c101 1 lecturenotes chapter7 Foster · 2013. 9. 27. · Electron Subshell Orbitals Electrons...

11/23/09

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© 2008 Brooks/Cole 1

Chapter 7: Electron Configurations and the Periodic Table


•  All types (“colors”) have the same velocity (through a vacuum).   c = speed of light = 2.99792458 x 108 ms-1 (exact)

•  Oscillating electric and magnetic fields.

Electric field

Magnetic field

•  Traveling wave  moves through space like the ripples on a pond

Electromagnetic Radiation and Matter


distance

λ

Am

plitu

de

0

-

+



γ-rays X-rays UV IR Microwave Radiowave FM AM Long radio waves

Frequency (Hz) 1024 1022 1020 1018 1016 1014 1012 1010 108 106 104 102 100

10-16 10-14 10-12 10-10 10-8 10-6 10-4 10-2 100 102 104 106 108

Wavelength (m)

400  450 500 550 600 650 700 Wavelength (nm)

Bacterial Animal Thickness Width Dog cell cell of a CD of a CD

Atom Virus

Visible light is a very small portion

of the entire spectrum

E increases from radio waves (low ν, long λ) to gamma rays (high ν, short λ)



Heated solid objects emit visible light •  Intensity and color distribution depend on T

Increasing filament T

Planck’s Quantum Theory


As T ↑, the wavelength of maximum intensity shifts

toward the blue


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Classical theory:   no restriction on the E emitted by hot atoms.   didn’t fit experimental data.



An anode (+) attracts e-. Current is measured.

vacuum

Anode (+)

Metal cathode (-)

window

“Light” can cause ejection of e- from a metal surface.

The Photoelectric Effect


If λ > threshold (E too low), no e- emission. Higher intensity does NOT cause e- emission if E < threshold !


metal λ (nm) color Cs 579 yellow K 539 green Na 451 blue Li 428 violet

Thresholds:

curr

ent

(# o

f eje

cted

e- )

increasing E

low I

threshold

High I


If the E of the ball: •  is low, it can’t eject an e-. •  exceeds the strength of the glue, an e- is released

Imagine photons (balls) hitting e- embedded in glue:

Higher intensity = more photons (balls). If E > threshold, more balls eject more e-.



+ =

+

=

Light waves waves cancel

waves

match



The Bohr Model of the Hydrogen Atom •  Heated solid objects emit continuous spectra. •  Excited atomic gases emit line spectra. •  Each element has a unique pattern.

400  500 600 700 wavelength (nm)

Hydrogen, H

400  500 600 700 wavelength (nm)

Mercury, Hg

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Neils Bohr (1913):

E = −2.179 x 10-18 J n = 1, 2, 3, . . . 1 n2

The Bohr Model of the Hydrogen Atom


E

nerg

y

n ∞ 3

2

1 ultraviolet emission

visible emission

ir emission

400  500 600 700 wavelength (nm)

absorption: ΔE > 0, n ↑ emission: ΔE < 0, n ↓

abso

rptio

n

Bohr’s model exactly predicts the H-atom spectrum.



H-atom transitions:

ΔE = −2.179 x 10-18 – J 1 nf

2 1 ni

2



Calculate the E and wavelength (in nm) for an H-atom n = 4 → n = 2 transition.

ΔE = −2.179 x 10-18 [(½)2 −(¼)2 ] J = −4.086 x 10-19 J = 4.086 x 10-19 J

(negative sign omitted. Losing energy = emission)

ν = ΔE/h = 4.086 x 10-19 J /6.626 x 10-34 Js

= 6.166 x 1014 s-1 = 6.166 x 1014 Hz

λ = c/ν = 2.9979 x 108 ms-1/6.166 x 1014 s-1

λ = 4.862 x 10-7 m = 486.2 nm



Bohr’s model predicts the H-atom:

Beyond the Bohr Model: Quantum Mechanics


λ = h mv

λ = wavelength (m) h = Planck’s constant (J s) m = mass (kg) v = velocity (m s-1)


Davidson and Germer (1927) observed e- diffraction by metal foils.

•  Wave-like behavior!

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Schrödinger equation (1926): •  Treats e- as standing waves (not particles).

•  Developed by analogy to classical equations for the motion of a guitar string.

