Honors Chemistry

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Honors Chemistry

• Chapter 7 Quantum Mechanics

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7.1 Wave Properties

• Wavelength (l) distance between two in-phase
  points
• Measured in meters
• Frequency (n) number of waves per second
• Measured in Hertz (Hz)
• Amplitude (y) distance of maximum displacement
  from rest position
• Amplitude corresponds to wave energy

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7.1 The Wave Equation

• v ln
• Find the wavelength of a 256 HZ (middle C) sound
  wave traveling at 343 m/s.
• v ln
• 343 m/s l (256 Hz)
• l 1.34 m
• Try this.
• Find the frequency of a 25.0 cm wave traveling at
  0.75 m/s.

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7.1 Electromagnetic Radiation

• James Clerk Maxwell (1873)
• Mathematical description of light waves
• Light is an electromagnetic wave
• Speed of light (c) is constant
• c 2.99792458 x 108 m/s
• To 3 sig dig, 3.00 x 108 m/s is fine
• Try this.
• Find the frequency of a 250 nm light wave.
  (Dont forget about the nano prefix!)

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7.1 Electromagnetic Spectrum

• Radio, micro, IR, ROYGBIV, UV, X, g
• long l ------------------------------- short l
• low n -------------------------------- high n
• Radio wave end of the spectrum is low energy
  radiation
• Gamma ray end is high energy radiation
• Black body radiation
• Wave theory fails to account for this!

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7.1 Quantum Theory

• Max Planck (1900)
• Energy is emitted and absorbed only in small,
  discrete packets called quanta
• Energy of a quantum of energy given byE hn
• h 6.626 x 10-34 Js (Plancks constant)
• Correctly accounts for blackbody curves
• Planck has no idea why it works!

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7.1 Quantum Theory

• Find the energy of a 2.50 x 1014 Hz light wave.
• E hn
• E (6.626 x 10-34 Js)(2.50 x 1014 Hz)
• E 1.66 x 10-19 J
• A quantum holds a tiny amount of energy!
• Try this.
• Find the energy of a 475 nm light wave.
• Hint Use the wave equation first!

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7.2 The Photoelectric Effect

• Albert Einstein (1905)
• Electrons ejected from surface of metal exposed
  to light
• Depends on frequency of light
• Electrons ejected at a certain cutoff frequency
• Above cutoff n, electrons leave with more energy
• Bright light ejects more electrons
• Quantum theory explains results
• Light is made of quanta called photons

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7.3 Spectroscopy

• Emission spectra light given off by glowing
  objects
• Can be continuous or discontinuous
• Line spectra series of bright lines emitted by
  gas phase atoms
• Pattern of bright lines is characteristic of the
  element that is glowing
• Absorption spectra dark lines in spectrum as
  light passes through a gas

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7.3 Bohrs Model

• Niels Bohr (1913)
• Electron energies are quantized
• Only certain orbits are allowed
• - RHEn ------ n2
• RH 2.18 x 10-18 J (Rydberg constant)
• n 1, 2, 3, 4, .

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7.3 Bohrs Model

• DE Ef E0
• -RH -RHDE ----- - -----
  nf2 n02
• Factor out RH
• 1 1 DE RH (----- -
  ----- ) n02 nf2

Link to Hydrogen energy states
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7.3 Bohrs Model

• Find the energy of a photon of light emitted by
  an electron jumping from level 5 down to level 2.
• DE RH (1/n52 1/n22)
• DE (2.18 x 10-18 J)(1/25 1/4)
• DE -4.58 x 10-19 J
• Try this.
• Find the energy of the jump from level 1 to level
  4.
• Find the frequency of the light produced.

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7.4 Duality

• Louis de Broglie (1924)
• Electrons can be treated as waves
• Each orbit must contain a whole number of
  wavesexplains orbit quantization!
• h l ---- mv
• mv is momentum (p), so we can write l h/p
• Verified by Davisson, Germer, and Thomson

Link to quantum atom model
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7.4 Duality

• Find the wavelength of a 3.00 kg duck flying at
  5.00 m/s.
• l h/mv
• l (6.626 x 10-34 Js) / (3.00 kg)(5.00 m/s)
• l 4.42 x 10-35 m
• Try this.
• Find the wavelength of an electron traveling at
  500,000 m/s. (me 9.11 x 10-31 kg)

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7.5 Uncertainty Principle

• Werner Heisenberg (1926)
• Complementary variables cannot be known to
  arbitrary precision
• dp dq h/2
• Minimum limits to uncertainties in values are
  inversely proportional
• Position and momentum are an important
  complementary pair
• dx dpx h/2

