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Electronic Structure of AtomsElectronic Structure of Atoms(i.e., Quantum Mechanics)(i.e., Quantum Mechanics)

Brown, LeMay Ch 6

AP Chemistry

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6.1: Light is a Wave

• Electromagnetic spectrum:– A form of radiant energy (can travel without

matter)– Both electrical and magnetic (properties are

perpendicular to each other)

• Speed of Light: c = 3.0 x 108 m/s (in a vacuum)Wavelength (): distance between wave peaks

(determines “color” of light)Frequency (): # cycles/sec (measured in Hz)

c =

3

6.2: Light is a Particle (Quantum Theory)• Blackbody radiation:

* Blackbody: object that absorbs all EM radiation that strikes it; it can radiate all possible wavelengths of EM; below 700 K, very little visible EM is produced; above 700 K visible E is produced starting at red, orange, yellow, and white before ending up at blue as the temperature increases

– discovery that light intensity (energy emitted per unit of time) is proportional to T4; hotter = shorter wavelengths

“Red hot” < “white hot” < “blue hot”

ch

h E

ch h E

Max Planck(1858-1947)

• Planck’s constant:Blackbody radiation can be explained if energy can be released or absorbed in packets of a standard size he called quanta (singular: quantum).

where Planck’s constant (h) = 6.63 x 10-34 J-s

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The Photoelectric Effect

• Spontaneous emission of e- from metal struck by light; first explained by Einstein in 1905– A quantum strikes a metal atom and the energy is

absorbed by an e-.– If the energy is sufficient, e- will leave its orbital,

causing a current to flow throughout the metal.

Albert Einstein(1879-1955)

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6.3: Bohr’s Model of the H Atom (and only H!)

Atomic emission spectra:– Most sources produce light that contains many wavelengths

at once.

– However, light emitted from pure substances may contain only a few specific wavelengths of light called a line spectrum (as opposed to a continuous spectrum).

– Atomic emission spectra are inverses of atomic absorption spectra.

Hydrogen: contains 1 red, 1 blue and 1 violet.

Carbon:

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Niels Bohr theorized that e-:– Travel in certain “orbits” around the nucleus, or, are only

stable at certain distances from the nucleus– If not, e- should emit energy, slow down, and crash into the

nucleus.

Allowed orbital energies are defined by:

principal quantum number (n) = 1, 2, 3, 4, …

Rydberg’s constant (RH) = 2.178 x 10-18 J

2

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2H

n n

10178.2

n

RE

Niels Bohr(1888-1962)

Johannes Rydberg(1854-1919)

As n approaches ∞, the e- is essentially removed from the atom, and E∞ = 0.

• ground state: lowest energy level in which an e- is stable• excited state: any energy level higher than an e-’s ground state

Incr

easi

ng E

nerg

y, E

Pri

ncip

al Q

uant

um N

umbe

r, n

54

3

2

1

E5

E4

E3

E2

E1

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ni = initial orbital of e-

nf = final orbital of e- in its transition

2

i2

f

Hn

1

n

1RE

2

i2

f

H

n

1

n

1

h

R

h

E

2

f2

i

H

n

1

n

1

h

R

h

E

Figure 1: Line series are transitions from one level to another.

SeriesTransition down to (emitted)

or up from (absorbed)…Type of EMR

Lyman 1 UV

Balmer 2 Visible

Paschen 3 IR

Brackett 4 Far IR

5432

1

n

Theodore Lyman

(1874 - 1954)

JohannBalmer

(1825 – 1898)

FriedrichPaschen

(1865 - 1947)

FrederickBrackett

(1896 – 1988)?

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6.4: Matter is a Wave

Planck said: E = h c /

Einstein said: E = m c2

Louis DeBroglie said (1924): h c / m c2

h / m c

Therefore:

m = h / c Particles (with mass) have an associated wavelength

h / mcWaves (with a wavelength) have an associated mass and velocity

Louisde Broglie

(1892 - 1987)

IBM – Almaden:

“Stadium Corral”

This image shows a ring of 76 iron atoms on a copper (111) surface. Electrons on this surface form a two-dimensional electron gas and scatter from the iron atoms but are

confined by boundary or "corral." The wave pattern in the interior is due to the density distribution of the trapped electrons. Their energies and spatial distribution can be quite

accurately calculated by solving the classic problem of a quantum mechanical particle in a hard-walled box. Quantum corrals provide us with a unique opportunity to study and

visualize the quantum behavior of electrons within small confining structures.

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Heisenberg’s Uncertainty Principle (1927)

It is impossible to determine the exact position and exact momentum (p) of an electron.

p = m v

• To determine the position of an e-, you have to detect how light reflects off it.

• But light means photons, which means energy. When photons strike an e-, they may change its motion (its momentum).

