selective recap of “shell model” (from schrödinger equation; orbitals, etc.) copyright ©...
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Selective Recap of “Shell Model” (from Schrödinger equation; orbitals, etc.)
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• An electron configuration describes the distribution of electrons in an atom (or ion)
• Electrons “exist in” orbitals, with only certain energy values (quantization)– Orbitals have “fuzzy” 3D “shape”—NOT ORBITS
• Only 2 electrons max per orbital not all electrons can be in the lowest energy level
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Recap (continued)
• Valence electrons are those in outermost n level (called the “valence shell”)
• Core electrons are those in any level “closer in” than the valence shell (i.e. with n < nvalence)
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• Notion of energy levels/shells (n = 1; n = 2, …)– Each level comprised of sublevels (s, p, d, f)– Each sublevel is made up of orbitals– Shells are “fuzzy”! Only “average” distance increases w/ n
For today, we’ll generally focus on the “level” or “shell” as a whole—not worry so much about sublevels or individual orbitals. In general, electrons in the same shell will be considered to have a similar average distance from the nucleus.
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Example: a P atom (Z=15)
• Electron config is: 1s2 2s2 2p6 3s2 3p3
• Nuclear charge is +15• 3 energy levels (highest n = 3)
3 “shells” [not orbits!]
(imagine them “fuzzy”!)
• 5 valence electrons (in n = 3 level)• 10 core electrons (in n = 1 & n = 2 levels)• This model explains many “periodic”
properties of elements
7–3
+15
2 e-
8 e-
5 e-
2 e-
8 e-
5 e-
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Periodic Properties (Observations)
• (first) Ionization Energy (of elements)• Atomic radii (of elements)• Charges of the monatomic cations and
anions of the “Main Group” elements– Review: Gp 1 is +1; Gp 2 is +2; etc.
• Some not exactly “periodic” properties:– Cation/anion sizes– Higher ionization energy patterns
KNOWING TRENDS is not EXPLAINING
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Ionization Energy (ies)
• (first) ionization energy (IE1): the energy needed to remove an electron from a gaseous atom:
X(g) X+(g) + e- ; E = IE1
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• (second) ionization energy (IE2): energy needed to remove the second electron from a gaseous atom:
X+(g) X2+(g) + e- ; E = IE2
• (nth) ionization energy (IEn): etc.
Note: IE2 is not the energy to remove two electrons!
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Table 8.1 Successive Ionization Energies (in kJ/mol) for the Elements in Period 3
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p. 342, Tro:
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Explanation? (Factors Affecting Force Holding Electrons to Nucleus)
• Coulomb’s Law force between an electron and the nucleus is determined by:– Average distance away (farther [higher n] means smaller
force)
– Magnitude of effective (“apparent”) nuclear charge (Zeff)
(Greater Zeff means stronger force)[Concept of Zeff sort of pushes the idea of electron-electron repulsion under
the rug; focuses on charge “neutralization” —more on this later]
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• S is the number of “shielding” (or screening) electrons. -- In simplified model, a shielding electron is any electron in a
“closer” energy level (i.e., smaller n value)
• Zeff = Zact – S (Zact = the actual charge of nucleus = Z)
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Zeff (for the n = 2 e-)
Zeff(v. e-) = Zact – S = +3 – 2 = +1
Zact
(Shielding)
Zeff(1s e-) = Zact – S = +3 – 0 = +3
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How does model explain why Gp I and Gp II cations have different charges?
