Need for Quantum PhysicsNeed for Quantum Physics Problems remained from classical Problems remained from classical

mechanics that relativity didn’t explainmechanics that relativity didn’t explain Blackbody RadiationBlackbody Radiation

• The electromagnetic radiation emitted by a The electromagnetic radiation emitted by a heated objectheated object

Photoelectric EffectPhotoelectric Effect• Emission of electrons by an illuminated metalEmission of electrons by an illuminated metal

Spectral LinesSpectral Lines• Emission of sharp spectral lines by gas atoms in Emission of sharp spectral lines by gas atoms in

an electric discharge tubean electric discharge tube

Development of Quantum Development of Quantum PhysicsPhysics

1900 to 19301900 to 1930• Development of ideas of quantum mechanicsDevelopment of ideas of quantum mechanics

Also called wave mechanicsAlso called wave mechanics Highly successful in explaining the behavior of atoms, Highly successful in explaining the behavior of atoms,

molecules, and nucleimolecules, and nuclei Quantum Mechanics reduces to classical Quantum Mechanics reduces to classical

mechanics when applied to macroscopic mechanics when applied to macroscopic systemssystems

Involved a large number of physicistsInvolved a large number of physicists• Planck introduced basic ideasPlanck introduced basic ideas• Mathematical developments and interpretations Mathematical developments and interpretations

involved such people as Einstein, Bohr, Schrinvolved such people as Einstein, Bohr, Schrödinger, ödinger, de Broglie, Heisenberg, Born and Diracde Broglie, Heisenberg, Born and Dirac

Photoelectric EffectPhotoelectric Effect When light is incident on certain metallic When light is incident on certain metallic

surfaces, electrons are emitted from the surfaces, electrons are emitted from the surfacesurface• This is called the This is called the photoelectric effectphotoelectric effect• The emitted electrons are called The emitted electrons are called photoelectronsphotoelectrons

The effect was first discovered by HertzThe effect was first discovered by Hertz The successful explanation of the effect The successful explanation of the effect

was given by Einstein in 1905was given by Einstein in 1905• Received Nobel Prize in 1921 for paper on Received Nobel Prize in 1921 for paper on

electromagnetic radiation, of which the electromagnetic radiation, of which the photoelectric effect was a partphotoelectric effect was a part

Photoelectric Effect SchematicPhotoelectric Effect Schematic When light strikes E, When light strikes E,

photoelectrons are photoelectrons are emittedemitted

Electrons collected at Electrons collected at C and passing through C and passing through the ammeter are a the ammeter are a current in the circuitcurrent in the circuit

C is maintained at a C is maintained at a positive potential by positive potential by the power supplythe power supply

Photoelectric Current/Voltage Photoelectric Current/Voltage GraphGraph

The current increases The current increases with intensity, but with intensity, but reaches a saturation reaches a saturation level for large level for large ΔV’sΔV’s

No current flows for No current flows for voltages less than or voltages less than or equal to –ΔVequal to –ΔVss, the , the stopping potentialstopping potential• The stopping potential The stopping potential

is independent of the is independent of the radiation intensityradiation intensity

Features Not Explained by Features Not Explained by Classical Physics/Wave TheoryClassical Physics/Wave Theory

No electrons are emitted if the No electrons are emitted if the incident light frequency is below incident light frequency is below some some cutoff frequencycutoff frequency that is that is characteristic of the material being characteristic of the material being illuminatedilluminated

The maximum kinetic energy of the The maximum kinetic energy of the photoelectrons is independent of the photoelectrons is independent of the light intensitylight intensity

More Features Not ExplainedMore Features Not Explained The maximum kinetic energy of the The maximum kinetic energy of the

photoelectrons increases with photoelectrons increases with increasing light frequencyincreasing light frequency

Electrons are emitted from the Electrons are emitted from the surface almost instantaneously, even surface almost instantaneously, even at low intensitiesat low intensities

Einstein’s ExplanationEinstein’s Explanation A tiny packet of light energy, called a A tiny packet of light energy, called a photonphoton, ,

would be emitted when a quantized oscillator would be emitted when a quantized oscillator jumped from one energy level to the next lower jumped from one energy level to the next lower oneone• Extended Planck’s idea of quantization to Extended Planck’s idea of quantization to

electromagnetic radiationelectromagnetic radiation The photon’s energy would be E = hThe photon’s energy would be E = hƒƒ Each photon can give all its energy to an electron Each photon can give all its energy to an electron

in the metalin the metal The maximum kinetic energy of the liberated The maximum kinetic energy of the liberated

photoelectron is KE = hphotoelectron is KE = hƒ – Eƒ – EWFWF EEWFWF is called the is called the work functionwork function of the metal of the metal

