Physics 3313 - Lecture 5 Wednesday February 3, 2010 Dr. Andrew Brandt Finish Ch. 2 HW 1 still due 02/08, HW2 assigned this pm due 2/10 Quiz on Ch. 2 Particle Properties of Waves Photoelectric Effect 2/3/2010 3313 Andrew Brandt

Relativistic Energy and Momentum Combining and one can obtain (2.12) These expressions relate the E, p, and m for single particles, but are only valid for a system of particles of mass M if which need not be true Since mc2 is an invariant quantity, this implies is also an invariant If m=0 this implies E = p = 0, but what if v = c? Then  =1/ 0 and E = p = 0/0, which is undefined! For a massless particle with v = c, then we could have E = pc for example the photon (which unfortunately has the symbol ) and 2/3/2010 3313 Andrew Brandt

Units Use W=qV to define electron volt (eV) a useful energy unit 1 eV = 1.6x10-19 C x 1V = 1.6x10-19 J Binding energy of hydrogen atom is 13.6 eV Uranium atom releases about 200 MeV when it splits in two (fission) (not a lot of Joules/fission, but there are a lot of atoms around…) Rest mass of proton (mp) is 0.938 GeV/c2 which is a fine unit for mass Units of momentum, p, MeV/c 2/3/2010 3313 Andrew Brandt

Relativistic Energy Problems From we can multiply by v to obtain simplifying gives which gives us a useful relation: An electron and a proton are accelerated through 10 MV, find p, v, and  of each (work problem on blackboard) Electron: Proton: 2/3/2010 3313 Andrew Brandt

Chapter 3 Quantum Theory/Particle Properties of Waves Classically we perceive particles and waves as different objects Particles: baseball, dust, electrons have properties such as charge, momentum and mass and can be counted as discrete objects Waves: vibrating strings, water, sound, light have wave properties such as superposition, diffraction, and interference, and are measured by wavelength, frequency, and intensity (not discrete objects) Modern Physics introduces wave-particle duality: in the microscopic world neither particles nor waves but aspects of both 2/3/2010 3313 Andrew Brandt

Electromagnetic Waves 1864 James Clerk Maxwell suggested that accelerating charges generate coupled E+M waves that travel indefinitely through space, both perpendicular to each other and direction of motion Changing magnetic field produces a current/electric field: Faraday’s Law: From symmetry if then etc. implies traveling waves with a velocity ; visible light is an EM wave (not vice-versa) 2/3/2010 3313 Andrew Brandt

Wave Properties of Light Superposition: adding wave amplitudes Constructive interference Diffraction: bending of light around corners All support wave nature of light Wavelength, period, frequency 2/3/2010 3313 Andrew Brandt

Photoelectric Effect Light illuminating a surface causes emission of “photo-electrons” (visible spectrum)—ironically first observed in Hertz experiment which posthumously validated Maxwell’s predictions Simple device for measuring photo-electric effect V0 is retarding potential: voltage above which no p.e.’s reach collector plate 2/3/2010 3313 Andrew Brandt

Properties of Photoelectric Effect Existence of photoelectric effect was not a surprise: light waves carry energy which could dislodge an electron (like an ocean wave moving a pebble) , but the details were surprising Very little time (nanoseconds) between arrival of light pulse and emission of electron, whereas might expect time for accumulation of enough energy (several eV) to liberate electrons Electron energy observed to be independent of intensity of light (bright light liberates more photoelectrons, not more energetic ones). Classically intensity is proportional to square of amplitude, so expect higher energy with higher intensity . 2/3/2010 3313 Andrew Brandt

Photoelectric Effect Properties (cont.) 3) At higher frequency  get higher energy electrons (blue 400 nm initiates p.e.’s with more energy than red 700 nm—takes larger potential V0 to stop then) Minimum frequency (0) required for photoelectric effect depends on material: slope=E/ =h (planck’s constant) 2/3/2010 3313 Andrew Brandt

Einstein Explains P.E. Effect Einstein 1905 (I had a good year) explained P.E. effect: energy of light not distributed evenly over classical wave but in discrete regions called quanta and later photons (draw) 1) EM wave concentrated in photon so no time delay between incident photon and p.e. emission 2) All photons of same frequency have same energy E=h, (h =Planck’s constant) so changing intensity changes number (I=Nh, where N is rate/area) but not energy Higher frequency gives higher energy Electrons have maximum KE when all energy of photon given to electron.  is work function or minimum energy required to liberate electron from material ( =h 0 ) 2/3/2010 3313 Andrew Brandt

Photoelectric Energy Formulas using 2/3/2010 3313 Andrew Brandt

Example for Iron a) Find  given b) If p.e.’s are produced by light with a wavelength of 250 nm, what is the stopping potential? = 4.96 - 4.5 = 0.46 eV (is this the answer?) NO! it is V0=0.46V (not eV) 2/3/2010 3313 Andrew Brandt

Speed of Person Revisited http://www.youtube.com/watch?v=HofoK_QQxGc 2/3/2010 3313 Andrew Brandt