1. The Wave-Particle Duality
Interference and diffraction experiments show that light behaves like a wave. The photoelectric effect, the Compton effect, and pair production demonstrate that light behaves like a particle.

2. Consider a double slit experiment in which only one photon at a time leaves the light source. After a long time, the screen will show a typical interference pattern.
Even though there is only one photon emitted at a time, we cannot determine which slit it will pass through nor where it will land on the screen.

3. The intensity pattern on the screen is representative of the probability that a photon will land in a given location (higher intensity = higher probability).

4. Waves and Particles
Like photons, the wavelength of a matter wave is given by
This is known as the de Broglie wavelength.

5. de Broglie Wavelength:
Waves and Particles
We know that light behaves as both a wave and a particle. The rest mass of a photon is zero, and its wavelength can be found from momentum.
Wavelength of a photon:
All objects, not just EM waves, have wavelengths which can be found from their momentum
de Broglie Wavelength:

6. Finding Momentum from K.E.
In working with particles of momentum p = mv, it is often necessary to find the momentum from the given kinetic energy K. Recall the formulas:
K = ½mv2 ; p = mv
Multiply first Equation by m:
mK = ½m2v2 = ½p2
Momentum from K:

7. Example 5: What is the de Broglie wavelength of a 90-eV electron
Example 5: What is the de Broglie wavelength of a 90-eV electron? (me = 9.1 x kg.) - e-
90 eV
Next, we find momentum from the kinetic energy:
p = x kg m/s
l = nm

8. What are the de Broglie wavelengths of electrons with the following values of kinetic energy?
(a) 1.0 eV and (b) 1.0 keV.
(a) The momentum of the electron is
and

9. (b) The momentum of the electron is
Example continued:
(b) The momentum of the electron is
and

10. What is the de Broglie wavelength of an electron moving with a speed of 0.6c?
This is a relativistic electron with
Its wavelength is

11. The Uncertainty Principle
Consider the following experiment.
Take the set up for Young’s double slit experiment.

12. The Uncertainty Principle
If we observe a beam of electrons through one slit with the other closed we get some intensity pattern.
Similarly if we now open that slit and cover the other a similar pattern is observed.
Classically, if both slits are open a pattern formed by a superposition should be the result.

13. The Uncertainty Principle+

14. The Uncertainty Principle
However no such pattern is obtained.
In order to understand this phenomenon the idea that a particle has a distinct path must be discarded.

15. The Uncertainty Principle
There is no such concept as the path of a particle.
This forms the content of what is called the uncertainty principle.

16. The Uncertainty Principle
The fact that an electron has no definite path means it also has no characteristics (quantities defining the motion).

17. Heisenberg Uncertainty Principle
Effect of taking a measurement

18. Heisenberg Uncertainty Principle
The uncertainty principle may be stated as:
If a measurement of position is made with precision and simultaneously measurement of momentum is made with precision , then the product of the uncertainties can not be smaller than the order of .

19. Heisenberg Uncertainty Principle
The uncertainty principle sets limits on how precise measurements of a particle’s momentum and position can be.
Could incorporate personal response system questions from the College Physics by G/R/R 2E ARIS site ( Instructor Resources: CPS by eInstruction, Chapter 28, Questions 6, 9, and 15.
where

20. The more precise a measurement of position, the more uncertain the measurement of momentum will be and the more precise a measurement of momentum, the more uncertain the measurement of the position will be.

21. The energy-time uncertainty principle is

22. An electron passes through a slit of width 1. 010-8 m
An electron passes through a slit of width 1.010-8 m. What is the uncertainty in the electron’s momentum component in the direction perpendicular to the slit but in the plane containing the slit?
The uncertainty in the electron’s position is half the slit width x=0.5a (the electron must pass through the slit).