Explanation of Classical Explanation of Classical “Problems”“Problems”

The effect is not observed below a The effect is not observed below a certain cutoff frequency since the certain cutoff frequency since the photon energy must be greater than photon energy must be greater than or equal to the work functionor equal to the work function• Without this, electrons are not emitted, Without this, electrons are not emitted,

regardless of the intensity of the lightregardless of the intensity of the light The maximum KE depends only on The maximum KE depends only on

the frequency and the work function, the frequency and the work function, not on the intensitynot on the intensity

More ExplanationsMore Explanations The maximum KE increases with The maximum KE increases with

increasing frequencyincreasing frequency The effect is instantaneous since The effect is instantaneous since

there is a one-to-one interaction there is a one-to-one interaction between the photon and the electronbetween the photon and the electron

Verification of Einstein’s TheoryVerification of Einstein’s Theory Experimental Experimental

observations of a observations of a linear relationship linear relationship between KE and between KE and frequency confirm frequency confirm Einstein’s theoryEinstein’s theory

The x-intercept is The x-intercept is the cutoff the cutoff frequencyfrequency

Planck’s LawPlanck’s Law Light not emitted continuously, but in discrete Light not emitted continuously, but in discrete

chunks (photons)chunks (photons)• E = hf, where h = “Planck’s constant”E = hf, where h = “Planck’s constant”• h = 6.626 h = 6.626 10 10–34 –34 J-sec = 4.1 J-sec = 4.1 10 10–15–15 eV–sec eV–sec

Example: FM radioExample: FM radio• f = 100 MHz = 10f = 100 MHz = 1088 Hz Hz• E = hf = 4.1 E = hf = 4.1 10 10–15–15 10 1088 = 4.1 = 4.1 10 10-7-7 eV per photon eV per photon

Example: 600 nm lightExample: 600 nm light• f = c / f = c / = 3 = 3 10 1088 / 600 / 600 10 10-7-7 = 5 = 5 10 101414 Hz = 500 THz Hz = 500 THz• E = hf = 4.1 E = hf = 4.1 10 10–15–15 (5 (5 10 101414) = 2.1 eV per) = 2.1 eV per photon photon

Photon Theory of LightPhoton Theory of Light Chunks of light are called “photons”Chunks of light are called “photons” Light consists of streams of photonsLight consists of streams of photons

• Emitted discretely, using Planck law and E = hfEmitted discretely, using Planck law and E = hf• Propagates as photonsPropagates as photons• Each photon absorbed discretelyEach photon absorbed discretely

Photons have particle Photons have particle andand wave properties wave properties• Wave:Wave: Frequency, wavelengthFrequency, wavelength• Particle:Particle: Energy of single photon is E = hfEnergy of single photon is E = hf

ExamplesExamples Calculating photon energy from wavelengthCalculating photon energy from wavelength

Example: Visible light, Example: Visible light, = 600 nm = 600 nm• E = 1240 / 600 = 2.1 eVE = 1240 / 600 = 2.1 eV

Example: Ultraviolet, Example: Ultraviolet, = 100 nm = 100 nm• E = 1240 / 100 = 12.4 eVE = 1240 / 100 = 12.4 eV higher energy (cell damage) higher energy (cell damage)

Example: X-Ray, Example: X-Ray, = 1 nm = 1 nm• E = 1240 / 1 = 1240 eVE = 1240 / 1 = 1240 eV very high energy (radiation very high energy (radiation

damage)damage)

1240eVnm

hcE hf

E

Wave Properties of ParticlesWave Properties of Particles In 1924, Louis de Broglie postulated In 1924, Louis de Broglie postulated

that that because photons have wave and because photons have wave and particle characteristics, perhaps all particle characteristics, perhaps all forms of matter have both propertiesforms of matter have both properties

Furthermore, the frequency and Furthermore, the frequency and wavelength of matter waves can be wavelength of matter waves can be determineddetermined

de Broglie Wavelength and de Broglie Wavelength and FrequencyFrequency

The The de Broglie wavelengthde Broglie wavelength of a of a particle is particle is

The frequency of matter waves isThe frequency of matter waves isph

mvh

hEƒ

The Davisson-Germer The Davisson-Germer ExperimentExperiment

They scattered low-energy electrons from a They scattered low-energy electrons from a nickel targetnickel target

They followed this with extensive diffraction They followed this with extensive diffraction measurements from various materialsmeasurements from various materials

The wavelength of the electrons calculated The wavelength of the electrons calculated from the diffraction data agreed with the from the diffraction data agreed with the expected de Broglie wavelengthexpected de Broglie wavelength

This confirmed the wave nature of electronsThis confirmed the wave nature of electrons Other experimenters have confirmed the Other experimenters have confirmed the

wave nature of other particleswave nature of other particles