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Electronic Structure of Atoms(i.e., Quantum

Mechanics)

- Brown, LeMay Ch 6
- AP Chemistry

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 (l) distance between wave peaks

(determines color of light) - Frequency (n) cycles/sec (measured in Hz)

c l n

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 lt white hot lt blue hot

- Plancks 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 Plancks constant (h) 6.63 x 10-34 J-s

Max Planck(1858-1947)

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)

6.3 Bohrs 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.

- 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,
- Rydbergs constant (RH) 2.178 x 10-18 J

Niels Bohr(1888-1962)

Johannes Rydberg(1854-1919)

5 4 3 2 1

E5 E4 E3 E2 E1

Increasing Energy, E

Principal Quantum Number, n

- As n approaches 8, the e- is essentially removed

from the atom, and E8 0. - ground state lowest energy level in which an e-

is stable - excited state any energy level higher than an

e-s ground state

- ni initial orbital of e-
- nf final orbital of e- in its transition

Theodore Lyman (1874 - 1954)

5 4 3 2 1

FriedrichPaschen(1865 - 1947)

n

?

JohannBalmer(1825 1898)

FrederickBrackett(1896 1988)

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

Series Transition down to (emitted)or up from (absorbed) Type of EMR

Lyman 1 UV

Balmer 2 Visible

Paschen 3 IR

Brackett 4 Far IR

6.4 Matter is a Wave

- Planck said E h c / l
- Einstein said E m c2
- Louis DeBroglie said (1924) h c / l m c2
- h / l m c
- Therefore

Louisde Broglie(1892 - 1987)

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

l h / mc Waves (with a wavelength) have an associated mass and velocity

IBM AlmadenStadium 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.

Heisenbergs 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)

Electron density distribution in H atom

6.5 Quantum Mechanics Atomic Orbitals

- Schrödingers wave function
- Relates probability (Y2) of predicting position

of e- to its energy.

ErwinSchrödinger(1887 1961)

- Where U potential energy
- x position t time
- m mass i v(-1)

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

6.6 Representations of Orbitals

- s orbital
- p orbitals

- d orbitals
- f orbitals very complicated

Figure 2 Orbital Quantum Numbers

Symbol Name Description Meaning Equations

n Principle Q.N. Energy level (i.e. Bohrs theory) Shell number n 1, 2, 3, 4, 5, 6, 7 n 1, 2, 3,

l Angular 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

ml Magnetic 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.

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)

6.7 Filling Order of Orbitals

- Aufbau principle e- enter orbitals of lowest

energy first ( postulated by Bohr, 1920)

7p

6d

6p

5d

5p

4d

4p

3d

3p

2p

- Relative stability average distance of e- from

nucleus

6.7 Filling Order of Orbitals

- Aufbau principle e- enter orbitals of lowest

energy first

- Relative stability average distance of e- from

nucleus

1s 2s 2p 3s 3p 3d 4s 4p 4d 4f 5s 5p

5d 5f 6s 6p 6d 7s 7p

- Use the diagonal rule
- (some exceptions do occur).
- Sub-level maxima
- s 2 e-
- p 6 e-
- d 10 e-
- f 14 e-

- Pauli exclusion principle (1925) no two e- can

have the same four quantum numbers e- in same

orbital have opposite spins (up and down) - Hunds 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 block

d block

f block

s2

s1

s2

1s 2s 3s 4s 5s 6s 7s

2p 3p 4p 5p 6p 7p

d1

3d 4d 5d 6d

3d 4d 5d 6d

4f 5f

Electronic Configurations

Element Standard Configuration Noble Gas Shorthand

Nitrogen

Scandium

Gallium

He 2s22p3

1s22s22p3

1s22s22p63s23p64s23d1

Ar 4s23d1

Ar 4s23d104p1

1s22s22p63s23p64s23d104p1

Element Standard Configuration Noble Gas Shorthand

Lanthanum

Cerium

Praseodymium

Xe 6s25d1

1s2 2s22p6 3s23p6 4s23d104p6 5s24d105p6 6s25d1

Xe 6s25d14f1

1s2 2s22p6 3s23p6 4s23d104p6 5s24d105p6 6s25d14f1

Xe 6s24f3

1s2 2s22p6 3s23p6 4s23d104p6 5s24d105p6 6s24f3

Notable Exceptions

- Cr Mo Ar 4s1 3d5 not Ar 4s2 3d4
- Cu, Ag, Au Ar 4s13d10 not Ar 4s23d9