4.德布罗意波、波粒二象性 De Broglie wave Wave-Particle Dualism The dual nature of light, particle and wave 光的波粒二象性 particle wave Cenergy) E v( frequency) (momentum)P h n (wavelength) These two natures are connected by h Eb=hv…() 2 E E+(P) hy h P=E/C (2)
The dual nature of light, particle and wave 光的波粒二象性 particle wave （energy） （frequency） （momentum） （wavelength） E P h These two natures are connected by h. (1) E = h / (2) h C h P = E C = = 2 2 0 2 E = E + (P c) 4.德布罗意波、波粒二象性 （De Br glie wave .Wave ö -Particle Dualism ）
De broglie assumed that the wavelength of predicted matter waves was given by the same relationship that held for light namely, or 2=h/p 德布罗意,L.V E ttt t wave tlit Y H particl which connects the wavelength of a light wave with the momentum of the associated photons De broglie wave
De Broglie assumed that the wavelength of predicted matter waves was given by the same relationship that held for light namely, or λ= h / P u Z X Y E H particle wave which connects the wavelength of a light wave with the momentum of the De Broglie wave associated photons
De broglie predicted that the wavelength of matter waves would also be given by 2=h/p where p would now be the momentum of the particle of matter. De broglie wave Example l what wavelength is predicted by De broglie wave for a bullet whose mass is mo=0.05kg and velocity is v=300m/s? Solve°V<<C h663×10-34 44×103(m)=44×1024(A) mn0.05×300
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 ( ) 0.05 300 6.63 10 3 5 3 4 0 m m V h − − = = = = 4.410-24(Å)
Example 1. What wavelength is predicted by De broglie wave for a bullet whose mass is mo=0.05kg and velocity is v=300m/s? olve V<<C h663×10-34 44×10-3(m)即44×1024A 0.05×300 Exp 2. What wavelength is predicted by De broglie wave for a beam of electrons whose kinetic energy is eu and velocity n isv? (V<<C) B From the law of KE mo y conservation of energy 发射电 e -mv=el 子阴级U加速电极
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 ( ) 0.05 300 6.63 10 3 5 3 4 0 m m V h − − = = = 即4.410-24Å U B K 发射电 子阴级 加速电极 e m0 V Exp 2. What wavelength is predicted by De Broglie wave for a beam of electrons whose kinetic energy is eU and velocity is v ? （VC） m V = eU 2 0 2 1 From the law of conservation of energy
B 加速电极 mo y QeL KE 发射电 e 子阴级U De broglie wavelength follows from h 12.3° P my v2emU VU 12.3 12.3 or|2===×10(m)or A 12.3 When u=100,元 √U 12.3(A)
U B K 发射电 子阴级 加 速 电 极 0 2 m eU V = P h = em U h 2 0 = = A U 12.3 m V h 0 = e m0 V or 10 ( ) 12.3 1 0 m U − = or U 12.3 = Å When U=100(V), 12.3 12.3 = = U (Å) m V = eU 2 0 2 1 De Broglie wavelength follows from