In many atoms, each individual electron is less affected by the effective nuclear charge due to the shielding action of the other electrons. For each electron in an atom, Slater's rule gives a constant screen value represented by the symbol σ.
The effective nuclear charge can be defined as the real nuclear charge (Z) after deducting the screen effect caused by the electrons between the nucleus and the valence electron.
Effective nuclear charge Z * = Z - σ where Z = atomic number, σ = screen constant.
To calculate the effective nuclear charge (Z *) we need the value of the screen constant (σ) which can be calculated using the following rules.
Steps
Step 1. Write the electronic configuration of the elements as indicated below
- (1s) (2s, 2p) (3s, 3p) (3d) (4s, 4p) (4d) (4f) (5s, 5p) (5d) …
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Structures electrons according to the Aufbau principle.
- Any electron to the right of the affected electron does not contribute to the screen constant.
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The screen constant for each group is determined by the sum of the following data:
- Each electron contained in the same group as the electron of interest, makes a contribution equal to 0.35 to the screen effect except for the 1s group, where the other electrons only contribute 0.35.
- If the group is of the type [s, p], the contribution is 0, 85 for each electron of the structure (n-1) and of 1, 00 for each electron of the structure (n-2) and those below.
- If the group is of the [d] or [f] type, the contribution is 1.00 for each electron to the left of that orbit.
Determine Screening Constant and Effective Nuclear Charge Step 2 Step 2. Let's take an example:
(a) Calculate the effective nuclear charge of the 2p electron of the nitrogen.
- Electronic configuration - (1s2) (2s2, 2p3).
- Screen constant, σ = (0, 35 × 4) + (0, 85 × 2) = 3, 10
- Effective nuclear charge, Z * = Z - σ = 7 - 3, 10 = 3, 90
Determine Screening Constant and Effective Nuclear Charge Step 3 Step 3. Another example:
(b) Calculate the effective nuclear charge and the screen constant detected in the 3p electron of the silicon.
- Electronic configuration - (1s2) (2s2, 2p6) (3s2, 3p2).
- σ = (0.35 × 3) + (0.85 × 8) + (1 × 2) = 9.55
- Z * = Z - σ = 14 - 9, 85 = 4, 15
Determine Screening Constant and Effective Nuclear Charge Step 4 Step 4. Yet another:
(c) Calculate the effective nuclear charge of the 4s and 3d electrons of the zinc.
- Electronic configuration - (1s2) (2s2, 2p6) (3s2, 3p6) (3d10) (4s2).
- For 4s electron:
- σ = (0.35 × 1) + (0.85 × 18) + (1 × 10) = 25.65
- Z * = Z - σ = 30 - 25.65 = 4.55
- For 3d electron:
- σ = (0.35 × 9) + (1 × 18) = 21.15
- Z * = Z - σ = 30 - 21, 15 = 8, 85
Determine Screening Constant and Effective Nuclear Charge Step 5 Step 5. And finally:
(d) Calculate the effective nuclear charge of one of the 6s electrons of the Tungsten (Atomic Number 74).
- Electronic configuration - (1s2) (2s2, 2p6) (3s2, 3p6) (4s2, 4p6) (3d10) (4f14) (5s2, 5p6) (5d4), (6s2)
- σ = (0.35 × 1) + (0.85 × 12) + (1 × 60) = 70.55
- Z * = Z - σ = 74 - 70, 55 = 3.45
Advice
- Read some texts on the shielding effect, the shield constant, the effective nuclear charge, Slater's rule, etc.
- If there is only one electron in an orbit, there will be no screen effect. And again, if the total of electrons present corresponds to an odd number, subtract one to get the real quantity to multiply to get the screen effect.
