What is the nature of

Part II

•Last week we surmised that photons must carry momentum in spite of the fact that they are massless.

•Last time we learned that Hertz showed that light is an electromagnetic phenomenon, and that electromagnetic waves behave much like any other wave-- they can be reflected, refracted, diffracted and polarized.

•However, we also learned last time we learned that, unless energy is quantized, the radiation of a blackbody will continue to increase with frequency—a delimma dubbed the ultraviolet catastophe—forcing Planck to theorize that the “oscillators” atomic walls must have quantized energy.

•You also had some great questions about the continuous blackbody spectrum emitted by heated solids. We’ll (briefly) revisit that in the context of what we learn today.

The observation that electromagnetic waves could eject electrons from the surface of a metal was first made by Hertz.

A simple experiment can be designed to measure the energy and intensity of the electrons ejected.

•Light shines on a metal plate emitting electrons

•The voltage on a battery can be gradually turned up until the electric field just stop the electrons from reaching the collector plate, thereby giving a measure of the kinetic energy.

•The energy in the light wave is spread out uniformly and continuously over the wavefront.

CIAtKmaxThe maximum kinetic energy of an ejected electron is therefore

timelight intensity

cross sectional area of atom

work function

absorption coefficient

which depends on the light intensity and the time over which it is exposed.

•The intensity of a light wave is proportional to the square of the amplitude of the electric field.

•The energy in the light wave is spread out uniformly and continuously over the wavefront.

…and therefore does not depend on frequency.

•The number of photoelectrons ejected depended on the intensity (as expected) but their maximum kinetic energy did not!

•The maximum kinetic energy depended only on the frequency, the slope of the linear relationship between the energy and the frequency gives “Planck’s constant”, h.

•The electrons were ejected immediately after the light started shining—the electron instantaneously absorbed enough energy to escape-provided there was enough energy to overcome the binding energy or “work function”.

•Even a high intensity source of low frequency light cannot liberate electrons.

We have to change our way of thinking about this picture:

Instead of continuous waves we have to

think of the energy as being localized in

quanta.

In the photoelectric effect, these discrete localized quanta of

energy, hv, are transferred entirely to

the electron

hvKmax

Part 2: Compton scattering: when you have a higher energy photon

Photoelectric effect- all of the incident photon’sEnergy is transferred to an electron, ejecting it.

Compton scattering-electron is ejected, but photon retains someenergy.

Pair-production-the photon’s energy is consumed to producean electron and a positron.

The unshifted peak comes from tightly bound electrons

Contrast, classical scattering:

Electrons would shake with the frequency of the incident wave

The incident and scattered wavelengths would be the same

Bragg spectroscopyBragg spectroscopy

,...3,2,1sin2 ndn

(a) Constructive interference occurs when:

(b) At other angles the waves do not interfere constructively

This is an important tool in crystallography as it is a sensitive measure of the spacing of the crystalline planes.

…and the answer is…drumroll please…

If light, which was previously thought of as a wave, has characteristics of particles, could it be true that particles must also be thought of as waves in some contexts in

order to fully describe their behavior?

Light:

•Interferes like a wave

•Diffracts like a waves

•Can be polarized like a wave

•Scatters like a particle