Problem 1E.5

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andrewcj 2C
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Problem 1E.5

Postby andrewcj 2C » Mon Oct 21, 2019 1:47 pm

I'm having a little trouble with problem 1E.5. It reads as follows:
Which of the following statements are true for many-electron atoms? If false, explain why.
(a) The effective nuclear charge Zeff 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 intuition says a is false, as more electrons should provide more shielding and reduce Zeff, b is false because electrons in the s-orbital aren't more effective, they're equally effective and c and d are false for the same reason as b, but I'm really unsure about it. Can someone help me out?

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Re: Problem 1E.5

Postby sarahsalama2E » Mon Oct 21, 2019 2:11 pm

(a) false--> the effective nuclear charge is the nuclear charge - shielding e-
(b) true--> because electrons in the s-orbital are closer to the nucleus and can penetrate to the nucleus of the atom, compared to electrons that are farther away
(c) false, l=1 is closer
(d) true= because s orbital is shielding nuclear charge from p orbital

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Re: Problem 1E.5

Postby asannajust_1J » Mon Oct 21, 2019 2:12 pm

My reasoning for this problem was:
a) is false since Zeff is dependent on the # e- because the amount of shileding that can occur is affected by the number of electrons. More electrons, more shielding, lower Zeff.
b) is true because the p and d orbitals are more effective at shielding since they are the closest to the nucleus, they can "block" the electrons in different orbitals.
c) this is false because e- with l=2 are in the d orbital which means they are less likely to penetrate than l=1 since they are in the p orbital and are better at shielding.
d) True because e- in the p orbital is further from the nucleus so it experiences a lower Zeff (nuclear charge) than an electron in the s orbital of the same shell.

Brian Tangsombatvisit 1C
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Re: Problem 1E.5

Postby Brian Tangsombatvisit 1C » Mon Oct 21, 2019 2:51 pm

You basically have to know that different orbitals within the same shell are different distances away from the nucleus; they are not all equidistant. Therefore, they provide varying levels of electron shielding / penetrance of the nucleus depending on how far away or close they are. The s-orbitals are closest to the nucleus, so they provide the most shielding to the other electrons, then the p-orbitals, then the d-orbitals (if there are any).

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