1. The photoelectric effect
PHY 102: Waves & Quanta
Topic 9
The photoelectric effect
John Cockburn Room E15)

2. EM radiation as waves
Anomalous result: the photoelectric effect
Photons

3. EM radiation as waves Interference (Young’s Slits)
Single-slit diffraction
X-ray diffraction…..
All show EM radiation behaving entirely as expected for classical waves.
However, as was discovered at the beginning of the 20th century, the behaviour of EM radiation is not always consistent with this…………

4. “real” intensity distribution for double slits…..
light behaving exactly like a wave………..
“ideal” pattern
Single slit pattern
“real” pattern

5. The photoelectric effect
In a metal, the flow of electric current is due to the flow of charged particles called electrons
The electrons are relatively free to move throughout the metal (electron “gas” or “sea”), so most metals are good conductors of electricity.
By shining light on a metal, some of these electrons can be “knocked out” of the metal to generate an electric current outside of the metal
Although basic photoelectric effect can be explained with wave model of light, the detailed results of such an experiment CAN NOT!...

6. The photoelectric effect
Metallic anode and cathode enclosed in evacuated glass tube (like old-fashioned “valve”)
Vacuum required so that electrons can flow from cathode to anode without scattering from gas molecules.
Monochromatic light is shone on the cathode, electrons flow from cathode to anode, current detected by galvanometer.
Potential divider
to vary anode-cathode
voltage Vac

7. The photoelectric effect
Pink lines: electric field lines
because electrons are negatively charged, they move in the opposite direction to the field lines.
When the cathode is illuminated with light of frequency above a certain “threshold frequency” a current is detected, ie photoelectrons must be ejected from the metal….

8. The photoelectric effect
When the cathode is illuminated with light of frequency above a certain “threshold frequency” a current is detected, ie photoelectrons must be ejected from the metal….Electrons emitted INSTANTANEOUSLY even for the lowest intensity of light
If the frequency of the incident light is below the threshold frequency, no electrons emitted, no matter how intense the light is.
If light were behaving entirely like a classical EM wave, its power would be proportional to intensity, but independent of frequency (mechanical wave energy proportional to amplitude and frequency, EM wave energy proportional to amplitude (intensity) only)
Would expect intense light of any frequency to generate photoelectrons, and also “time delay” for photoemission due to light of low intensity…………..

9. The photoelectric effect: detailed results
current proportional to light intensity
battery polarity reversed to
impede flow of photoelectrons from
cathode to anode

10. The photoelectric effect: detailed results
Stopping potential proportional to light frequency
battery polarity reversed to
impede flow of photoelectrons from
cathode to anode

11. Significance of the stopping potential
If we assume the electrons in the metal behave like a classical ideal gas (?), then they won’t all have the same velocity (Maxwell velocity distribution)
In other words, they won’t all have the same kinetic energy
The stopping potential is the voltage required to stop the MOST ENERGETIC electrons from leaving the metal

12. The work function
It requires a certain amount of energy to extract the electrons from the metal: imagine the electrons as being trapped at the bottom of a well:
E=0 
maximum electron energy
The work function of a metal is the least amount of energy required to remove electrons from the metal, ie the energy required to remove the most energetic electrons

13. The work function
Imagine we have incident light with energy Ep represented by length of arrow)
Emax=Ep-
E=0   Ep
So, we expect the emitted photoelectrons to have a distribution of energies up to a maximum of Ep - . So, going back to the stopping potential V0, we must have:

14. Einstein’s postulate
A beam of light can be treated as a stream of particles (PHOTONS) with zero rest mass
Each photon has energy:
where h is a constant (Planck’s constant, h ≈ 6.63 x Js)
f, λ, c, are frequency, wavelength and velocity of light (in vacuum) respectively.
Light intensity is proportional to PHOTON FLUX (no of photons passing through unit area per second)

15. Results of photoelectric effect: the photon model
When the cathode is illuminated with light of frequency above a certain “threshold frequency” a current is detected, ie photoelectrons must be ejected from the metal….Electrons emitted INSTANTANEOUSLY even for the lowest intensity of light
Photons behave like “bullets” with energy hf, which can “hit” the electrons. If f is high enough, a single photon can instantaneously remove an electron from the metal 
Photo current is proportional to light intensity (if f is above threshold frequency).
Light intensity = number of photons hitting surface per second
Current = number of electrons emitted from surface per second. 

16. Results of photoelectric effect: the photon model
So, in terms of the photon model, the stopping potential is related to the photon frequency, Planck’s constant, and the work function of the metal:
By measuring V0 as a function of f, we can measure Planck’s constant and the work function of the metal……………………………….

17. Example Calculation 1
In a photoelectric experiment a reverse potential of 2V is required to stop the flow of current for light of a certain frequency. Calculate a) the maximum kinetic energy and b) the maximum velocity of the emitted photoelectrons……..

18. Example Calculation 2
In a photoelectric experiment, stopping potentials of 1V, 2 V and 3V are measured for light of wavelengths 600nm, 400nm and 300nm respectively. Use these data to determine the work function of the cathode material and the value of Planck’s constant………….

19. Example Calculation 2