PH 103 Dr. Cecilia Vogel Lecture 17

Review Outline  Quantum Mechanics  What is quantization?  Photon  Two pieces of evidence:  blackbody radiation  photoelectric effect  Relativistic velocity transformation

Familiar Quantization  Electric charge  At first glance, it seems you could have any charge (any value in Coulombs)  If very accurately measured, find charge is always integer*1.602X C = Ne  Charge is due to individual, indivisible electrons  Charge is quantized  in other words, only certain values are possible.  Other familiar examples:  individual molecules in “continuous” material  individual pixels in “continuous” image

Photon  What is a photon?  Individual, indivisible bit of light energy  a massless particle  How much energy?  For light of frequency, f,  each photon has an energy, E photon = hf  example:  UV light with frequency 1X10 15 Hz  One photon has energy (6.626X Js)(1X10 15 Hz)  One photon has energy 6.626X J

Photon  Each photon has an energy, E photon = hf  N photons have energy E = Nhf  N = integer!!  Cannot have half a photon!  example:  UV light with frequency 1X10 15 Hz  One photon has energy 6.626X J  Two photons have energy X J  How many photons have 100 J of energy?  N=E/hf = 1.5X10 20 photons  So 1.5X10 20 photons / s = 100 W

Evidence for photons Evidence that light is made up of massless particles called photons :  In blackbody radiation, light is emitted one photon at a time.  In the photoelectric effect, light is absorbed one photon at a time.  In Compton scattering, light collides with an electron one photon at a time.  … and so much more

Blackbody (Thermal) Radiation  A blackbody is an idealization  ignore characteristic spectrum  for simplification  Blackbody thermal radiation  light and other EM waves  given off by an object due to temperature  glowing

 Warm Familiar Thermal Radiation  lots infrared  some red  White hot Power spectrum  no visible  infrared/heat  Red hot  all colors  IR & UV

 Peak of emission is at wavelength: Blackbody Radiation Power spectrum  Plug in T in Kelvin

Failure of Classical Theory  Physicists attempted to describe radiation  using wave theory of light  and classical thermal physics  Predicted  lots of high frequency light  at all temps!  called the “ultraviolet catastrophe”

Photon Theory  Max Plank’s theory:  Light must be given off as individual photons (he didn’t use that term)  Each photon has energy E= hf.  High frequency light made up of high energy photons.  Requires a lot of energy to produce even one.  High-frequency photons are harder to produce, so less likely to be produced.  In fact as f , E   not just unlikely, impossible to produce one  power spectrum goes to zero as f 

Warning  Never believe a theory just because it fits the experiment it was made up to fit!  It should explain other experiments.  Or make predictions that can be verified.

Photoelectric Effect  Light strikes a metal, the light is absorbed, knocking electrons off the metal’s surface.  Light energy converted to electrical energy.  The electrons could absorb energy from a wave or a particle of light  but wave theory can’t explain the details...  Particle (photon) theory can. PHOTO- -ELECTRIC

PEE – Failure of Classical Theory  If light’s frequency is below the critical frequency, f<f c,  then the photoelectric effect doesn't happen.  When the photoelectric effect does happen  the electron gets more energy from higher frequency light  Classical wave theory of light cannot explain why frequency should have any effect.

PEE – Critical Frequency If light’s frequency is below the critical frequency, f<f c,  then the photoelectric effect doesn't happen  Photon theory (with E=hf) explains:  Low frequency light means low energy photons.  If f<f c, then the photon doesn’t have enough energy to free the electron from the metal.

PEE - Critical Frequency If light’s frequency is below the critical frequency, f<f c,  then the photoelectric effect doesn't happen.  But if f=f c, the energy of the photon is just barely enough to free the electron from the metal.  = energy needed to free electron   For effect to occur hf >  f > f c   If f>fc, the effect does occur  The electron gets all the photon’s energy, hf

PEE – Kinetic Energy When the effect does occur, increasing the frequency of the light increases the kinetic energy of the electrons that are released  Photon theory explains:  photon’s energy, hf, is absorbed by electron,  some energy is used to free electron,  rest of energy is kinetic energy.

PEE – Kinetic Energy The kinetic energy of the ejected electrons increases with the frequency of the light 0000 K f fcfc No effect -- Slope=h

Test it Yourself