WernerHeisenberg

(1901 – 1976)

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Electron density distribution in H atom

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6.5: Quantum Mechanics & Atomic Orbitals

Schrödinger’s wave function:• Relates probability () of predicting

position of e- to its energy.

dt

dihU

dx

d

m

hE

2

22

2

Where: U = potential energy

x = position t = time

m = mass i =√(-1)

ErwinSchrödinger(1887 – 1961)

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Probability plots of 1s, 2s, and 3s orbitals

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6.6: Representations of Orbitals

s orbital

p orbitals

d orbitals

f orbitals: very complicated

Figure 2: Orbital Quantum NumbersSymbol Name Description Meaning Equations

nPrinciple

Q.N.

Energy level

(i.e. Bohr’s theory)

Shell number

n = 1, 2, 3, 4, 5, 6, 7

n = 1, 2, 3, …

lAngular

Momentum Q.N.

General probability

plot (“shape” of the orbitals)

Subshell number

l = 0, 1, 2, 3

 

l = 0 means “s”

l = 1 means “p”

l = 2 means “d”

l = 3 means “f”

l = 0, 1, 2, …, n – 1

 

Ex: If n = 1, l can only be 0; if n = 2, l can be 0 or 1.

Symbol Name Description Meaning Equations

mlMagnetic

Q.N.3-D orientation of the orbital

s has 1

p has 3

d has 5

f has 7

ml = -l, -l +1, …,

0, l, …, +l

 

There are

(2l + 1) values.  

ms Spin Q.N.Spin of the electron

Parallel or antiparallel

to field

ms = +½ or

-½

* s, p, d, and f come from the words sharp, principal, diffuse, and fundamental.

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Permissible Quantum Numbers

(4, 1, 2, +½)

(5, 2, 0, 0)

(2, 2, 1, +½)

Not permissible; if l = 1, ml = 1, 0, or –1 (p orbitals only have 3 subshells)

Not permissible; ms = +½ or –½

Not permissible; if n = 2, l = 0 or 1 (there is no 2d orbital)

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1. Aufbau principle: e- enter orbitals of lowest energy first (* postulated by Bohr, 1920)

1s

2s

3s

4s

5s

6s

7s

2p

3p

4p

5p

6p

3d

4d

5d

6d

4f x 7

5f x 7

Increasing Energy

7p

6.7: Filling Order of Orbitals

• Relative stability & average distance of e- from nucleus

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1. Aufbau principle: e- enter orbitals of lowest energy first

Increasing Energy

1s

2s

3s

4s

5s

6s

7s

3d

4d

5d

6d

4f x 7

5f x 7

2p

3p

4p

5p

6p

7p

• Relative stability & average distance of e- from nucleus

6.7: Filling Order of Orbitals

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Use the “diagonal rule” (some exceptions do occur).

Sub-level maxima: s = 2 e-

p = 6 e-d = 10 e-f = 14 e-…

1s

2s 2p

3s 3p 3d

4s 4p 4d 4f

5s 5p 5d 5f

6s 6p 6d

7s 7p

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2. Pauli exclusion principle (1925): no two e- can have the same four quantum numbers; e- in same orbital have opposite spins (up and down)

3. Hund’s rule: e- are added singly to each equivalent (degenerate) orbital before pairing

Ex: Phosphorus (15 e-) has unpaired e- inthe valence (outer) shell.

1s 2s 2p 3s 3p

WolfgangPauli

(1900 – 1958)

FriedrichHund

(1896 - 1997)

6.9: Periodic Table & Electronic Configurations

s block p blockd blockf block

s1 s2

p1p2p3p4p5 p6

d2 d3 d5 d5 d6 d7 d8d10d10

f1 f2 f3 f4 f5 f6 f7 f8 f9 f10f11f12f13f14

s2

1s2s3s4s5s6s7s

2p3p4p5p6p7p

4f5f

3d4d5d6d

3d4d5d6d

d1

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Electronic Configurations

Element Standard ConfigurationNoble Gas Shorthand

Nitrogen

Scandium

Gallium

[He] 2s22p3

[Ar] 4s23d1

[Ar] 4s23d104p1

1s22s22p3

1s22s22p63s23p64s23d1

1s22s22p63s23p64s23d104p1

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Element Standard ConfigurationNoble Gas Shorthand

Lanthanum

Cerium

Praseodymium

[Xe] 6s25d1

[Xe] 6s25d14f1`

1s2 2s22p6 3s23p6 4s23d104p6

5s24d105p6 6s25d1

1s2 2s22p6 3s23p6 4s23d104p6

5s24d105p6 6s25d14f1

[Xe] 6s24f31s2 2s22p6 3s23p6 4s23d104p6

5s24d105p6 6s24f3

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Notable Exceptions

Cr & Mo: [Ar] 4s1 3d5 not [Ar] 4s2 3d4

 

Cu, Ag, & Au: [Ar] 4s13d10 not [Ar] 4s23d9