Textbook Exercise 1E.5

[Arezo Ahmadi 3J]

Hi, I was looking at this problem and had a question about one of the statements: Which of the following statements are true for many-electron atoms? If false, explain why. (a) The effective nuclear charge Zeffe is independent of the number of electrons present in an atom. (b) Electrons in an s-orbital are more effective than those in other orbitals at shielding other electrons from the nuclear charge because an electron in an s -orbital can penetrate to the nucleus of the atom. (c) Electrons having l = 2 are better at shielding than electrons having l = 1. (d) Zeff e for an electron in a p-orbital is lower than for an electron in an s -orbital in the same shell.

My question is about part (c), as I do not understand why it is a false statement. I interpreted this statement in which electrons with l = 2 would have more electrons and thus be more expanded with a larger atomic radius, allowing those electrons to be better at shielding than electrons with l = 1 because those electrons would be more attracted to the nucleus due to the increase in protons. I was wondering if I could get an explanation about why this statement is true and the concepts behind electron shielding and when there is better or weaker electron shielding.

Thank you in advance!

[Crystal Yu 1D]

It is false because electrons with l=2 are located in the d orbitals. Electrons with l=1 are located in the p orbitals. For electrons with the same principle quantum number (n), the p orbitals would be located closer to the nucleus and thus be better at shielding because it has more opportunities to shield. I hope this makes sense! :)

[Lily Kiamanesh 2G]

Yes, electrons found closer to the nucleus are essentially "blocking" further electrons from fully experiencing the attraction from the positive charge of the nucleus. P-orbital electrons are closer to the nucleus than d-orbital electrons, so they block, or shield, more.

[Jordi M 2I]

Yes the p orbital is better at shielding because it is closer to the nucleus than the d orbital. The p orbital shields the d and f orbitals on the same quantum level from the nucleus. If the question asked, the s orbital would be even better at shielding since it would shield p, d, and f orbital electrons.

[Anna Yang 1A]

I believe closer proximity to the nucleus is linked to better shielding as the orbitals closer to the nucleus are able to shield the ones further away; thus the s-orbital shields the p, d, and f while the p shields the d and f and so on. Therefore, the d orbital would not be better at shielding than the p orbital, but it would be better at shielding than the f.