Lecture 11_Shielding and Penetration_Main group electron configurations

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Oct 30, 2023

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Announcements for September 25 th , 2023 Monday Reading : Chapter 7, Sections 1 – 2; Chapter 6, Sections 7 – 9 Wednesday Reading: Chapter 6, Sections 7 – 9 Friday Reading: Chapter 7, Sections 3 – 4 The plan: Polyelectronic atoms! Effective nuclear charge (shielding, penetration), electron spin, and electron configurations • Homework 3 due September 26 th by 11:59 PM • Exam 1 is Wednesday, September 27 th 7:00 pm – 9:00 pm in Meyerson Hall, Room B1 • Conflict exam is scheduled for 8:00 am – 10:00 am in DRL 3N1H • You had to sign up last week to attend the conflict • Quiz 3 is Tuesday, September 26 th

Given below are the radial distribution functions for the 1s, 2s, and 3s orbitals. Identify which orbital belongs to each plot. Which orbital provides the greatest shielding ? Do the remaining two orbitals penetrate within the volume of the orbital you identified? 1. We know these belong to s-orbitals! How do we identify them? Red curve: Blue curve: Green curve: 2. What is shielding? 3. Which orbital shields best? 4. What is penetration? 5. Do the remaining orbitals penetrate volume of 1s?

Given below are the radial distribution functions for the 2 nd shell subshells. Identify the which orbital belongs to each plot. Which orbital provides the greatest shielding ? If each orbital contained 1 e - , which would experience a greater Z eff ? 1. We know these belong to 2 nd shell orbitals! How do we identify them? Red curve: Blue curve: 2. Which orbital shields best? 3. Z eff is related to closeness! In which orbital is it more probable for the e - to see the nucleus? Angular node _______________________________! Major part of why ___________________________!

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Which orbital provides the greatest degree of shielding: 2p or 3s? (a) 2p-orbital (b) 3s-orbital (c) They are the same! (d) Not possible to discern – they are too different 1. Sketch either the RDFs or orbital pictures – either can help you out! 2. Since the orbitals are in different shells, only one quantum number matters (as your sketches will illustrate)! Which is it?

A fourth quantum number is needed to rationalize the filling of shells for multielectron atoms: m s (electron spin) {n, ℓ, m ℓ , m s } → Rationalizes the emergence of shells • Physically: Intrinsic magnetic moment of the e - • m s = +1/2 (up) or -1/2 (down) for 1 e - • Orientation of magnetic field • Similar to m ℓ • Limits ___________________________!!! What is mass? → Particle’s response to mechanical force What is charge? → Particle’s response to external electric field What is spin? → _____________________________________ A full collection of quantum numbers is like specifying an e - ’s zip code {n, ℓ} → {n, ℓ, m ℓ } → Magnetism is due to unpaired e - ’s

Paramagnetic – A substance that has ______________________________________________________ • Attracted to an external magnetic field • Paramagnetism increases as the number of ______ electrons with __________ spins increases Diamagnetic – A substance in which all electron spins are _______________________ • Repelled by an external magnetic field Ground state paramagnetic elements in the 2 nd period: Li, B, C, N, O, F Magnetism is a consequence of unpaired electron spins in atomic-level systems Paramagnetism Diamagnetism Ground state diamagnetic atoms in the 2 nd period: Be, Ne

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MRI (magnetic resonance imaging) uses spin to noninvasively map out human body MRI contrast agents enable greater resolution of tissue imaging • Must be selective to tissue (e.g., cancer), water soluble, and unreactive • Chelating ligands meet ALL criteria • Gd +3 (Element 64) is paramagnetic H 2 O exchange at metal gives contrast Excited proton spins relax faster due to electron spins

Arranging electrons in atoms follows 3 rules 1) The Pauli Exclusion Principle: No two electrons in an atom may share the same four quantum numbers (distinct physical states!) 2) The Aufbau Principle: Electrons are added to the atomic orbitals by first filling the lowest energy orbital available 3) Hund’s Rule: Degenerate orbitals are consecutively filled with one electron, of equal spin, before pairing

The Pauli Exclusion Principle: No two electrons in an atom may share the same four quantum numbers “Just as protons are added one-by-one to the nucleus to build-up the atomic core, electrons are sequentially added to atomic orbitals to complete the atom” There is a preferential order to how electrons are added to an atom n ℓ m ℓ m s Quantum numbers, electron 1: 1 0 0 +1/2 Quantum numbers, electron 2: 1 0 0 -1/2 Electronic configuration written as He: ______ n=2 1s Energy Element: nℓ occupancy n=2 1s Energy n ℓ m ℓ m s Quantum numbers, electron 1: 1 0 0 +1/2 Quantum numbers, electron 2: 1 0 0 +1/2 He – Atomic Number (Z): 2 Electrons: 2