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7.5 Uncertainty Principle

• Find the uncertainty in velocity of an electron
  confined to a hydrogen atom (dx 0.037 nm).
• dx dpx h/2
• (3.7 x 10-11 m) dp 5.27 x 10-35 Js
• dp 1.4 x 10-24 kg m/s
• p mv
• 1.4 x 10-24 kg m/s (9.11 x 10-31 kg) dv
• dv 1.5 x 106 m/s

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7.5 Uncertainty Principle

• Try this
• Find the uncertainty in position of a 20.0 mg fly
  whose position is known to within 0.5 mm.
• Uncertainty limits are not significant for
  macroscopic objects, but they are significant to
  subatomic particles
• Cannot know the position and momentum of an
  electron at the same time!
• Concept of orbits will not work

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7.5 Quantum Mechanics

• Erwin Schrödinger (1926)
• Schrödinger equation treat electron as a
  standing wave surrounding the nucleus
• Schrödinger equation is ugly!
• Solve for amplitude function (y)
• Remember amplitude is energy
• Produces an energy diagram like Bohrs, but this
  one actually works
• Wave function has no physical meaning

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7.5 Copenhagen Interpretation

• Max Born (1926)
• y2 denotes probability
• Electron is delocalized
• Wave function collapses on observation
• electron density refers to magnitude of the
  probability wave for the electron
• Orbital spatial probability distribution
• Electron clouds
• Objections Schrödingers Cat
• Other interpretations

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7.6 Quantum Numbers

• Set of numbers that describe the distribution of
  electrons in the atom
• Principal Quantum Number (n)
• n 1, 2, 3, 4,
• Corresponds to the n value used by Bohr
• Describes energy level of the shell
• Defines the size of the electron cloud

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7.6 Quantum Numbers

• Angular Momentum Quantum Number (l)
• l 0, 1, 2, , n 1
• There are a total of n values
• Sublevels of the energy level
• Angular distribution of electron cloud
• For hydrogen, sublevels are degenerate
• Correspond to fine structure spectral lines
• l 0 is s orbital l 2 is d orbital
• l 1 is p orbital l 3 is f orbital

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7.6 Quantum Numbers

• Magnetic Quantum Number (ml)
• ml -l, , 0, , l
• There are a total of 2l 1 values
• Number of degenerate orbitals in sublevel
• Spatial orientation of the orbital
• Zeeman Effect
• Electron Spin Quantum Number (ms)
• ms ½, -½
• Two possible electron spin states
• Spin up, spin down

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7.7 Atomic Orbitals

• s, p, d, f orbitals
• Radial probability distributions
• distance from nucleus of high e- probability

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7.7 Atomic Orbitals

• Angular probability distributions
• Show regions of high e- probability
• Cool 3d pictures

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7.7 Orbital Energies

• n determines energy
• For H, all subshells are degenerate
• Multielectron atomseach subshell liesat a
  different energy
• Shielding effect
• Fill lowest energyorbitals first

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7.7 The Diagonal Rule

• Rule of thumb
• Shows the orderin which orbitalsare filled
• Paramagnetic
• Unpaired e-
• Attracted to mag
• Diamagnetic
• Paired e-
• Not attracted

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7.8 Electron Configurations

• H has 1 electron
• Put it in 1s
• Write it 1s1
• Read one-s-one
• What about He?
• You got it1s2
• Keep filling 1s until it is full
• But when is it full?

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7.8 Pauli Exclusion Principle

• No two electrons may share the exact set of
  quantum numbers
• Consider Heliums 1s2 configuration
• First electron n 1, l 0, ml 0, ms ½
• Second electron same n, l, ml
• ms must be -½
• No room for more electrons in 1s orbital
• Each orbital can hold only two electrons!

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7.8 Electron Configurations

• What is the electron configuration of Li?
• 1s2 2s1
• What about N?
• 1s2 2s2 2p3
• But how are p electrons organized?
• Hunds Rule arrange electrons in such a way as
  to maximize total spin state
• Put e-s in separate orbitals, same spin

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7.9 Aufbau Principle

• Build up on previous e- configurations
• Each atom adds one more e-
• Express configuration with noble gas core
• Al 1s2 2s2 2p6 3s2 3p1
• First 3 terms are the same as Ne config.
• Write it as Ne 3s2 3p1

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7.9 Exceptions

• Particularly stable configurations
• Full sublevel
• Half-full sublevel
• Some transition metals rearrange
• Cr Ar 4s2 3d4
• Just missed the stable half-full 3d5
• Kick one e- up to d to get Ar 4s1 3d5
• What other family would do this?
• Cu Ar 4s2 3d9 ? Ar 4s1 3d10

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7.9 Periodicity of Electron Configuration