• Removal of a core e- is difficult because it has huge Zeff and smaller distances strong Coulomb’s Law force attracting it to nucleus
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• Diff. Groups Diff. # v e-’s diff. # of ionizations to “reach” the core diff. charge of “stable” ion
• Gp I atoms have 1 valence e- gets really hard to remove an electron AFTER one is gone
(IE2 is huge) +1 ion is “stable”)
• Gp II atoms have 2 valence e-’s gets really hard to remove an electron after TWO are
gone (IE3 is huge) +2 ion is “stable”)
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Closer Look: Na vs Mg(also see pictures on board)
• Na (Z = 11)
– 1s2 2s2 2p6 3s1
– Zeff (3s electron [valence]) = +11 – 10 = +1
– Zeff (2p electron [core]) = +11 – 2 = +9 !!! (2nd electron)
The 8 electrons in the n = 2 level were shielding for the 3s electron, but not for those in the n = 2 level!
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• Mg (Z = 12)
– 1s2 2s2 2p6 3s2
– Zeff (3s electron [valence]) = +12 – 10 = +2
– Zeff (2p electron [core]) = +12 – 2 = +10 !!! (3rd electron)
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Table 8.1 Revisited (focus on IE1)
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Figure 8.10 The Values of First Ionization Energy for the Elements in the First 5 Periods
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Figure 8.16. Ionization energy increases across a row and decreases down a family
I1’s (in kJ/mol)
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How does model explain why IE1 values increase as you move across a row (focus on main groups)?
• Across a row, Zeff (= Zact – S) increases
– Zactual increases with each element (proton added to nucleus)
– S remains same (b/c electrons being added to outer “shell”)
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• No “base” distance issue to consider—outer electron coming from same energy level in all elements in row
• Larger Zeff, similar base distance stronger force Harder to pull away larger IE !
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Recall: First Ionization Energies decrease as you go down a family(Table from Zumdahl)
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How does model explain why IE1 values decrease as you move down a family?
• Down a family, Zeff is SAME– Try it out! (This is not “obvious”)
• Na and K both have Zeff = +1 (only one valence electron all BUT one are shielding electrons!)
– Results from the “shell” model; each time a new energy level starts to fill, a whole level of electrons becomes shielding, so Zeff drops back down to +1)
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• Valence electrons are “one shell farther out” for each row you go “down”
• Same Zeff, farther away energy level weaker force Easier to pull away smaller IE !
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Ionic Radii Trends
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Fig. 7.34 (Zumdahl) and Fig. 8.10 (Tro)
Atomic radii get smaller across a row, and larger down a family
Atomic Radii (in pm)
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How does model explain why atomic radii decrease as you move across a row
(focus on main groups)?
• Across a row, Zeff increases– See earlier slide for ionization energy trend!
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• No “base” distance issue to consider—outer electron coming from same energy level in all elements in row
• Larger Zeff, similar base distance stronger force Outer electrons are pulled in closer
Across a row, increasing Zeff and stronger force pulling inward results in both trends: Stronger force greater ionization energy and shell is “pulled in closer”
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How does model explain why atomic radii increase as you move down a family?
• Down a family, Zeff is SAME– See earlier slide for ionization energy
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• Valence electrons are “one shell farther out” for each row you go “down”
• Same Zeff, farther away energy level larger atomic radius !
Down a column, outer electrons are in higher energy (bigger n) levels and are thus farther away. This makes ionization energy smaller, but radius bigger
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What about forming anions? (Electron Affinity)
• Electron affinity (EA): the energy change associated with adding an electron to a gaseous atom:
X(g) + e- X-(g); E = EA
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• Trends pretty “poor”. Main idea is that only HALOGENS have significantly exothermic EAs.
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Fig. 18.17 (Tro)
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(From Zumdahl)
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How does model explain why adding an electron is favorable for halogens,
but not noble gases?
• Near the right of a row Zeff is quite large
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• There’s “space left” in the p sublevel for halogens, but not noble gases!
Config is s2 p5 for halogens,
but s2 p6 for noble gases
• Added electron goes into the valence shell in a halogen (where it can “see” the nucleus), but into the next higher energy level in a noble gas (where Zeff will be ~0!)
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How does model explain why adding an electron is favorable for halogens,
but not noble gases?
~0 Zeff;
No attraction for added electron!
