Wave Particle DualityWave Particle Duality

Chapter 5Chapter 5

Lecture ObjectivesLecture Objectives

Explain how the photoelectric effect is Explain how the photoelectric effect is induced by light energy.induced by light energy.

Indicate what is meant by the duality of light.Indicate what is meant by the duality of light. Discuss the wavelike properties of light that Discuss the wavelike properties of light that

reveal its wavelike nature.reveal its wavelike nature. State Heisenberg’s Uncertainty Principle as it State Heisenberg’s Uncertainty Principle as it

relates to atoms.relates to atoms. Indicate what information Schroedinger’s Indicate what information Schroedinger’s

Wave Equation gives us about the electron.Wave Equation gives us about the electron.

The Photoelectric EffectThe Photoelectric Effect

In 1886 and 1887, Heinrich Hertz discovered In 1886 and 1887, Heinrich Hertz discovered that UV light can cause electrons to be that UV light can cause electrons to be ejected from a metal surface. ejected from a metal surface.

According to the classical wave theory of According to the classical wave theory of light, the intensity of the light determines light, the intensity of the light determines the amplitude of the wave, and so a greater the amplitude of the wave, and so a greater light intensity should cause the electrons on light intensity should cause the electrons on the metal to oscillate more violently and to the metal to oscillate more violently and to be ejected with a greater kinetic energy. be ejected with a greater kinetic energy. – N.B. Intensity=Amplitude, so brighter light N.B. Intensity=Amplitude, so brighter light

should have greater amplitudeshould have greater amplitude

The Photoelectric EffectThe Photoelectric Effect

In contrast, the experiment showed In contrast, the experiment showed that the kinetic energy of the ejected that the kinetic energy of the ejected electrons depends on the electrons depends on the frequencyfrequency of the light. of the light.

The light intensity affects only the The light intensity affects only the number of ejected electrons and not number of ejected electrons and not their kinetic energies. their kinetic energies.

Planck's Constant and the Planck's Constant and the Energy of a PhotonEnergy of a Photon

In 1900, Max Planck asked: how does the In 1900, Max Planck asked: how does the radiation an object emits relate to its radiation an object emits relate to its temperature?temperature?

His formula only made sense if he His formula only made sense if he assumed that the energy of a vibrating assumed that the energy of a vibrating molecule was molecule was quantized.quantized.

The energy would have to be proportional The energy would have to be proportional to the frequency of vibration, and it to the frequency of vibration, and it seemed to come in little "chunks" of the seemed to come in little "chunks" of the frequency multiplied by a certain constant. frequency multiplied by a certain constant.

This constant came to be known as This constant came to be known as Planck's constantPlanck's constant, or , or hh, and it has the , and it has the value h=6.266 x10-32 J s.value h=6.266 x10-32 J s.

Einstein’s Explanation of the Einstein’s Explanation of the Photoelectric EffectPhotoelectric Effect

Based on Planck's work, Einstein Based on Planck's work, Einstein proposed that light also delivers its proposed that light also delivers its energy in chunks; light would then energy in chunks; light would then consist of little particles, or consist of little particles, or quantaquanta, , called called photonsphotons, each with an energy , each with an energy of Planck's constant times its of Planck's constant times its frequency, E=hfrequency, E=h. .

Einstein’s Explanation of the Einstein’s Explanation of the Photoelectric EffectPhotoelectric Effect

In that case, the frequency of the light In that case, the frequency of the light wouldwould make a difference in the photoelectric effect. make a difference in the photoelectric effect. – Higher-frequency photons have more energy, so Higher-frequency photons have more energy, so

they should make the electrons come flying out they should make the electrons come flying out fasterfaster

– Thus, switching to light with the same intensity Thus, switching to light with the same intensity but a higher frequency should increase the but a higher frequency should increase the maximum kinetic energy of the emitted electrons. maximum kinetic energy of the emitted electrons.

– If you leave the frequency the same but crank up If you leave the frequency the same but crank up the intensity, the intensity, moremore electrons should come out electrons should come out (because there are more photons to hit them), but (because there are more photons to hit them), but they won't come out any they won't come out any fasterfaster, because each , because each individual photon still has the same energy. individual photon still has the same energy.

Einstein’s Explanation of the Einstein’s Explanation of the Photoelectric EffectPhotoelectric Effect

And if the frequency is low enough, And if the frequency is low enough, then none of the photons will have then none of the photons will have enough energy to knock an electron enough energy to knock an electron out of an atom. out of an atom.

So if you use really low-frequency So if you use really low-frequency light, you shouldn't get light, you shouldn't get anyany electrons, no matter how high the electrons, no matter how high the intensity is. intensity is.

If you use a high frequency, you If you use a high frequency, you should still knock out some electrons should still knock out some electrons even if the intensity is very low. even if the intensity is very low.

Experimental Proof of Experimental Proof of Einstein’s Theory for the Einstein’s Theory for the

Photoelectric EffectPhotoelectric Effect In 1913-1914, R.A. Millikan did a series In 1913-1914, R.A. Millikan did a series

of extremely careful experiments of extremely careful experiments involving the photoelectric effect. involving the photoelectric effect.

He found that all of his results agreed He found that all of his results agreed exactly with Einstein's predictions about exactly with Einstein's predictions about photons, not with the wave theory. photons, not with the wave theory.

Einstein actually won the Nobel Prize for Einstein actually won the Nobel Prize for his work on the photoelectric effect, not his work on the photoelectric effect, not for his more famous theory of relativity.for his more famous theory of relativity.

Wave-Particle Duality of Wave-Particle Duality of LightLight

Some experimental results, like Millikan’s, Some experimental results, like Millikan’s, seem to prove beyond all possible doubt seem to prove beyond all possible doubt that light consists of particlesthat light consists of particles

Others, like Young’s experiment, insist, Others, like Young’s experiment, insist, just as irrefutably, that it's waves.just as irrefutably, that it's waves.

We can only conclude that light is We can only conclude that light is somehow both a wave and a particle--or somehow both a wave and a particle--or that it's something else we can't quite that it's something else we can't quite visualize, which appears to us as one or visualize, which appears to us as one or the other depending on how we look at it.the other depending on how we look at it.