Wave-Particle Duality of Light.

So Light acts like a wave, but ...

The Photoelectric Effect

Testing the wave-particle duality of light.

Light knocks electrons out of metal surfaces as if it were made of particles --- photons. For light of frequency f, each photon has energy hf.

In 1902, P.Lenard studied how the energy of the emitted photoelectrons varied with the intensity of the light.

He used a carbon arc light, and could increase the intensity a thousand-fold. The ejected electrons hit another metal plate, the collector, which was connected to the cathode by a wire with a sensitive ammeter, to measure the current produced by the illumination.

To measure the energy of the ejected electrons, Lenard charged the collector plate negatively, to repel the electrons coming towards it. Thus, only electrons ejected with enough kinetic energy to get up this potential hill would contribute to the current.

Lenard discovered that there was a well defined minimum voltage that stopped any electrons getting through, we'll call it V_stop. This means that there is a threshold kinetic energy that the electrons must have in order to reach the detector.

Contrary to intuition, Lenard found that V_stop did not depend at all on the intensity of the light! Doubling the light intensity doubled the number of electrons emitted, but did not affect the energies of the emitted electrons.

But Lenard did something else. With his very powerful arc lamp, there was sufficient intensity to separate out the colors and check the photoelectric effect using light of different colors. He found that the maximum energy of the ejected electrons did depend on the color --- the shorter wavelength, higher frequency light caused electrons to be ejected with more energy. This was, however, a fairly qualitative conclusion as his experimental apparatus lacked good the means to make a reliable measurement. Still this was a puzzling result at the time.

Let's examine some of the implications of Lenard's experiment in terms of whether light is a wave or a particle:

If its a wave, then:

Wave Theory: Light is an oscillating electric field. Only the electric field strength should affect electrons.

Prediction: Sufficiently intense light should eject electrons no matter what the frequency.

But this is not what was observed.

No Time delay:

Wave Theory: The power in a light beam is spread out. The area near an electron intercepts very little.

Prediction: It should take some time for an electron to absorb enough energy to be ejected.

Again, this is not observed.

Particle model works:

Particle theory: A photon with energy hf strikes an electron and ejects it from the metal.
hf = K.E. + w

w = work to remove electron from metal
K.E. = kinetic energy of ejected electron.

Einstein won the Nobel Prize for this Explanation!

For each metal, there is a threshold frequency. Light frequencies below the threshold eject no electrons, no matter how intense the light.

Light frequencies above the threshold eject electrons, no matter how low the intensity.

When the light source is turned on, the electrons begin to be ejected immediately.

No matter how weak the light source, if the frequency is above the threshold, there is no time delay.

Voltmeter measures reverse potential V₀ to stop the current.
eV₀ = K.E._max

So Light is also a particle. Energy of light is in the form of a particle. Transport of the energy through space is in the form of a wave.