27-3 Photon Theory & 27-3 Photon Theory & Photoelectric EffectPhotoelectric Effect

• 1905 Einstein extended the 1905 Einstein extended the quantum theory of light by quantum theory of light by proposing a new theoryproposing a new theory

• Einstein argued that when an Einstein argued that when an oscillating body emits light the oscillating body emits light the body’s energy must decrease in body’s energy must decrease in energy by an amount of nhf.energy by an amount of nhf.

• Then to conserve energy, the light Then to conserve energy, the light should be emitted in packets or should be emitted in packets or quanta each with an energy ofquanta each with an energy of

• E=hfE=hf• Where f is the frequency of the Where f is the frequency of the

emitted lightemitted light• h is still Planck’s constant h is still Planck’s constant

PhotonsPhotons

• This suggests that light is This suggests that light is transmitted as tiny particles, transmitted as tiny particles, photons.photons.

Photoelectric EffectPhotoelectric Effect

• When light shines on a surface, When light shines on a surface, electrons are found to be emittedelectrons are found to be emitted

• This is the photoelectric effectThis is the photoelectric effect• Happens with many materials, Happens with many materials,

most easily observed on metals.most easily observed on metals.

• Both the EM (electromagnetic) wave Both the EM (electromagnetic) wave theory and the photon theory predicts theory and the photon theory predicts that electrons should be emitted when a that electrons should be emitted when a light shines on the metallight shines on the metal

• The theories give different predictions in The theories give different predictions in the details of the photoelectric effect.the details of the photoelectric effect.

• Maximum kinetic energy (KEMaximum kinetic energy (KEmaxmax) of the ) of the emitted electrons can be measured.emitted electrons can be measured.

• Reverse the voltage so C is Reverse the voltage so C is negativenegative

• Emitted electrons will be Emitted electrons will be repelled by negative repelled by negative electrodeelectrode

• But if the voltage is small But if the voltage is small enough the fastest enough the fastest electrons will still make it to electrons will still make it to C and a current will flowC and a current will flow

• Increase the voltage until Increase the voltage until just when the current just when the current reaches zero-no electrons reaches zero-no electrons have sufficient KEhave sufficient KE

• This is called the stopping This is called the stopping potential or stopping potential or stopping voltage, Vvoltage, V00

KEmax= eV0

Wave TheoryWave Theory

• Assumes monochromatic light and Assumes monochromatic light and the two important properties of a the two important properties of a light wave are its intensity and its light wave are its intensity and its frequency (or wavelength)frequency (or wavelength)

• When these two properties are When these two properties are varied the wave theory makes the varied the wave theory makes the following predictionsfollowing predictions

• Increase the light intensity and the Increase the light intensity and the number of photoelectrons and number of photoelectrons and their energy should increasetheir energy should increase

• Frequency of light shouldn’t affect Frequency of light shouldn’t affect the KE of the photoelectrons. Only the KE of the photoelectrons. Only the intensity matters.the intensity matters.

Photon TheoryPhoton Theory• Very different predictionsVery different predictions• First in monochromatic light all photons First in monochromatic light all photons

have the same energy (hf). Increasing have the same energy (hf). Increasing the intensity just increases the number the intensity just increases the number of photons not the energy of each of photons not the energy of each photon.photon.

• An ejected electron happens because of An ejected electron happens because of a collision with a single photona collision with a single photon

• And all energy is transferred to the And all energy is transferred to the electron and the photon no longer existselectron and the photon no longer exists

• Electrons are held in the metal by some Electrons are held in the metal by some attractive force a minimum energy, Wattractive force a minimum energy, W00, is , is required to just get an electron out required to just get an electron out through the surface.through the surface.

• WW00 is called the work function is called the work function

• If the frequency of the incoming light is If the frequency of the incoming light is so low no electrons are emitted because so low no electrons are emitted because of the work function. hf<Wof the work function. hf<W00

• If hf>WIf hf>W0 0 then electrons will be ejected then electrons will be ejected and energy will be conserved.and energy will be conserved.

• The energy above the WThe energy above the W00 shows up as KE shows up as KE

• The least tightly held electrons will The least tightly held electrons will be emitted with the maximum KE be emitted with the maximum KE thethe

• hf=KEhf=KEmaxmax + W + W00

• These would be just the surface These would be just the surface electrons, most electrons require electrons, most electrons require more energy to just be released so more energy to just be released so the KE will be much lessthe KE will be much less

Predictions of the Photon Predictions of the Photon TheoryTheory

• Increase in intensity just produces more Increase in intensity just produces more photons not the resulting KEphotons not the resulting KE

• As the frequency of the light increases As the frequency of the light increases the maximum KE of the released the maximum KE of the released electrons increases linearlyelectrons increases linearly

• KEKEmaxmax=hf-W=hf-W00

• There is a minimum frequency or There is a minimum frequency or “cutoff” frequency below which no “cutoff” frequency below which no electrons will be ejected no matter how electrons will be ejected no matter how intense the lightintense the light

• Photon theory predictions are very Photon theory predictions are very different from the wave theory.different from the wave theory.

• RA Millikan did careful experiments RA Millikan did careful experiments that proved Einstein’s photon that proved Einstein’s photon theorytheory

27-4 Energy, Mass & 27-4 Energy, Mass & Momentum of a PhotonMomentum of a Photon

• Because a photon is traveling at the Because a photon is traveling at the speed of light it is a relativistic speed of light it is a relativistic particleparticle

• Relativistic formulas for dealing with Relativistic formulas for dealing with mass, energy and momentum must mass, energy and momentum must be usedbe used

• And after the derivations And after the derivations

h

c

hf

c

Ep

27-6 Photon Interactions; Pair 27-6 Photon Interactions; Pair ProductionProduction

• Four type of interactions that a photon can Four type of interactions that a photon can undergo as it passes into matterundergo as it passes into matter

• 1. Photoelectric effect: photon is completely 1. Photoelectric effect: photon is completely absorbed, electron is ejectedabsorbed, electron is ejected

• 2. Photon may be totally absorbed by 2. Photon may be totally absorbed by electron, but not have enough energy to eject electron, but not have enough energy to eject it; the electron moves into an excited stateit; the electron moves into an excited state

• 3. The photon can scatter from an atom and 3. The photon can scatter from an atom and lose some energy (lose of frequency not lose some energy (lose of frequency not speed)speed)

• 4. The photon can produce matter, an 4. The photon can produce matter, an electron-positron pair. (positron has same electron-positron pair. (positron has same mass as electron, but opposite charge.)mass as electron, but opposite charge.)