Matter Waves

1. Louis de Broglie 1892-1987 Matter Waves

2. Matter Waves • Louis de Broglie was a physics graduate student when he suggested that matter had a wave nature. • Recall that EMR acts as a wave in some experiments; diffraction, refraction, interference • EMR also acts like a particle; photoelectric effect, momentum

3. Matter Waves • De Broglie stated that since EMR has momentum and acts like a wave, perhaps matter, which has momentum, also acts like a wave. • • He used Compton’s momentum of EMR formula, p=h/λ and equated it to the formula for momentum of matter, p=mv

5. De Broglie wave equation • De Broglie wavelength is more significant for small masses traveling at high speeds rather than large masses traveling at low speeds

6. Matter Waves • Matter waves have the wavelength of

7. Matter Waves • This was not a popular idea. In fact, de Broglie’s thesis was held up until Einstein reviewed his work and agreed with it. • To prove the existence of such waves is very difficult because they are so small.

8. Example • Calculate the wavelength of a 50 kg skier moving at 16 m/s.

9. Solution

10. This means what? • This wavelength (8.3 x 10-37 m) is about a billion, trillion times smaller than a hydrogen atom! • This wavelength is so small that it is completely unobservable.

11. Examples • Calculate the wavelength of an electron moving at 1.0 x 106 m/s.

12. Solution

13. What does this mean? • This wavelength (7.3 x 10-10 m) is in about the same wavelength of x-rays. • This is observable.

14. Eg) Determine the De Broglie wavelength for an alpha particle traveling at 0.015c.

15. Eg) An electron is accelerated by a potential difference of 220V. Determine the De Broglie wavelength for the electron.

16. Davisson-Germer Experiment • • Soon after de Broglie’s idea was presented, Davisson and Germer observed evidence that beams of e¯ fired at the crystal lattice of metals diffract to produce nodes and ant-nodes. • .

17. Davisson and Germer Experiment • The experiment was firstly performed in 1927 by the captioned scientists. • This experiment demonstrated the wave nature of the electron, confirming the earlier hypothesis of de Broglie. Putting wave-particle duality on a firm experimental footing, it represented a major step forward in the development of quantum mechanics. • 54 keV electron beam is normally incident to a nickel crystal (lattice spacing d = 0.215 nm). • Animation Davisson-Germer Exp. Modern Physics Chapter One

18. Rotating the electron detector, the first peak (maximum) was detected at  = 50o Modern Physics Chapter One

19. Å Using the theory for X-ray diffraction in crystal (Bragg ‘s Law) Constructive interference occurs at d sin  = n  where n = 1, 2, 3, … For d = 2.15 ,  = 50o, n = 1 Modern Physics Chapter One

20. Momentum and wavelength of electron beam Rest energy of electron Eo Kinetic energy of electron K = qV = 54 eV<<Eo Classical (or non-relativistic) calculation is OK!

21. Å Wavelength of electron beam: Modern Physics Chapter One

22. Definite position in space Extended infinitely in space How to compromise the two different natures in one single entity De Broglie wave This experiment demonstrates that: Classical particle (with mass, position and momentum) also behaves like a wave. particle wave Modern Physics Chapter One