•  Called “wave mechanics” or “quantum mechanics”  Explains the structure of all atoms and molecules.

 Complicated math; important results.



An electron density (probability) map plots ψ2 for each point in space.

Bigger value = darker shade.


ψ2 = probability of finding an e- at a point in space.


Each ψ describes a different energy level.

The H-atom ground-state

orbital



Quantum Numbers

•  Most important in determining the orbital energy.

•  Defines the orbital size.

•  Orbitals with equal n are in the same shell.


Quantum Numbers

l 0 1 2 3 4 5 ... Code s p d f g h ...

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Quantum Numbers

Every (n, l, ml) set has a different shape and/or orientation.

l = 0, or 1, or 2 if n = 3 and l = 2 (3d), ml is -2, -1, 0, 1 or 2. if n = 3 and l = 1 (3p), ml is -1, 0, or 1. if n = 3 and l = 0 (3s), ml must be 0.


Quantum Numbers Number of Number of Maximum

Electron Subshell Orbitals Electrons Electrons Shell type Available Possible for nth Shell (n) (=2l + 1) in Subshell (=2n2)

1 s 1 2 2 2 s 1 2

p 3 6 8 3 s 1 2

p 3 6 d 5 10 18

4 s 1 2 p 3 6 d 5 10 f 7 14 32

5 s 1 2 p 3 6 d 5 10 f 7 14 g* 9 18 50


Electron Spin Experiments showed a 4th quantum no. was needed

•  +½ or −½ only.

View an e- as a spinning sphere. Spinning charges act as magnets.


s Orbitals l = 0 orbital: Every shell (n level) has one s orbital.

Distance from nucleus, r (pm)

Pro

babi

lity

of fi

ndin

g e-

at

dist

ance

r fro

m n

ucle

us

Spherical. Larger n value = larger sphere

1s 2s 3s


p Orbitals

Three p orbitals (l = 1): px, py and pz

Related to ml = -1, 0, +1.


Five d orbitals (l = 2):

3dxz 3dxy 3dyz 3dx - y 3dz 2 2 2

d Orbitals

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−2.179 x 10-18

n2 E = (in J/atom).

Hydrogen Atom Energies


All other atoms are more complex.

Subshells do not have equal E.

Many-Electron Atoms

Note: E3s ≠ E3p ≠ E3d.

But, E3px = E3py = E3pz

Also: 3d is above 4s (but E4s≈ E3d)

1s

2s 2p

3s 3p

3d 4s

Ene

rgy

4p


•  Add e- to orbitals in increasing E order

Atom Electron Configurations

Paired spins: +½ and -½ ; ↑↓ Unpaired spins: all +½ or -½ ; ↑↑… or ↓↓…


H

He Li

Be B

C

N O

F Ne

1s 2s 2p Electron configurations Expanded Condensed 1s1 1s1

1s2 1s2 1s22s1 1s22s1

1s22s2 1s22s2

1s22s22p1 1s22s22p1 1s22s22p12p1 1s22s22p2

1s22s22p12p12p1 1s22s22p3 1s22s22p22p12p1 1s22s22p4

1s22s22p22p22p1 1s22s22p5

1s22s22p22p22p2 1s22s22p6

1s

2s 2p

3s 3p

Ene

rgy



Increasing (n + l), then increasing n

1s

2s

3s

4s

5s

6s

7s

8s

2p

3p

4p

5p

6p

7p

3d

4d

5d

6d

5f

4f

n value

8

7

6

5

4

3

2

1

l value

0 1 2 3

n + l = 1

n + l = 2 n + l = 3

n + l = 4 n + l = 5

n + l = 6 n + l = 7

n + l = 8



Main group s block

2 s

4 s

5 s

6 s

7 s

3 s

1s

5 f

4 f

6d

4d

3d

5d

6d

5d

4d

3d 4p

5p

6p

7p

3p

2p

1s

Lanthanides and actinides f block

Transition elements d block

Main group p block

Block identities show where successive e- add. Note: d “steps down”, f “steps down” again.


