1. photon-matter interactions Contents: Photoelectric effect Compton scattering Pair production

2. Photons: Electromagnetic energy is quantized into localized bundlesحزم موضعية moving with velocity c and having energy proportional to the frequency and momentum inversely proportional to the wavelength These particle like bundles are called photons

3. 3 1- Photoelectric effect 1- Photoelectric effect Fig.(1)

4. Photoelectric Effect Einstein received the Nobel Prize for his explanation of this. (He did NOT receive the prize for his theory of relativity.) Einstein suggested that light consisted of discrete units of energy,  E = hf. Electrons could either get hit with and absorb a whole photon, or they could not. There was no in-between (getting part of a photon).

5. Photoelectric Effect If the energy of the unit of light (photon) was not large enough to let the electron escape from the metal, no electrons would be ejected. (Hence, the existence of f-cutoff.) If the photon energy were large enough to eject the electron from the metal (here, W is the energy necessary to eject the electron), then the following equation would apply:

6. Photoelectric Effect energy of the photon absorbed (hf) goes into ejecting the electron (W) plus any extra energy left over which would show up as kinetic energy (KE). Put into a nice equation: hf = W + e*V stop where f is the frequency of the light W is the “WORK FUNCTION”, or the amount of energy needed to get the electron out of the metal V stop is the stopping potential When V stop = 0, f = f cutoff, and hf cutoff = W.

7. 7 The photocurrent is constant above the threshold frequency under a constant illumination, regardless of the frequency. The photocurrent is proportional with the intensity. The energy of electron is proportional with the frequency. For a particular electrode and frequency of light, a stopping voltage V s exists. No photocurrent can be collected regardless of the intensity of light. there is no time lag تاخير between the start of illumination and the start of the photocurrent. Measurements have shown that if there is a time lag, it is less than. (10 -9 s)

8. 8 Energy of photoelectrons is proportional to the frequency; Existence of threshold frequency f fofo fig(2)shows the existence of a threshold frequency, f 0, below which no photoelectrons are emitted. (Actually, a threshold energy called the work function,, is associated with the binding energy of an electron in a metal fig(2) A plot of kinetic energy versus frequency.

9. it illustrates that K max or V s is independent of light intensity I. The increase in current (or number of electrons per second) with increasing light intensity fig (3) A plot of photocurrent versus applied voltage. The graph shows that K max is independent of light intensity I for light of fixed frequency.

10. 10 Stopping voltage varies with (1)electrode material for the same frequency (2) increases with frequency of light for the same electrode Work function W=hf 0 f0f0 f0f0

11. hf

12. Photoelectric Effect * Most metals have a work function on the order of several electron volts. Copper has a work function of 4.5 eV. *Therefore, the cut-off frequency for light ejecting electrons from copper is: hf cutof = 4.5 eV, or f cutoff = 4.5 x (1.6 x 10 -19 C) x (1 V) / 6.63 x 10 -34 J-sec = 1.09 x 10 15 Hz, Ex.1 or cutoff = c/ f cutoff, or cutoff = (3 x 10 8 m/s) / (1.09 x 10 15 cycles/sec) = 276 nm (in the UV range)

13. Ex.2 Light of wave length (300 nm) falls on sodium metal,the work function of sodium is 2.46 eV find the maximum kinetic energy of the ejected electrons and the cut-off wave length. Sol.

14. Light of wavelength 2000 Å falls on aluminum surface, which has work function of 4.2 eV. Calculate (a) maximum kinetic energy of photoelectrons. (b) minimum kinetic energy of photoelectrons. (c) cut-off wavelength. (d) stopping potential. Sol. (a) Maximum kinetic energy of photoelectrons Ex.3

15. ( C) ( d)

16. Modern Physics Chapter One 16 Failure of classical theory In 1902, Philipp Eduard observed that the energy of the emitted electrons increased with the frequency of the light. This was at odds with James Clerk Maxwell's wave theory of light, which predicted that the energy would be proportional to the intensity of the radiation. Within the experimental accuracy, (about 10 -9 second), there is no time delay for the emission of photoelectrons. In terms of wave theory, the energy is uniformly distributed across its wavefront. A period of time is required to accumulate enough energy for the release of electrons.

17. 17 Wave nature of particles We have presented the particulate nature of light. To the other end, the traditionally recognized “particles” also demonstrate wave behaviors. Wave behaviors include– interference and diffraction.

18. 18 Momentum and wavelength of electron beam Rest energy of electron E o Kinetic energy of electron K = qV = 54 eV<<E o Classical (or non-relativistic) calculation is OK!

19. 19 Wavelength of electron beam: Å