Question

Number of statements which is/are correct as per Slater's rule?

Answer 1

3

Answer 2

Let's analyze each statement based on Slater's rules for calculating effective nuclear charge (Z$_{eff}$).

(i) Z$_{eff}$ always increases with increase in atomic number

• Across a period: Z$_{eff}$ generally increases because the nuclear charge (Z) increases while shielding from electrons in the same shell is incomplete.
• Down a group: Z$_{eff}$ for valence electrons remains relatively constant or slightly decreases. While Z increases, the number of inner shielding electrons also increases significantly, compensating for the increased nuclear charge.
• Therefore, the statement "always increases" is incorrect.

(ii) Total eight electrons contribute $\sigma$ = 0.85 in calculation of Z$_{eff}$ of last electron of Chlorine

• Chlorine (Cl) has electronic configuration $1s^2 2s^2 2p^6 3s^2 3p^5$. The last electron is a $3p$ electron (n=3).
• According to Slater's rules, electrons in the (n-1) shell contribute 0.85 to the shielding constant ($\sigma$).
• For a $3p$ electron in Cl, the (n-1) shell is the 2nd shell ($2s^2 2p^6$), which contains 8 electrons.
• These 8 electrons indeed contribute $8 \times 0.85$ to $\sigma$.
• This statement is correct.

(iii) The value of Z$_{eff}$ is more for Mg than Na

• Na ($1s^2 2s^2 2p^6 3s^1$, Z=11):
  • $\sigma_{Na} = (0 \times 0.35) + (8 \times 0.85) + (2 \times 1.00) = 0 + 6.80 + 2.00 = 8.80$
  • Z$_{eff (Na)} = 11 - 8.80 = 2.20$
• Mg ($1s^2 2s^2 2p^6 3s^2$, Z=12):
  • $\sigma_{Mg} = (1 \times 0.35) + (8 \times 0.85) + (2 \times 1.00) = 0.35 + 6.80 + 2.00 = 9.15$
  • Z$_{eff (Mg)} = 12 - 9.15 = 2.85$
• Z$_{eff}$ for Mg (2.85) is greater than for Na (2.20). This is consistent with the trend across a period.
• This statement is correct.

(iv) The value of $\sigma$ is more for Mg than Na

• From calculations in (iii): $\sigma_{Na} = 8.80$ and $\sigma_{Mg} = 9.15$.
• The value of $\sigma$ is indeed more for Mg than Na.
• This statement is correct.

(v) The value of Z$_{eff}$ is higher for Na as compared to Na$^+$

• Na: Z$_{eff (Na)} = 2.20$ (calculated above for the valence $3s$ electron).
• Na$^+$ ($1s^2 2s^2 2p^6$, Z=11): The outermost electrons are $2p$ electrons (n=2).
  • $\sigma_{Na^+} = (7 \times 0.35) + (2 \times 0.85) = 2.45 + 1.70 = 4.15$
  • Z$_{eff (Na^+)} = 11 - 4.15 = 6.85$
• Z$_{eff}$ for Na$^+$ (6.85) is significantly higher than for Na (2.20). This is because the same nuclear charge is acting on fewer electrons, and the remaining electrons are in a lower shell, experiencing less shielding.
• Therefore, the statement is incorrect.

(vi) Z$_{eff}$ is higher for Cl$^-$ as compared to Cl

• Cl ($1s^2 2s^2 2p^6 3s^2 3p^5$, Z=17):
  • $\sigma_{Cl} = (6 \times 0.35) + (8 \times 0.85) + (2 \times 1.00) = 2.10 + 6.80 + 2.00 = 10.90$
  • Z$_{eff (Cl)} = 17 - 10.90 = 6.10$
• Cl$^-$ ($1s^2 2s^2 2p^6 3s^2 3p^6$, Z=17): The outermost electrons are $3p$ electrons (n=3).
  • $\sigma_{Cl^-} = (7 \times 0.35) + (8 \times 0.85) + (2 \times 1.00) = 2.45 + 6.80 + 2.00 = 11.25$
  • Z$_{eff (Cl^-)} = 17 - 11.25 = 5.75$
• Z$_{eff}$ for Cl$^-$ (5.75) is lower than for Cl (6.10). Adding an electron increases electron-electron repulsion and shielding, thus decreasing the effective nuclear charge.
• Therefore, the statement is incorrect.

Number of correct statements = 3 (statements ii, iii, and iv).