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