8.1.3 Schrodinger equation and quantum numbers 1.Schrodinger equation og02g+0型.-8m(E-W9 x2 0y2 0z2 Ψ：a wave function E:the overall energy of an electron V:the potential energy m:the mass of an electron h:Planck's constant x,y,z:the cartesian coordinates
1.SchrÖdinger equation 8.1.3 Schrödinger equation and quantum numbers zyx ： cartesian the,, scoordinate V： energy potential the E： electronan ofenergy overall the Ψ： function wavea m： electronan of mass the h：Planck s' constant ( ) VE Ψ h m zΨ yΨ xΨ −= − ∂∂ + ∂∂ + ∂∂ 22 2 2 2 2 2 2 8 π
2.Quantum numbers 平n1m(x,y,2） 1 The principle quantum number,n n=1,2,3,... 2The angular momentum quantum number,/ 1=0,1,2,.n-1 3 The magnetic quantum number,m m=+l,.0.,-1 4The electron spin quantum number,ms 1 1 ms 2 m=- 2
2. Quantum numbers ① The principle quantum number, n l = n − 1,...2,1,0 ③ The magnetic quantum number, m ④ The electron spin quantum number, m s , 2 1 m s = = +lm ......,0,...... − l 2 1 ms −= ②The angular momentum quantum number, l n=1, 2, 3,…… ),,( ,, Ψ zyx mln
The principle quantum number,n: The value of n determines the total energy of the electron.The energy of the electron in the H atom varies only with the value of n. 2.179×10 18 E 22 The different values of n corresponds to different electron shells: n=12 3 4 5. K L M N
• The value of n determines the total energy of the electron. The energy of the electron in the H atom varies only with the value of n. J 10179.2 2 18 n E − × −= • The different values of n corresponds to different electron shells: The principle quantum number, n： n = １２３４５… K L M N O…
The angular momentum quantum number,/ 1=0,1,2,3...n-1 Each value of corresponds to different types of subshells s,p,d,f...within a shell I decides the shapes of angular function of y The magnetic quantum number,m: m=0,士1，士2..士1； m is related to the spatial orientation of an orbital in a given subshell
The angular momentum quantum number, l ： l = 0，1，2，3……n－1 Each value of l corresponds to different types of subshells s, p, d, f…within a shell. l decides the shapes of angular function of ψ The magnetic quantum number, m： m= 0，±1, ±2……±l ； m is related to the spatial orientation of an orbital in a given subshell
The spin quantum number ms 1 ms= 29 m= 2 发射源 狭缝 磁铁 集束板 高等化学教学资源库○等敏：出，牡 @-①-⊙-⊙-@ Experimental set-up for electron spin phenomena
The spin quantum number ms , 2 1 ms = 2 1 ms −= Experimental set-up for electron spin phenomena