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The more effectively an orbital allows its electron to penetrate the electron ‘cloud,’ the __________ Z eff becomes • Lower n shells ________ higher n shells from nucleus • Lower ℓ subshells ________ higher ℓ subshells from nucleus For multielectron atoms, orbital energies additionally depend on ℓ Angular nodes limit how strongly an electron can interact with the nuclear core 𝐸 2𝑠 < 𝐸 2? 𝐸 3𝑠 < 𝐸 3? < 𝐸 3? 0 Probability at nucleus Non-zero probability at nucleus 𝐸 ??𝑢???? = 𝑘 𝑍 ??? 𝑒 − 𝑟 1s 2s 2p 𝐸 4𝑠 < 𝐸 4? < 𝐸 4? < 𝐸 4? Higher Z eff → Lower E Relative subshell orbital energies:

Multielectron atoms are understood in quantum: Complex emission due to broken degeneracy Energy 1s 2s 3s 4s 2p 3p 4p 3d 4d 4f . . . . . n = 1 n = 2 n = 3 n = 4 Energy 1s 2s 3s 4s 2p 3p 3d . . . n = 1 n = 2 n = 3 n = 4 4f 4d 4p H-atom Multielectron atoms 𝐸 ?𝑠 < 𝐸 ?? < 𝐸 ?? < 𝐸 ?? Within a shell, subshell with lower ℓ will have lower energy

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The Aufbau Principle: Electrons are added to the atomic orbitals, first filling the lowest energy orbital available “Just as protons are added one-by-one to the nucleus to build-up the atoms, electrons are added to the atomic orbitals” n ℓ m ℓ m s Quantum numbers, electron 1: 1 0 0 +1/2 Quantum numbers, electron 2: 1 0 0 -1/2 Quantum numbers, electron 3: ? Li – Atomic Number (Z): 3 Electrons: 3 2s 1s Energy Li: __________ n ℓ m ℓ m s Quantum numbers, electron 1: 1 0 0 +1/2 Quantum numbers, electron 2: 1 0 0 -1/2 Quantum numbers, electron 3: 2 0 0 +1/2 • No configuration is possible where the third electron uniquely occupies the 1s orbital (Pauli Exclusion Principle) 2s 1s Energy • Go to next shell, start with 2s-subshell

What are the electron configurations and atomic energy level diagrams for Be, B, and C? Be B C 1. Determine atomic number, Z (= electron count for atoms) 2. Draw energy atomic energy level diagram and add electrons

Maximize # of unpaired electrons to achieve ground state configuration! All other non-Pauli-violating configurations are excited states! Carbon, C, 6 electrons 2p 2 2s 2 1s 2 Energy C: 1s 2 2s 2 2p 2 Why parallel spins? Electrons avoid one another more readily when spins aligned (Pauli repulsion); does not violate Pauli Exclusion Principle Carbon, C, 6 electrons 2p 2 2s 2 1s 2 Energy C: 1s 2 2s 2 2p 2 Hund’s Rule: Degenerate orbitals are consecutively filled with one electron, of equal spin, before pairing Carbon, C, 6 electrons 2p 2 2s 2 1s 2 Energy C: 1s 2 2s 2 2p 2

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Oxygen, O, 8 electrons Moving across the 2 nd period: Please provide the orbital energy level diagram and electron configuration for ground-state N, O, F, and Ne Fluorine, F, 9 electrons Nitrogen, N, 7 electrons Neon, Ne, 10 electrons

Na: 3s 1 Moving down a group, electrons fill new shells • ___________ electrons are closer to the nucleus and are uninvolved in bonding • ___________ electrons generally occupy the outermost shell of an atom – determine the reactivity and bonding behavior of atoms Sodium, Na, Z = 11 Energy 3s n = 1 n = 2 n = 3 n = 4 ℓ = 0 Na: [Ne] ____ K: [Ar] ____ Li: [He] ____ Mg: [Ne] ____ Ca: [Ar] ____ Be: [He] ____ n = 1 ℓ = 0 n = 2 ℓ = 0 n = 2 ℓ = 1 n = 3 ℓ = 0 m ℓ = 0 m ℓ = 0 m ℓ = 0 m ℓ = -1, 0, +1 [Noble gas] ≡ [Ne] 3s 1 6 1 Lowest ℓ subshell of 3 rd shell

Please provide the orbital energy level diagram and complete electron configuration for ground-state P and Ca Phosphorus, P, 15 electrons Calcium, Ca, 20 electrons What happened to 3d-orbitals???

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