Need for Quantum Physics Problems remained from classical mechanics that relativity didn’t explain Problems remained from classical mechanics that relativity didn’t explain Blackbody Radiation Blackbody Radiation The electromagnetic radiation emitted by a heated objectThe electromagnetic radiation emitted by a heated object Photoelectric Effect Photoelectric Effect Emission of electrons by an illuminated metalEmission of electrons by an illuminated metal Spectral Lines Spectral Lines Emission of sharp spectral lines by gas atoms in an electric discharge tubeEmission of sharp spectral lines by gas atoms in an electric discharge tube

Development of Quantum Physics 1900 to to 1930 Development of ideas of quantum mechanicsDevelopment of ideas of quantum mechanics Also called wave mechanics Also called wave mechanics Highly successful in explaining the behavior of atoms, molecules, and nuclei Highly successful in explaining the behavior of atoms, molecules, and nuclei Quantum Mechanics reduces to classical mechanics when applied to macroscopic systems Quantum Mechanics reduces to classical mechanics when applied to macroscopic systems Involved a large number of physicists Involved a large number of physicists Planck introduced basic ideasPlanck introduced basic ideas Mathematical developments and interpretations involved such people as Einstein, Bohr, Schrödinger, de Broglie, Heisenberg, Born and DiracMathematical developments and interpretations involved such people as Einstein, Bohr, Schrödinger, de Broglie, Heisenberg, Born and Dirac

Photoelectric Effect When light is incident on certain metallic surfaces, electrons are emitted from the surface When light is incident on certain metallic surfaces, electrons are emitted from the surface This is called the photoelectric effectThis is called the photoelectric effect The emitted electrons are called photoelectronsThe emitted electrons are called photoelectrons The effect was first discovered by Hertz The effect was first discovered by Hertz The successful explanation of the effect was given by Einstein in 1905 The successful explanation of the effect was given by Einstein in 1905 Received Nobel Prize in 1921 for paper on electromagnetic radiation, of which the photoelectric effect was a partReceived Nobel Prize in 1921 for paper on electromagnetic radiation, of which the photoelectric effect was a part

Photoelectric Effect Schematic When light strikes E, photoelectrons are emitted When light strikes E, photoelectrons are emitted Electrons collected at C and passing through the ammeter are a current in the circuit Electrons collected at C and passing through the ammeter are a current in the circuit C is maintained at a positive potential by the power supply C is maintained at a positive potential by the power supply

Photoelectric Current/Voltage Graph The current increases with intensity, but reaches a saturation level for large ΔV’s The current increases with intensity, but reaches a saturation level for large ΔV’s No current flows for voltages less than or equal to –ΔV s, the stopping potential No current flows for voltages less than or equal to –ΔV s, the stopping potential The stopping potential is independent of the radiation intensityThe stopping potential is independent of the radiation intensity

Features Not Explained by Classical Physics/Wave Theory No electrons are emitted if the incident light frequency is below some cutoff frequency that is characteristic of the material being illuminated No electrons are emitted if the incident light frequency is below some cutoff frequency that is characteristic of the material being illuminated The maximum kinetic energy of the photoelectrons is independent of the light intensity The maximum kinetic energy of the photoelectrons is independent of the light intensity

More Features Not Explained The maximum kinetic energy of the photoelectrons increases with increasing light frequency The maximum kinetic energy of the photoelectrons increases with increasing light frequency Electrons are emitted from the surface almost instantaneously, even at low intensities Electrons are emitted from the surface almost instantaneously, even at low intensities

Einstein’s Explanation A tiny packet of light energy, called a photon, would be emitted when a quantized oscillator jumped from one energy level to the next lower one A tiny packet of light energy, called a photon, would be emitted when a quantized oscillator jumped from one energy level to the next lower one Extended Planck’s idea of quantization to electromagnetic radiationExtended Planck’s idea of quantization to electromagnetic radiation The photon’s energy would be E = hƒ The photon’s energy would be E = hƒ Each photon can give all its energy to an electron in the metal Each photon can give all its energy to an electron in the metal The maximum kinetic energy of the liberated photoelectron is KE = hƒ – E WF The maximum kinetic energy of the liberated photoelectron is KE = hƒ – E WF E WF is called the work function of the metal E WF is called the work function of the metal

