Dual Nature of Radiation and Matter - Quick Revision
Electron emission and work function
- Free electrons are held inside a metal by the attraction of positive ions; the minimum energy to pull one out is the work function (phi0), measured in eV (1 eV = 1.6 x 10^-19 J).
- Emission can be produced by thermionic (heating), field (strong electric field, ~10^8 V/m), or photoelectric (light) processes.
Photoelectric effect (experimental facts)
- Photocurrent is proportional to intensity (above threshold frequency).
- For a given frequency, stopping potential is independent of intensity.
- There is a threshold frequency f0; below it no emission occurs however intense the light.
- Emission is instantaneous (~10^-9 s), even for dim light.
- Stopping potential: photocurrent drops to zero at the cut-off potical V0, with Kmax = e V0.
Photon (particle) picture
- Light is made of photons, each of energy E = hf = hc/lambda and momentum p = hf/c = h/lambda.
- Photons are electrically neutral and travel at speed c; intensity = number of photons per unit area per unit time.
- The wave theory fails to explain the threshold frequency, intensity-independence of Kmax, and the instantaneous emission.
Einstein's photoelectric equation
- Kmax = hf - phi0 = h(f - f0); emission needs f >= f0 where f0 = phi0/h.
- In terms of stopping potential: e V0 = hf - phi0, so the V0 versus f graph is a straight line of slope h/e (used by Millikan to find h).
Wave nature of matter (de Broglie)
- Moving particles have a matter wave of wavelength lambda = h/p = h/(mv).
- From kinetic energy: lambda = h/sqrt(2mK); for an electron accelerated through V volts, lambda = 1.227/sqrt(V) nm.
- lambda is independent of charge and is significant only for sub-atomic particles (small mass, small momentum); for macroscopic bodies it is far too small to measure.
Useful constants
- h = 6.63 x 10^-34 J s, c = 3 x 10^8 m/s, e = 1.6 x 10^-19 C, hc = 1240 eV nm.