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The first 20 elements have only s and p e-:


Valence Electrons


atom configuration core valence N 1s2 2s2 2p3 [He] 2s2 2p3

Note: # of valence e- = A group #

Mn 1s2 2s2 2p6 3s2 3p6 3d 5 4s2 [Ar] 3d

5 4s2 Se 1s2 2s2 2p6 3s2 3p6 3d10 4s2 4p4 [Ar] 3d10 4s2 4p4 Si 1s2 2s2 2p6 3s2 3p2 [Ne] 3s2 3p2

Valence Electrons


Lewis dot symbols: •  Dots represent valence e-. •  Usually only used for s- and p-block elements.

N

Valence Electrons


1A 2A 3A 4A 5A 6A 7A 8A ns1 ns2 ns2np1 ns2np2 ns2np3 ns2np4 ns2np5

ns2np6

Li Be B C N O F Ne

Na Mg Al Si P S Cl Ar

• • •

• • •

• •

• • ••

• • •

••

•

••

• ••

••

••

• ••

••

•• ••

• • •

• • •

• •

• • •

• • ••

•

•• •

••

••

•• • ••

••

•• ••

••

Valence Electrons


Electron Configurations of Transition Metals

Complete 5s and 4d. 2 e- into 5p:

[Kr] 4d10 5s2 5p2

Sn (5th period, group 4A). Noble-gas core: [Kr]

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[Ar] 3d10 4s1 Cu has lower E with filled d-block and half-filled s-block

Ni (4th; 8B; 8 e- into 3d)

Cu (4th; 1B; 9 e- into 3d)

[Kr] 4d5 5s2

[Ar] 3d8 4s2

[Ar] 3d9 4s2



Sc 3d1 4s2

Y 4d1 5s2

La 5d1 6s2

Ti 3d2 4s2

Zr 4d2 5s2

Hf 5d2 6s2

V 3d3 4s2

Nb 4d4 5s1

Ta 5d3 6s2

W 5d4 6s2

Fe 3d6 4s2

Ru 4d7 5s1

Os 5d6 6s2

Co 3d7 4s2

Rh 4d8 5s1

Ir 5d7 6s2

Ni 3d8 4s2

Pt 5d9 6s1



Ion Electron Configurations Same approach. Positive ion: remove one e- for each “+” Negative ion: add one e- for each “-”


“A-group” ions usually adopt the nearest noble-gas configuration… … many ions are isoelectronic.

Ion Electron Configurations


Transition Metal Ions

Fe [Ar] 3d6 4s2 → Fe2+ [Ar] 3d6

Mn [Ar] 3d5 4s2 → Mn2+ [Ar] 3d5

→ Fe3+ [Ar] 3d5

→ Mn4+ [Ar] 3d3

→ Mn7+ [Ar]


Spinning e- = tiny magnet. If all e- are paired: Paramagnetism & Unpaired Electrons

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Paramagnet Ferromagnet

Paramagnetism & Unpaired Electrons


•  Estimate of atomic size   ½(homonuclear bond length)   Cl = 100 pm (Cl2 bond = 200 pm)   H = 37 pm (H2 bond =74 pm)

Cl Cl

200 pm

100 pm •  Radii are additive.

  HCl has a (37 + 100) = 137 pm bond

Periodic Trends: Atomic Radii



Incr

easi

ng S

ize

Increasing Size


•  p+ add to the nucleus. •  Larger charge pulls all e- in, shrinking the atom.



Group 1A Group 2A Group 3A Li Li+ Be Be2+ B B3+

152 90 112 59 85 25

Na Na+ Mg Mg2+ Al Al3+

186 116 160 86 143 68

K K+ Ca Ca2+ Ga Ga3+

227 152 197 114 135 76

Rb Rb+ Sr Sr2+ In In3+

248 166 215 132 167 94

Main block: outer shell completely removed.

e-/e- repulsion reduced (fewer e- ).

Periodic Trends: Ionic Radii


Group 6A Group 7A

O O2- F F-

73 126 72 119

S S2- Cl Cl- 103 170 100 167

Se Se2- Br Br-

119 184 114 182

Te Te2- I I- 142 207 133 206

More e-/e- repulsion (more e-). The shell swells.