Explanation of Classical “Problems” The effect is not observed below a certain cutoff frequency since the photon energy must be greater than or equal to the work function The effect is not observed below a certain cutoff frequency since the photon energy must be greater than or equal to the work function Without this, electrons are not emitted, regardless of the intensity of the lightWithout this, electrons are not emitted, regardless of the intensity of the light The maximum KE depends only on the frequency and the work function, not on the intensity The maximum KE depends only on the frequency and the work function, not on the intensity

More Explanations The maximum KE increases with increasing frequency The maximum KE increases with increasing frequency The effect is instantaneous since there is a one-to-one interaction between the photon and the electron The effect is instantaneous since there is a one-to-one interaction between the photon and the electron

Verification of Einstein’s Theory Experimental observations of a linear relationship between KE and frequency confirm Einstein’s theory Experimental observations of a linear relationship between KE and frequency confirm Einstein’s theory The x-intercept is the cutoff frequency The x-intercept is the cutoff frequency

Planck’s Law Planck’s Law Light not emitted continuously, but in discrete chunks (photons) Light not emitted continuously, but in discrete chunks (photons) E = hf, where h = “Planck’s constant”E = hf, where h = “Planck’s constant” h =  10 –34 J-sec = 4.1  10 –15 eV–sech =  10 –34 J-sec = 4.1  10 –15 eV–sec Example: FM radio Example: FM radio f = 100 MHz = 10 8 Hzf = 100 MHz = 10 8 Hz E = hf = 4.1  10 –15  10 8 = 4.1  eV per photonE = hf = 4.1  10 –15  10 8 = 4.1  eV per photon Example: 600 nm light Example: 600 nm light f = c / = 3  10 8 / 600  = 5  Hz = 500 THzf = c / = 3  10 8 / 600  = 5  Hz = 500 THz E = hf = 4.1  10 –15  (5  ) = 2.1 eV per photonE = hf = 4.1  10 –15  (5  ) = 2.1 eV per photon

Photon Theory of Light Chunks of light are called “photons” Chunks of light are called “photons” Light consists of streams of photons Light 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 and wave properties Photons have particle and wave properties Wave:Frequency, wavelengthWave:Frequency, wavelength Particle:Energy of single photon is E = hfParticle:Energy of single photon is E = hf

Examples Calculating photon energy from wavelength Calculating photon energy from wavelength Example: Visible light, = 600 nm Example: Visible light, = 600 nm E = 1240 / 600 = 2.1 eVE = 1240 / 600 = 2.1 eV Example: Ultraviolet, = 100 nm Example: Ultraviolet, = 100 nm E = 1240 / 100 = 12.4 eV higher energy (cell damage)E = 1240 / 100 = 12.4 eV higher energy (cell damage) Example: X-Ray, = 1 nm Example: X-Ray, = 1 nm E = 1240 / 1 = 1240 eV very high energy (radiation damage)E = 1240 / 1 = 1240 eV very high energy (radiation damage)

Wave Properties of Particles In 1924, Louis de Broglie postulated that because photons have wave and particle characteristics, perhaps all forms of matter have both properties In 1924, Louis de Broglie postulated that because photons have wave and particle characteristics, perhaps all forms of matter have both properties Furthermore, the frequency and wavelength of matter waves can be determined Furthermore, the frequency and wavelength of matter waves can be determined

de Broglie Wavelength and Frequency The de Broglie wavelength of a particle is The de Broglie wavelength of a particle is The frequency of matter waves is The frequency of matter waves is

The Davisson-Germer Experiment They scattered low-energy electrons from a nickel target They scattered low-energy electrons from a nickel target They followed this with extensive diffraction measurements from various materials They followed this with extensive diffraction measurements from various materials The wavelength of the electrons calculated from the diffraction data agreed with the expected de Broglie wavelength The wavelength of the electrons calculated from the diffraction data agreed with the expected de Broglie wavelength This confirmed the wave nature of electrons This confirmed the wave nature of electrons Other experimenters have confirmed the wave nature of other particles Other experimenters have confirmed the wave nature of other particles