Summary of solution v(,0,y)=R()o()(0) R()=e∑br=e∑ k=0 o(0)=P(cosB)=(1-cos?e)2 G(cos e) G(2)=2a, cos em 2丌 The Application of the number of nodes 2021/8/21 Che mistry De partne nt of Fudan University 16
Physical ChemistryI Chapter II Atomic Structure and Spectrum 2021/8/21 Chemistry Department of Fudan University 16 (r,,) = R(r)( )() Summary of solution ( ) im e − = 2 1 ( ) P(cos ) ( cos ) G(cos) m 2 2 = = 1− − = = l m n n an G z 0 ( ) cos The Application of the number of nodes max max k k 0 ( ) l ar k ar l k k k l k l k R r e b r e r b r − − − + = = = =
Phusical chemiatry Chapter II Atomic Structure and Spectrum term Associated Laguerre function . e Is level gca n=2=0. )exp(r/2 2s level 8πaa 2a r n=2,l=1,m=1 exp (-r/2ao)sin ee 8 v兀aa r 2p level n=2,l=1,m=0 exp(r/2ao)cos 0 gca r n=21=1m=-1 exp(r/2ao)sin ee 8√πao 2021/8/21 Che mistry De partne nt of Fudan University 17
Physical ChemistryI Chapter II Atomic Structure and Spectrum 2021/8/21 Chemistry Department of Fudan University 17 term Associated Laguerre function 1s level exp( r / a ) a 1 0 3 0 n 1,l 0,m 0 − = = = = 2s level ) exp( r / 2a ) 2a r (1 8 a 1 0 0 3 0 n 2,l 0,m 0 − − = = = = 2p level = = = − = − i 0 0 3 0 n 2,l 1,m 1 exp( r / 2a )sin e a r 8 a 1 − = = = = exp( r / 2a ) cos a r 4 a 1 0 0 3 0 n 2,l 1,m 0 − = = =− − = i 0 0 3 0 n 2,l 1,m 1 exp( r / 2a )sin e a r 8 a 1
Radial function Radial properties Radial distribution Radial probability density 2.0 1.5 0D5 .0 3 5 ere The radial wavefunction of some states of hydrogen atom 2021/8/21 Che mistry De partne nt of Fudan University
Physical ChemistryI Chapter II Atomic Structure and Spectrum 2021/8/21 Chemistry Department of Fudan University 18 Radial properties Radial function Radial distribution Radial probability density The radial wavefunction of some states of hydrogen atom
numbers ;” n=2 =0 m=土 2 Maximum 2 Electrons 3d 3p 10a 15a 25 Hydrogen 2s Radial probability 2021/8/21 Che mistry De partne nt of Fudan University 19
Physical ChemistryI Chapter II Atomic Structure and Spectrum 2021/8/21 Chemistry Department of Fudan University 19 Hydrogen 2s Radial Probability
Quantu numbers n=2 m。=±1 1,0,1 Maximum me 2p 6 Electrons 3d 3p 5 10 15 25 Hydrogen 2p radial probability 2021/8/21 Che mistry De partne nt of Fudan University
Physical ChemistryI Chapter II Atomic Structure and Spectrum 2021/8/21 Chemistry Department of Fudan University 20 Hydrogen 2p Radial Probability