Screening constant (Sigma) calculation using Slater's rule for 4s electron.

1. Screening constant (σ) calculation using Slater's rule for 4s electron +

Correct Answer — General Method

For a 4s electron, calculate σ by Slater's rules according to the electron configuration of the atom.

Slater's Rules for a 4s Electron

For an electron in the ns or np orbital, such as 4s, Slater's rules are:

σ = 0.35 × (other electrons in the same 4s,4p group) + 0.85 × (electrons in the n−1 shell) + 1.00 × (electrons in n−2 or lower shells)

The electron being considered is not counted in calculating σ.

For a 4s electron:

• Other electrons in 4s, 4p → 0.35 each
• Electrons in 3s, 3p, 3d → 0.85 each
• Electrons in 1s, 2s, 2p → 1.00 each

Example: Calculate σ for a 4s Electron of Potassium (K, Z = 19)

Electronic configuration of K:

K: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s¹

We want the shielding constant for the 4s¹ electron.

Step 1: Same group

There are no other electrons in the 4s/4p group.

0 × 0.35 = 0

Step 2: n−1 shell

The n−1 shell is the third shell: 3s² + 3p⁶ = 8 electrons

8 × 0.85 = 6.80

Step 3: n−2 and lower shells

1s² + 2s² + 2p⁶ = 10 electrons

10 × 1.00 = 10

Step 4: Total screening constant

σ = 0 + 6.80 + 10
σ = 16.80

Therefore:

For K, σ(4s) = 16.80

Effective Nuclear Charge

After calculating σ, effective nuclear charge is:

Z_eff = Z − σ

For K:

Z_eff = 19 − 16.80
Z_eff = 2.20

Thus, the 4s electron of potassium experiences an effective nuclear charge of approximately +2.20.

Important Exam Point

Do not use one fixed σ value for every 4s electron. The screening constant depends on the atomic number and electronic configuration of the atom/ion being considered. For example, for Ca:

Ca: [Ar]4s²

For one 4s electron, the other 4s electron contributes:

1 × 0.35

while the eight 3s/3p electrons contribute:

8 × 0.85

and the ten electrons in n−2 and lower shells contribute:

10 × 1.00

Hence:

σ = 0.35 + 6.80 + 10
σ = 17.15

JEE/NEET Shortcut

For a 4s/4p electron, remember:

Same shell/group → 0.35
One shell below → 0.85
Two or more shells below → 1.00

Then use:

Z_eff = Z − σ

30 Related MCQs with Solutions

1. According to Slater's rule, the contribution of another electron in the same ns/np group is:

A. 0.10

B. 0.35

C. 0.85

D. 1.00

Answer: B. 0.35

2. For a 4s electron, electrons in the 3s and 3p orbitals contribute:

A. 0.35 each

B. 0.50 each

C. 0.85 each

D. 1.00 each

Answer: C. 0.85 each

3. For a 4s electron, electrons in 1s, 2s and 2p contribute:

A. 0.35 each

B. 0.50 each

C. 0.85 each

D. 1.00 each

Answer: D. 1.00 each

4. Which electron is excluded while calculating its own screening?

A. All inner electrons

B. The electron under consideration

C. All 1s electrons

D. All d electrons

Answer: B

5. The electronic configuration of K is:

A. [Ar]4s¹

B. [Ne]3s²

C. [Ar]3d¹

D. [Kr]5s¹

Answer: A. [Ar]4s¹

6. The screening constant for the 4s electron of K is:

A. 10.00

B. 16.80

C. 18.15

D. 19.00

Answer: B. 16.80

7. For K, the 3s²3p⁶ electrons contribute:

A. 6.80

B. 8.00

C. 10.00

D. 2.80

Answer: A. 6.80

8. For K, the electrons in 1s²2s²2p⁶ contribute:

A. 3.50

B. 6.80

C. 8.50

D. 10.00

Answer: D. 10.00

9. Effective nuclear charge is calculated using:

A. Z + σ

B. Z − σ

C. σ − Z

D. Z × σ

Answer: B. Z − σ

10. The Z_eff of the 4s electron in K is:

A. 1.20

B. 2.20

C. 3.20

D. 4.20

Answer: B. 2.20

11. Slater's rules are used to estimate:

A. Atomic mass

B. Effective nuclear charge

C. Neutron number

D. Melting point

Answer: B

12. The shielding effect causes the outer electron to experience:

A. Full nuclear charge

B. Reduced effective nuclear attraction

C. No nuclear attraction

D. Negative nuclear charge

Answer: B

13. For a 4s electron, which orbital belongs to the same principal shell?

A. 3p

B. 3d

C. 4p

D. 2p

Answer: C. 4p

14. For an ns/np electron, the n−1 shell contributes:

A. 0.35 per electron

B. 0.50 per electron

C. 0.85 per electron

D. 1.50 per electron

Answer: C

15. For a 4s electron, the n−2 shell corresponds to:

A. n=3

B. n=2

C. n=1

D. n=5

Answer: B. n=2

16. For K, the number of electrons contributing 1.00 each is:

A. 2

B. 8

C. 10

D. 18

Answer: C. 10

17. For Ca ([Ar]4s²), another 4s electron contributes:

A. 0.35

B. 0.85

C. 1.00

D. 2.00

Answer: A. 0.35

18. The screening constant for one 4s electron of Ca is:

A. 16.80

B. 17.15

C. 18.00

D. 20.00

Answer: B. 17.15

19. For Ca, the approximate Z_eff of a 4s electron is:

A. 1.85

B. 2.85

C. 3.85

D. 4.85

Answer: B. 2.85

20. Which quantity increases when σ decreases for a fixed Z?

A. Z_eff

B. Atomic mass

C. Neutron number

D. Principal quantum number

Answer: A. Z_eff

21. Greater shielding generally causes:

A. Greater effective nuclear attraction

B. Lower effective nuclear attraction

C. No change in attraction

D. Nuclear decay

Answer: B

22. Which electrons shield a 4s electron most effectively according to Slater's rules?

A. Same 4s/4p group: 0.35 each

B. 3s/3p: 0.85 each

C. 2s/2p: 1.00 each

D. All have equal contribution

Answer: C. 2s/2p electrons contribute 1.00 each

23. Which factor is NOT directly used in calculating σ by Slater's rule?

A. Number of electrons

B. Electron grouping

C. Principal shell position

D. Atomic mass

Answer: D. Atomic mass

24. If σ increases while Z remains constant, Z_eff:

A. Increases

B. Decreases

C. Becomes infinite

D. Becomes negative necessarily

Answer: B. Decreases

25. The 4s electron of K is shielded by how many inner-shell electrons?

A. 8

B. 10

C. 18

D. 19

Answer: C. 18 inner-shell electrons

26. In Slater's method, the shielding contribution of a 3d electron to a 4s electron is:

A. 0.35

B. 0.50

C. 0.85

D. 1.00

Answer: C. 0.85

27. For a 4s electron in a transition-metal atom, which group is especially important to check?

A. 1s only

B. 3d electrons

C. 5s electrons only

D. 6p electrons

Answer: B. 3d electrons

28. The main purpose of the shielding constant σ is to represent:

A. Nuclear charge reduction due to other electrons

B. Number of protons

C. Number of neutrons

D. Atomic volume

Answer: A

29. For a 4s electron, which contribution is strongest per electron?

A. Same-group electron

B. n−1 electron

C. n−2 or lower electron

D. All are equal

Answer: C. 1.00 per electron

30. The correct sequence for calculating Z_eff is:

A. Find Z → find σ → calculate Z−σ

B. Find σ → calculate Z+σ

C. Find atomic mass → calculate σ

D. Find neutrons → calculate σ

Answer: A

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