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

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Electronic Structure of Atoms(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 (l) distance between wave peaks
  (determines color of light)
• Frequency (n) cycles/sec (measured in Hz)

c l n
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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)
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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 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.

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

Niels Bohr(1888-1962)
Johannes Rydberg(1854-1919)
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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

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

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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
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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
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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.

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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)
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Electron density distribution in H atom
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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)

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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

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• d orbitals
• f orbitals very complicated

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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.
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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.
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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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6.7 Filling Order of Orbitals

1. 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

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6.7 Filling Order of Orbitals

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

• Relative stability average distance of e- from
  nucleus

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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-

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• 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)
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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
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Electronic Configurations
Element Standard Configuration Noble Gas Shorthand
Nitrogen
Scandium
Gallium
He 2s22p3
1s22s22p3
1s22s22p63s23p64s23d1

Ar 4s23d1
Ar 4s23d104p1
1s22s22p63s23p64s23d104p1
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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
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Notable Exceptions

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