1. Chapter 38: Photons and Quantum Mechanics
Question: What did Albert Einstein win the Nobel Prize in Physics for ?
Special Relativity ? General Relativity ?
Swedish Academy: The Nobel Prize in Physics 1921 was awarded to Albert Einstein "for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect".

2. Chapter 38: Photons and Quantum Mechanics
Our learning goals in this chapter:
To consider the fundamental constituent of light, the photon
To study the ejection of an electron by an incident photon, the photoelectric effect
To understand how the photon concept explains x-ray production, x-ray scattering (Compton scattering), and e+ e- pair production
To interpret light diffraction and interference in the photon picture
To introduce the Heisenberg uncertainty principle

3. Photoelectric Effect

4. Photoelectric Effect
Interesting fact: Blue light striking cesium causes the cesium to emit electrons. Red light does not.
Einstein’s explanation: Light comes in photons. To emit an electron, the cesium atom must absorb a single photon whose energy exceeds the ionization energy of the outermost electron in cesium. A blue photon has enough energy; a red photon does not.
Photoelectric effect

5. Photoelectric Effect Apparatus
Done at UH in PHYS274L

6. Photoelectric Effect Master Equations
Maximum kinetic energy of the electron is the energy from the photon minus the “work function” ϕ
“Stopping potential” V0
The current at which the photoelectron current stops

7. Photon Quantization Master Equations
where h=6.63 x 10-34J-s
Question: How can we express the photon energy in terms of the photon wavelength ?
Ans: use f = c/λ (Recall c=λf)
Question: What is the photon momentum in terms of wavelength or frequency ?
(but wait, the massless photon has momentum ?)
From special relativity

8. Einstein’s explanation of the photoelectric effect
A photon carries a discrete amount of energy. For light of frequency f and wavelength λ, this energy is E = hf or E = (hc)/λ, where h is Planck’s constant × 10−34 J • s.
This explains how the energy of an emitted electron in the photoelectric effect depends on the frequency of light used (see Figure on the right).
The momentum of a photon of wavelength λ is p = h/λ.
“Photons are quantized”

9. The photoelectric effect—examples
This is also called ϕ, in the master equation
for the PE effect

10. The photoelectric effect— many applications
Photons enter the scope and hit a plate ejecting electrons, which then pass through a disk with millions of tiny channels. The current in each channel is amplified.
Night vision scopes
Solar cells: by the photoelectric effect, photons excite electrons into the conduction band
Solar cells

11. Photon quantization— example
A laser pointer with a power output of 5.00mW emits red light (λ=650nm).
a) What is the magnitude of the momentum of each photon ?
Since light is quantized we only need the frequency or wavelength for this problem.
Could also use E=hc/lambda
b) What is the energy of each photon ?

12. Photon quantization— example
A laser pointer with a power output of 5.00mW emits red light (λ=650nm).
b) How many photons does the laser pointer emit each second ?
Calculated in a)
How do we calculate the number of photons per second with this information ?
Huge but each photon has a very small energy

13. Photoelectric effect— example (how to determine h)
For a particular cathode material in a photoelectric effect experiment, you measure stopping potentials V0=1.0 V for light of wavelength λ=600nm, 2.0 V for 400nm and 3.0V for 300 nm.
a) Determine the work function, ϕ for this material, and then the value of Planck’s constant h.
Question: Suppose we plot V0 vs f (frequency). What does the graph look like ?
The vertical intercept is -ϕ/e=-1.0V
The slope of the graph is h/e

14. Photoelectric effect— example (how to determine h)
For a particular cathode material in a photoelectric effect experiment, you measure stopping potentials V0=1.0 V for light of wavelength λ=600nm, 2.0 V for 400nm and 3.0V for 300 nm.
The slope of the graph is h/e
Let’s take the 3.0V and -1V (y-intercept) points to calculate the slope.