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You may recall the formula: V = W/q Potential difference between two points is the work per unit charge to move the charge between those points. The work done gives the charge potential energy (U). U = qV or V = U/q In the photoelectric effect, electrons will move against a potential difference until their kinetic energy is not sufficient. The potential difference that causes this is Vo. Assuming the loss of K means a gain in U we get: Kmax = eVo where e is an electron or Kmax = qVo 1 eV = 1.60 x 10-19 J How does the photoelectric effect impact the wave theory? Wave theory: Energy carried in a wave (light) is determined by intensity 1st Law ­ Rate of photoelectron emission α intensity of incident light ­ if light is more intense, more energy is absorbed by electrons ­ if more energy is absorbed, more electrons are emitted ­ 1st law agrees with wave theory 2nd Law ­ KE of electrons is independent of intensity ­ the KE of the electrons should be determined by the energy absorbed by the light, which is determined by intensity ­ light of any frequency should work if intense enough ­ even at low intensity, electrons should eventually "soak up" enough energy to be emitted ­ 2nd law doesn't agree with wave theory 3rd Law ­ KE of electrons is dependent on frequency ­ 3rd law doesn't agree with wave theroy ­ KE should be determined by intensity rather than frequency (according to wave theory) Quantum Theory Max Planck studied radiation from a hot object ­ explained experimental evidence by saying that radiant energy is absorbed and radiated as multiples of h • f, where h is a constant and f is the frequency ­ energy is absorbed and radiated by matter in "bundles" he called quanta (now called photons) ­ the amount of energy absorbed and released is equal to the difference between energy levels in atoms ­ E = hf (h = 6.626 x 10­34 J•s) Einstein used this concept to explain the photoelectric effect ­ light radiation consists of a stream of photons having energy equal to hf ­ photons are absorbed by the electrons on the emitter ­ if hf > w, emission occurs ­ if hf < w, no emission occurs ­ Einsteins Photoelectric Equation: ­ or ­ K = hf ­ φ ½ mv2= hf ­ φ Experiments prove that light acts as both a particle (quantum theory) and a wave (electromagnetic theory). We say that light has a dual character: Wave/Particle Duality For transmission of light, wave theory works well. For absorption/emission, particle theory works well. Einstein's Photoelectric Equation 1) Yellow light with a frequency of 5.43 x 1014 Hz strikes a cesium surface. If the photoelectric work function of cesium is 3.42 x 10­19 J, what is the maximum velocity a photoelectron emitted from the surface can have? (mass of electron = 9.11 x 10­31 kg) hf − φ = ½ mv2 (6.626x10-34 Js)(5.43x1014 Hz) - 3.42x10-19 J = ½(9.11x10-31 kg)v v = 1.98 x 105 m/s 2) The photoelectric work function for gold is 8.50 x 10­19 J. What is the maximum velocity of emitted photoelectrons caused by illumination from radiation with a wavelength of 2.20 x 10­7 m? 2