Added electron still “sees” nucleus because S is still low)
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Model also explains why Gp VI anions are -2, Gp V anions are -3
• Gp VI atoms have valence config s2 p4
There “room” for 2 electrons in the p sublevel
(after that it will be unfavorable to add any more because they’ll have to go into the next higher energy level and be shielded from the nucleus)
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• Gp V atoms have valence config s2 p3
There “room” for 3 electrons in the p sublevel
(after that it will be unfavorable to add any more because they’ll have to go into the next higher energy level and be shielded from the nucleus)
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Cations of same element are smaller;Anions of same element are larger
• Same element same number of protons
Thus:
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• If fewer electrons, less electron-electron repulsion electrons (shells) pulled in CLOSER (smaller radius)
• If more electrons, greater electron-electron repulsion electrons (shells) pushed farther away (larger radius)
In cases where the only difference between two species is the number of electrons, THEN electron-electron repulsion is key (and is looked at “explicity”). Otherwise, Zeff & valence n-level are considered.
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Radius increases when an electron is added to an atom (more e--e- repulsion)
(Also See Fig. 8.14 in Tro)
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Radius decreases when an electron is removed from an atom (less e--e- repulsion)
(Also See Fig. 8.13 in Tro)
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Reminder: What we just discussed was:# of protons is the same
(but the number of electrons differs)
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(largest radius) S2- > S- > S > S+ > S2+ (smallest radius)
(__________ IE1) S2- > S- > S > S+ > S2+ (__________ IE1)
Quick Quiz: What do you think is the trend in ionization energy?
smallest largest
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Let’s flip it around: What if the number of electrons is the same
(but the number of protons differs)?
• Same # TOTAL electrons “isoelectronic” same exact electron configuration!
same exact # of shielding electrons (S)
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• If fewer protons, smaller Zeff
electrons pulled in LESS tightly (larger radius; smaller IE)
• If more protons, greater Zeff
electrons pulled in MORE tightly (smaller radius; larger IE)
(______radius) O2- > F- > Ne > Na+ > Mg2+ > Al3+ (_______ radius)
Thus:
largest smallest
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Figure 8.8 (Zumdahl) Sizes of Ions Related to Positions of the Elements on the Periodic Table
The enclosed five ions are isoelectronic—they have the same number of electrons [and the same configuration]. The size decreases as there are MORE PROTONS in the nucleus (greater Zeff here).
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Why do Metals Tend to Form Cations & Nonmetals Tend to Form Anions?
• Again, Zeff!
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• Zeff smallest at left; increases as you move right
• Metal atoms: low Zeff - Easy to remove an electron(s) [so cations are formed]- Not very favorable to add an electron [metal “anions” rare]
• Nonmetal atoms: high Zeff - Is (relatively) favorable to add an electron [to form
anions] AS LONG AS THERE IS “ROOM” (no room in noble gases!)
- Hard to remove an electron(s) [so nonmetal “cations” rare]
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Fig. 8.19: Trends in Metallic Character
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• IE1 increases• Radius decreases• Metallic Character Decreases• Less cation, more anion formation (except for noble gases, neither)
Because (according to QM “shell” model of atoms):• Zeff (for v. e-’s) increases to right• (avg) distance of v. shell decreases up a family Stronger attraction for v. shell e-’s up and right!• But not favorable to add e-’s to (n + 1) level
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Review: Periodic Properties We’ve Discused and Explained with Shell Model
• (first) Ionization Energy (of elements)• Atomic radii (of elements)• Electron Affinities• Metallic Character• Charges of the monatomic cations and anions of the
“Main Group” elements– Review: Gp I, II cations; Gp V,VI, VII anions
• Some not exactly “periodic” properties:– Cation/anion sizes (radii); 1) of same element and 2) in
isoelectronic series
– Higher ionization energy patterns
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(Small IE1 for alkali metals)
(Large IE1 for noble gases)
(~0 EA for noble gas)
(negative EA for halogens)