Question

1. Using Slater’s Rule, determine the effective nuclear charge experienced by the following:

a. A p-electron in fluorine, b. an s-electron in calcium ion c. and a d-electron in copper.

Answer 1

Slater Rule:

  Slater's Rule is that the actual charge felt by an electron is equal to what you'd expect the charge to be from a certain number of protons, but minus a certain amount of charge from other electrons.

Step 1: Write the electron configuration of the atom.

Step 2: Slater's Rules is now broken into two cases:

• the shielding experienced by an s- or p- electron,
  • electrons within same group shield 0.35, except the 1s which shield 0.30
  • electrons within the n-1 group shield 0.85
  • electrons within the n-2 or lower groups shield 1.00
• the shielding experienced by n-d or n-f valence electrons
  • electrons within the same group shield 0.35
  • electrons within the lower groups shield 1.00

Step 3: Effective nuclear charge Z_eff = Z-S

Z- Nuclear charge (number of protons)

S - Shielding constant (calculated from slater rule)

1) p-electron in fluorine

F: (1s²)(2s²,2p⁵) [ In second shell 7 electrons are there but we have to put only 6 electrons in the calculation

because because we are calculating shielding constant for one of the second shell p-electron]

   S = 1.00(0) + 0.85(2) + 0.35(6) = 3.8

Z_eff = Z-S

= 9 - 3.8

Z_eff = 5.2

2) s-electron in calcium ion:

Ca²⁺: (1s²)(2s²,2p⁶)(3s²,3p⁶)(4s⁰) [ calcium ion means Ca²⁺ .s- electron in calcium ion means 3s electron]

S = 1.00(2) + 0.85(8) + 0.35(1)

S = 8.15

Z_eff = Z-S

= 20 - 8.15

Z_eff = 11.85

3) d-electron in copper:

Cu: (1s²)(2s²,2p⁶)(3s²,3p⁶)(3d¹⁰)(4s¹)

Ignore the group to the right of the 3d electrons. These do not contribute to the shielding constant.

S = 1.00(18) + 0.35(9)

S = 21.1

Z_eff  = Z-S

= 29 - 21.15

Z_eff = 7.85