1. Wave Behaviour of Particles
SACE Stage 2 Physics
Wave Behaviour of Particles

2. De Broglie’s Postulate
De Broglie argued that if photons can behave as particles then particles can behave as waves.
Where;
p = momentum of particle (mv)
h = Planck’s constant
l = wavelength of particle

3. De Broglie’s Postulate
Cricket ball;

4. De Broglie’s Postulate
Electron;
This wavelength is comparable in size to an X-ray wavelength.

5. De Broglie’s Postulate
It would appear that if the wave properties of particles are to be observed we must look toward very tiny particles with small momentum. These may produce large enough wavelengths,
for wave effects to be observed. The existence of wave properties has been confirmed by experiment.

6. Davisson–Germer Experiment
Electrons have wavelength in the same order as X-rays. These can then be diffracted in the reflection or transmission of a beam of electrons by a crystal.

7. Davisson–Germer Experiment
A parallel beam of constant energy electrons was incident normal to the surface of a Nickel crystal. Some electrons were reflected back from the crystal. The number reflected at angle  was measured with a detector consisting of a plate P behind another plate D. A retarding voltage VR a little less than the accelerating voltage V allowed only electrons reflected from the crystal with little energy loss to produce a current in meter M. Low energy electrons were used.
This ensured electrons would be reflected from the surface of the Nickel as low energy electrons lose energy rapidly in a solid.

8. Davisson–Germer Experiment
V = 54 volt
electron gun + - VR
electrons P C D M
Constructive interference for one particular angle 
dsin = N

9. Davisson–Germer Experiment
Energy of incident electrons

10. Davisson–Germer Experiment
Momentum of the electron,

11. Davisson–Germer Experiment
de Broglie wavelength of the electrons,

12. Davisson–Germer Experiment
Reinforcement occurs when,
First order reinforcement when m=1,

13. Davisson–Germer Experiment
Conclusion:
Close correspondence for the wavelength of an electron obtained experimentally and theoretically using de Broglie’s hypothesis provided strong evidence for the validity of the de Broglie thesis.

14. Application – Electron Microscope
The human eye can see things up to about 0.1mm un-aided. Magnifyning glasses and microscopes have enabled to see things (resolve) that are much smaller.
Violet light has a wavelength of 4 x 10-7m and only the best light microscopes can enable us to see comparable sized objects.
Need a wavelength a lot smaller.
Using de Broglie’s ideas, physicists used the wavelength of an electron to view these very small objects. Instead of glass lenses, magnetic lenses are used.

15. Application – Electron Microscope