Slater approximate method for central field Z+=- Z-0j o:Screen constant The presence of other electrons around a nucleus“screens”an electron from Z'=Z-o the full charge of the nucleus. Z*:Effective nuclear charge R1=(2E)r-e Z-0i n*:Effective principal quantum number n n*=n(when n≤3) B=(Z-G) -e2 n*=3.7(when n=4) n 4π8o0 --R(Z-0 n*=4.0(when n=5) Z-02 -13.6eV-( n Lithium Z=3 7*2 2 3-2 En =-R E,=-R =-13.6 n2 n Predicted:E =-30.6 eV Z*2 -5.4=-13.6 Actual:E =-5.4 eV 5.4×22 13.6 Z*=1.26 1.26=3- 0=1.74Slater approximate method for central field σ: Screen constant Z*: Effective nuclear charge Z = Z −σ * i i i i i i r Z r r Z V σ −σ ˆ = − + = − The presence of other electrons around a nucleus “screens” an electron from the full charge of the nucleus. * 2 1 1 , (2 ) n Z R r e i n r n n l σ ξ ξ ξ − = = − − + n*: Effective principal quantum number 2 * 2 * 0 0 2 2 * 13.6eV ( ) ( ) 4 ( ) n Z n Z R a e n Z E i i i i σ σ πε σ − = ⋅ − = − ⋅ − ⋅ − = － n*=n (when n ≤ 3) n*=3.7 (when n = 4) n*=4.0 (when n = 5) E Z n R n = − ⎛ ⎝ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ * 2 2 Lithium , Z = 3 Predicted: E1 = -30.6 eV Actual: E1 = -5.4 eV -5.4 -13.6 2 2 2 = ⎛ ⎝ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ Z * Z* . . = 54 2 × 13 6 2 Z* = 1.26 1.26 = 3 - σ σ = 1.74 + - - - 2 2 2 3 13.6 ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ⎟ = − ⎠ ⎞ ⎜ ⎝ ⎛ = − n Z En R