The dual nature of light, particle and wave

4.德布罗意波、波粒二象性 （De Br glie wave .Wave-Particle Dualism ） ö h The dual nature of light, particle and wave 光的波粒二象性 particle wave （energy）（frequency）（momentum）（wavelength） These two natures are connected by h.

De Broglie assumed that the wavelength of predicted matter waves was given by the same relationship that held for light namely, or X Y Z which connects the wavelength of a light wave with the momentum of the λ= h / P wave particle associated photons. De Broglie wave

De Broglie predicted that the wavelength of matter waves would also be given by λ= h / P where P would now be the momentum of the particle of matter. De Broglie wave Example 1. What wavelength is predicted by De Broglie wave for a bullet whose mass is m0=0.05kg and velocity is v=300m/s? Solve, ∵V << C = 4.410-24(Å)

Example 1. What wavelength is predicted by De Broglie wave for a bullet whose mass is m0=0.05kg and velocity is v=300m/s? m0 Exp 2. What wavelength is predicted by De Broglie wave for a beam of electrons whose kinetic energy is eU and velocity is v ? （VC） e B K 发射电子阴级 U 加速电极 Solve, ∵V << C 即4.410-24Å From the law of conservation of energy,

m0 加速电极 e B K Å or 发射电子阴级 U (Å) De Broglie wavelength follows from or When U=100(V),

Demonstration of De Broglie wave 加速电极 B G 电流计 K Ni单晶发射电子阴级 M U 1) C. J. Davisson and L. H. Germer Test 戴维逊--革末实验 Figure shows the apparatus of Davisson and Germer. 实验装置：

加速电极 B Ni单晶 G I 电流计 K a Ni单晶 d 发射电子阴级 M U 1）C. J. Davisson and L. H. Germer Test 实验装置： φ=50° U=54(v) a=0.215nm d=0.0908nm

加速电极 Experi- mentalvalue is given by φ=50o . This is excellent agreement. B G 电流计 K Ni单晶发射电子阴级 M U 实验装置： suppose electrons are waves. De Broglie wavelength of electron waves would be given by From Bragg’s law φ=51o

2) G.P. Thomson electron diffraction test 1927 年汤姆逊（G·P·Thomson）以600伏慢电子 (=0.5Å)射向铝箔，也得到了像X射线衍射一样的衍射，再次发现了电子的波动性。 1937年戴维逊与GP汤姆逊共获当年诺贝尔奖. G·P·Thomson为电子发现人J·J·Thmson的儿子. 尔后人们又发现了质子、中子的衍射.

3) Electron double-slit diffraction test 电子双缝实验 1961年琼森（Claus Jönsson）将一束电子加速到50Kev，让其通过一缝宽为a=0.510-6m，间隔为d=2.010-6m的双缝,当电子撞击荧光屏时,发现了类似于光的双缝衍射的图样. 大量电子一次性行为

电子双缝实验 — 一个电子多次重复性行为

Scanning tunnelling microscope 扫描隧道显微镜

中文书：19—15, 19—16, 外文书：48—1. 扫描隧道显微镜中的原子形象

The dual nature of light, particle and wave