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Isoelectronic Ions O2- F- Na+ Mg2+

Ionic radius (pm) 126 119 116 86 Number of protons 8 9 11 12 Number of electrons 10 10 10 10

Increasing nuclear charge decreasing size


Mg(g) Mg+(g) + e- ΔE = Ionization Energy

Periodic Trends: Ionization Energies

Also called IE1


Across a period: IE ↑. Smaller atom = more tightly held e-

Down a group: IE ↓. Larger atom = less tightly held e-



•  IE2 > IE1

•  Mg+ holds the 2nd e- more tightly. •  Huge increase if e- removal breaks a complete

shell (the core).

Mg(g) Mg+ (g) + e- ΔE = IE1

Mg+(g) Mg2+(g) + e- ΔE = IE2



Table 7.8 Ionization Energies Required to Remove Successive Electrons Ionization Energy Li Be B C N O F Ne (MJ/mol) 1s22s1 1s22s2 1s22s22p1 1s22s22p2 1s22s22p3 1s22s22p4 1s22s22p5 1s22s22p6

IE1 0.52 0.90 0.80 1.09 1.40 1.31 1.68 2.08 IE2 7.30 1.76 2.43 2.35 2.86 3.39 3.37 3.95 IE3 11.81 14.85 3.66 4.62 4.58 5.30 6.05 6.12 IE4 21.01 25.02 6.22 7.48 7.47 8.41 9.37 IE5 32.82 37.83 9.44 10.98 11.02 12.18 IE6 47.28 53.27 13.33 15.16 15.24 IE7 64.37 71.33 17.87 20.00 IE8 Core electrons 84.08 92.04 23.07 IE9 106.43 115.38 IE10 131.43



F(g) + e- F-(g) ΔE = Electron Affinity

•  Usually exothermic (EA is negative)

•  EA increases from left to right.

•  Metals have low EA; nonmetals have high EA.

•  Some tables list positive numbers.

 a sign-convention choice.

Periodic Trends: Electron Affinities

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Table 7.9 Electron Affinities (kJ/mol) 1A 2A 3A 4A 5A 6A 7A 8A (1) (2) (13) (14) (15) (16) (17) (18)

H -73

Li -60 Na -53 K -48 Rb -47

Ne >0 Ar >0 Kr >0 Xe >0

He >0

Be >0 Mg >0 Ca -2 Sr -5

B -27 Al -43 Ga -30 In -30

C -122 Si -134 Ge -119 Sn -107

N >0 P -72 As -78 Sb -103

O -141 S -200 Se -195 Te -190

F -328 Cl -349 Br -325 I -295

Periodic Trends: Electron Affinities


Ion Formation and Ionic Compounds Ionic compound formation is very exothermic:

K(s) + ½ F2(g) → KF(s) ΔHf° = -567.3 kJ

Two, of several, steps are:

K → K+ + e- IE = 419 kJ [Ne] 4s1 [Ne]

F + e- → F- EA = -328 kJ [He] 2s2 2p5 [He] 2s2 2p6 = [Ne]


Energy in Ionic Compound Formation

K(g) K+(g)

F(g) F-(g)

K(s) + ½ F2(g) KF(s) ΔHf°

+

ΔH2 = ½ Bond E

ΔH1 = ΔHsub

ΔH3 = IE

ΔH4 = EA

ΔH5 = Lattice E

ΔHf° = ΔH1 + ΔH2 + ΔH3 + ΔH4 + ΔH5 (H is a state function)


Energy in Ionic Compound Formation

K(g) K+(g)

F(g) F-(g)

K(s) + ½ F2(g) KF(s) ΔHf° = -567.3 kJ

+

ΔH2 = +79 kJ

ΔH1 = +89 kJ

ΔH3 = +419 kJ

ΔH4 = -328 kJ

Lattice Energy

Lattice Energy = ΔHf° - ΔH1 - ΔH2 - ΔH3 - ΔH4 = -567.3 – 89 – 79 – 419 – (-328) = -826 kJ

Lattice energies are hard to measure


Compound Charges of Ions r + + r- Lattice Energy Melting Point (kJ/mol) (K)

NaCl +1, -1 116 + 167 = 283 pm -786 1073 BaO +2, -2 149 + 126 = 275 pm -3054 2193 MgO +2, -2 86 + 126 = 212 pm -3791 3073

Energy in Ionic Compound Formation Table 7.10 Effect of Ion Size and Charge on Lattice E and Melting Point

c101 1 lecturenotes chapter7 Foster · 2013. 9. 27. · Electron Subshell Orbitals Electrons...

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