than the wavelength of light. A microscope that uses a beam of electrons instead of light will be able to see much better detail. This leads to the invention of the electron microscope.

Electron Microscope Ant’s head, magnified 2,000 times

Summary Light has momentum p = h/λ When a photon collides with an electron, the electron scatters and emits a low energy photon. This is a perfectly elastic collision, as if the photon was a particle Matter can have wavelength λ = h/p The smaller and slower, the greater the wavelength Slow moving electrons can act like photons in this sense, being able to diffract and interfere.