Selective Recap of “Shell Model” (from Schrödinger equation; orbitals, etc.) Copyright © Houghton Mifflin Company. All rights reserved.7–17–1 An electron.

Selective Recap of “Shell Model” (from Schrödinger equation; orbitals, etc.)

Copyright © Houghton Mifflin Company. All rights reserved. 7–1

• 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

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)


• 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.

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-

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


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


• (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!


Table 8.1 Successive Ionization Energies (in kJ/mol) for the Elements in Period 3

p. 342, Tro:

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]


• 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)

Zeff (for the n = 2 e-)

Zeff(v. e-) = Zact – S = +3 – 2 = +1

Zact

(Shielding)

Zeff(1s e-) = Zact – S = +3 – 0 = +3

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


• 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”)

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!


• Mg (Z = 12)

– 1s2 2s2 2p6 3s2

– Zeff (3s electron [valence]) = +12 – 10 = +2

– Zeff (2p electron [core]) = +12 – 2 = +10 !!! (3rd electron)


Table 8.1 Revisited (focus on IE1)


Figure 8.10 The Values of First Ionization Energy for the Elements in the First 5 Periods


Figure 8.16. Ionization energy increases across a row and decreases down a family

I1’s (in kJ/mol)

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”)


• 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 !


Recall: First Ionization Energies decrease as you go down a family(Table from Zumdahl)

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)


• 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 !

Ionic Radii Trends



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)

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!


• 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”

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


• 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

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


• Trends pretty “poor”. Main idea is that only HALOGENS have significantly exothermic EAs.


Fig. 18.17 (Tro)

(From Zumdahl)

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


• 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!)


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)

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)


• 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)

Cations of same element are smaller;Anions of same element are larger

• Same element same number of protons

Thus:


• 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.

Radius increases when an electron is added to an atom (more e--e- repulsion)

(Also See Fig. 8.14 in Tro)

Radius decreases when an electron is removed from an atom (less e--e- repulsion)

(Also See Fig. 8.13 in Tro)

Reminder: What we just discussed was:# of protons is the same

(but the number of electrons differs)


(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

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)


• 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

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).

Why do Metals Tend to Form Cations & Nonmetals Tend to Form Anions?

• Again, Zeff!


• 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]

Fig. 8.19: Trends in Metallic Character


• 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

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


(Small IE1 for alkali metals)

(Large IE1 for noble gases)

(~0 EA for noble gas)

(negative EA for halogens)

Selective Recap of “Shell Model” (from Schrödinger equation; orbitals, etc.) Copyright © Houghton Mifflin Company. All rights reserved.7–17–1 An electron.

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