1-1-2 The Movement of Electrons inAtoms Is Statistical 统计性（1）DeBroglie'sEquation德布罗意方程（1924）dual nature of lightEinstein mass-energy relation : E = mc2E=hvP = mc =E /c = hv/c= h/22=h/P=h/myde BroglieequationDe Broglie'swave orthe particle's wave.16
16 1-1-2 The Movement of Electrons in Atoms Is Statistical 统计性 （1）De Broglie’s Equation 德布罗意方程（ 1924） dual nature of light Einstein mass-energy relation : E = mc2 E = h P = mc = E /c = h /c = h/ = h/P = h / mv de Broglie equation De Broglie’s wave or the particle’s wave
KMPFigure8-3Davissson-GermerElectrondiffractionstestin1927
17 V K D M P θ Figure 8-3 Davissson - GermerElectron diffractions test in 1927
(2) The Heisenberg Uncertainty Principle(in1927)海森堡不准确关系Ax·△P≥h/2元Ax·Av≥h/2元mAP: the uncertainty in momentumAx : the uncertainty in position of the particleAv: the uncertainty in its speedm: the mass of the particle in kgh = 6.626 X 10-34Js18
18 (2) The Heisenberg Uncertainty Principle(in1927) 海森堡不准确关系 ∆x ·∆P ≥ h / 2π ∆x ·∆v ≥ h / 2πm ∆P : the uncertainty in momentum ∆x : the uncertainty in position of the particle ∆v: the uncertainty in its speed m: the mass of the particle in kg h = 6.626 × 10-34J∙s
Usually electrons move at a speed near tolight speed,its sizeis largely smaller than 10-10 m. Thus to locate it precisely, Axshould be less than 1o-1l m, then the uncertainty in the speedoftheelectron△v > h / 2元m·△x= 6.626 × 10-34 / 2 × 3.14 × 9.11 × 10-31 × 10-11= 1.16x107 (m·s-1)19
19 Usually electrons move at a speed near to light speed, its size is largely smaller than 10-10 m. Thus to locate it precisely, ∆x should be less than 10-11 m, then the uncertainty in the speed of the electron ∆v ≥ h / 2πm ·∆x = 6.626 10-34 / 2 3.14 9.11 10-31 10-11 = 1.16107 (m∙s-1 )
Table 8-1 ComparisonsonMovementsof SubmicroscopicParticlesandMacroscopicalObjectsSubmicroscopicParticles/r<10-8mMacroscopical ObjectsQuantummechanicalmodelNewtonmechanical lawF=ma02Y/0x2+ 02 Y/0y2+ 02 Y/0z2= -8元2m (E - V)/ h2The state of objects (speedThestateofsubmicroscopicand position) at any instantparticles (energyandpossibility)canbepreciselydeterminedatanyinstantcanbe expressedby W(x, y, z).△x·△v≥h/2元m20
20 Table 8-1 Comparisons on Movements of Submicroscopic Particles and Macroscopical Objects ◼ Macroscopical Objects Newton mechanical law F = ma The state of objects (speed and position) at any instant can be precisely determined. ◼ Submicroscopic Particles/ r < 10-8 m Quantum mechanical model ∂ 2Ψ/∂x 2+ ∂2Ψ/∂y 2+ ∂2Ψ/∂z 2 = -8π2m (E – V)Ψ/ h 2 The state of submicroscopic particles (energy and possibility) at any instant can be expressed by Ψ(x, y, z). ∆x ·∆v ≥ h / 2πm