Question

Calculate the Z_eff for the valence electrons in the atoms Li to Ne using (a) the assumption that o equals the number of inner-shell electrons and (b) Slater's rules. Plot both sets of results on the same graph and discuss.

Answer 1

Atom	Atomic Number	Electronic configuration
Li Be B C N O F Ne	3 4 5 6 7 8 9 10	1s2 2s1 1s2 2s2 1s2 2s2p1 1s2 2s2p2 1s2 2s2p3 1s2 2s2p4 1s2 2s2p5 1s2 2s2p6

a. Calculating  Z_eff when σ is the number of inner shell electrons ie electrons in the n-1 shell ie only taking the contribution from the 1s² electrons

Z_eff of Li valence electron = 3 - 2 = 1

Z_eff of Be valence electron = 4 - 2 = 2

Z_eff of B valence electron = 5 - 2 = 3

Z_eff of C valence electron = 6 - 2 = 4

Z_eff of N valence electron = 7 - 2 = 5

Z_eff of O valence electron= 8 - 2 = 6

Z_eff of F valence electron = 9 - 2 = 7

Z_eff of Ne valence electron = 10 - 2 = 8

b. Effective nuclear charge Z_eff is given as: Z_eff = Z - σ

where Z is the atomic number or the number of protons and σ is the screening or the shielding constant

When we calculate the Z_eff of the valence electrons of the atoms from Li to Ne as per the Slater's rules:

Z_eff of Li valence electron= 3 - σ = 3 - (2 x 0.35) = 3 - 0.70 = 2.30

Z_eff of Be valence electron = 4 - (1 x 0.35 + 2 x 0.85) = 1.95

Z_eff of B valence electron = 5 - (2 x 0.35 + 2 x 0.85) = 2.60

Z_eff of C valence electron = 6 - (3 x 0.35 + 2 x 0.85) = 3.25

Z_eff of N valence electron = 7 - (4 x 0.35 + 2 x 0.85) = 3.9

Z_eff of O valence electron = 8 - (5 x 0.35 + 2 x 0.85) = 4.55

Z_eff of F valence electron = 9 - (6 x 0.35 + 2 x 0.85) = 5.2

Z_eff of Ne valence electron = 10 - (7 x 0.35 + 2 x 0.85) = 5.85

Z_eff graph is plotted with both the Z_eff calculated values as given below

y-axis gives Z_eff and x-axis gives the atomic number of the elements from Be to Li as given in the table above. Series1 gives the plot for Z_eff considering only the inner shell electrons and Series2 gives the plot from calculations using the Slaters rule.

Answer 2

Formula: Zeff = Z -

Part (a).

Li: Zeff = 3 - 2 = 1

Be: Zeff = 4 - 2 = 2

B: Zeff = 5 - 2 = 3

C: Zeff = 6 - 2 = 4

N: Zeff = 7 - 2 = 5

O: Zeff = 8 - 2 = 6

F: Zeff = 9 - 2 = 7

Ne: Zeff = 10 - 2 = 8

Part (b).

Li: Zeff = 3 - (2*0.85) = 1.3

Be: Zeff = 4 - (1*0.35 + 2*0.85) = 1.95

B: Zeff = 5 - (2*0.35 + 2*0.85) = 2.6

C: Zeff = 6 - (3*0.35 + 2*0.85) = 3.25

N: Zeff = 7 - (4*0.35 + 2*0.85) = 3.9

O: Zeff = 8 - (5*0.35 + 2*0.85) = 4.55

F: Zeff = 9 - (6*0.35 + 2*0.85) = 5.2

Ne: Zeff = 10 - (7*0.35 + 2*0.85) = 5.85