1. Chapter 29 Photoelectric Effect

2. The Wave-Particle Duality
Scientists now accept the wave-particle duality as an essential part of nature:
Waves can exhibit particle-like characteristics, and particles can exhibit wave-like characteristics.

3. Photon Model of Light
Although the ideas of the photon model of light are attributed to Einstein, the first work suggesting energy could be quantized was done by Max Planck, while studying blackbody radiation curves.

4. How can we measure temperature?
Can perform in-situ measurements, although this has its drawbacks
Localised in space and time
Dangerous (or at least uncomfortable)
Not as accurate as you might think (equilibration times, instrument “trauma”….)
Fortunately, we can calculate the temperature of an object without touching it

5. Quantifying Blackbody Radiation
Collisions cause electrons in atoms/molecules to become excited, and photons to be emitted
In this way internal energy converted into electromagnetic energy
Heated solids produce continuous spectra dependent only on temperature
How can we quantify the relationship between internal kinetic energy (temperature) and emission of radiation? Why does a burning log glow?
Planck’s blackbody radiation law is a mathematical description of the spectral distribution of radiation emitted from a perfect radiator (blackbody)

6. Radiation is the process in which
energy is transferred by means of
electromagnetic waves.
A material that absorbs completely
is called a perfect blackbody.
The absorbed energy is emitted by vibrating atoms of the blackbody object.

7. Quantifying Blackbody Radiation
The spectral radiant exitance from an active lava varies by orders of magnitude
Remote measurements of radiated energy provide a route for monitoring thermal emission and quantifying surface temperature.

8. Photon Model of Light
In 1900, Planck was able to solve the problem by constraining the energy of the vibrating atoms to be a series of discrete, or “quantized” values, such that:
How do we know the surface temperature of the sun?

9. Photon Model of Light
Planck’s conclusions implied that the lowest energy carried by EM waves was equal to hf. Einstein was the first to take Planck’s idea seriously.

10. Photoelectric Effect
Evidence for particle (photon) nature of light comes from a phenomenon called the photoelectric effect, in which electrons are emitted from a metal surface when light shines on it.
In the photoelectric effect, light with a sufficiently high frequency ejects electrons from a metal surface. These photoelectrons, as they are called, are drawn to the positive collector, thus producing a current.

11. Energy of a Photon
In 1905 Einstein presented an explanation of the photoelectric effect that took advantage of Planck’s work concerning blackbody radiation. It was primarily for his theory of the photoelectric effect that he was awarded the Nobel Prize in physics in In his photoelectric theory, Einstein proposed that light of frequency f could be regarded as a collection of discrete packets of energy (photons), each packet containing an amount of energy E given by: (where h is Planck’s constant)

12. When light shines on a metal, a photon, with energy hf, can give up its energy to an electron in that metal.
The minimum energy required to remove the least strongly held electrons is called the work function, W0. The value of W0 is specific to the metal.
The photon energy comes in discrete packets called quanta, (plural for quantum).

13. KEmax depends on the frequency of light incident on the metal.
The minimum frequency necessary for an electron to leave the lattice structure of the metal (with 0 KE) is the threshold frequency, f0 .
Electrons will not leave the metal at f < f0.
W0 = hf0

15. Plank’s Constant E = hf (h = 6.626 x 10-34 J s)
In his studies of black-body radiation, Maxwell Planck discovered that electromagnetic energy is emitted or absorbed in discrete quantities.
Planck’s Equation:
E = hf (h = x J s)
Light consists of tiny bundles of energy called photons, each having a well-defined quantum of energy.
E = hf
Photon

16. Energy in Electron-volts
Photon energies are so small that the energy is better expressed in terms of the electron-volt.
One electron-volt (eV) is the energy of an electron when accelerated through a potential difference of one volt.
1 eV = 1.60 x J
1 keV = 1.6 x J
1 MeV = 1.6 x J

17. First we find f from wave equation: c = fl
Example 1: What is the energy of a photon of yellow-green light (l = 555 nm)?
First we find f from wave equation: c = fl
E = 3.58 x J
E = 2.24 eV Or
Since 1 eV = x J

18. Useful Energy Conversion
Since light is often described by its wavelength in nanometers (nm) and its energy E is given in eV, a conversion formula is useful. (1 nm = 1 x 10-9 m)
If l is in nm, the energy in eV is found from:
Verify the answer in Example

19. The Photo-Electric Effect
Cathode
Anode
Incident light
Ammeter + - A C
When light shines on the cathode C of a photocell, electrons are ejected from A and attracted by the positive potential due to battery.
There is a certain threshold energy, called the work function W, that must be overcome before any electrons can be emitted.

20. Photo-Electric Equation
Cathode
Anode
Incident light
Ammeter + - A C
Threshold wavelength lo
The conservation of energy demands that the energy of the incoming light hc/l be equal to the work function W of the surface plus the kinetic energy ½mv2 of the emitted electrons.

21. Example 2: The threshold wavelength of light for a given surface is 600 nm. What is the kinetic energy of emitted electrons if light of wavelength 450 nm shines on the metal? A
l = 600 nm
; K = 2.76 eV – 2.07 eV
K = eV Or
K = 1.10 x J

22. THE MOMENTUM OF A PHOTON AND THE COMPTON EFFECT
The phenomenon in which an X-ray photon is scattered from an electron, with the scattered photon having a smaller frequency than the incident photon, is called the Compton effect.

23. Compton Effect
Compton showed that the difference between the wavelength λ’ of the scattered photon and the wavelength λ of the incident photon is related to the scattering angle θ by: