波函数和电子云

2.3Thewefunctionandelectroncloud2.3.1Thewe-functionsofhydrogen-likeionsFig.(left)The-rand2-rdiagramofthe1sstateofthehydrogenatom.(right)The-rofthe2sstate.r=2a0r=4a0ARadialProbability

Distribution

ofApples2.3.2TheradialdistributionfunctionTheprobabilityoffindingelectronintheregionofspace

r+dr,θ+dθ,φ+dφWhatistheprobabilityofelectronatr+dr,(inathinsphericalshellcenteredattheorigin)?NormalizedsphericalharmonicsRadialdistributionfunction=wefunction

2=probabilitydensityr2R2=radialprobabilityfunctionfunctionCalculatingthemostprobableradiusExpectationvalueofrExample:pleasederivetheradialprobabilitydistributionfunctionoftheH1sorbitalandtheradiumofitsmaximum.ItsradicalprobabilitydistributionfunctionisToderivetheradiumofitsmaximum,weheFig.Theradialdistributiondiagram(D(r)-r)Theradialdistributionfunctionhas(n-l)maximaand(n-l-1)nodalsurfacesAsphericalsurfacewiththeelectrondensityofzeroiscalledanode,ornodalsurface.2.3.3Theangularfunction(Ylm(

))

AngularpartItindicatestheangulardistributionfunctionofanatomicorbitalandistheeigenfunctionofM2

andMz

operators.Angularfunction(Ylm(

))s-Orbital(l=0,2l+1=1)Y00

p-Orbital(l=1,2l+1=3)Y10

Y1

1p-Orbitalpxpypzd-Orbital(l=2,2l+1=5)

Y2

1Y20Y22lmlorbital00s10pz±1px±1py20d2z2-x2-y2=dz2±1dxz±1dyz±2dx2–y2±2dxyd-OrbitalNodesAnodeisasurfaceonwhichanelectronisnotfound.For