Models of the Atom

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Models of the Atom

• Rutherford, Bohr, De Broglie and Quantum Physics

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Nature of Electrons

• Originally called cathode rays
• Reversing magnet shows that they are charged
  particles

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Plum Pudding Model(Thompson - 1890s)
Positively charged material
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Rutherford Experiment (1911)
Alpha Particle is 2n2p or helium nucleus
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Another View
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Results of Rutherford Experiment

• Most alpha particles pass through undeflected
• Conclusion atom is mostly empty space
• Some deflected at very large angles, even
  backward
• Conclusionpositive charge is concentrated in a
  small region of atom
• Animation

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Rutherfords Planetary Model of Hydrogen Atom
Size of nucleus 10-15 m
Size of atom 10-10 m
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Two problems

• Stability
• Continuous spectrum not seen

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Atomic Spectra

• Observe with gas discharge tube
• Glow due to accelerated
• electrons striking atoms in low
• pressure gas and exciting them
• Light from tube found to
• contain discrete wavelengths

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Spectrometer Set Up
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Emission Spectrum

• Use diffraction grating or prism spectrometer to
  see
• Compare to white light spectrum(continuous)

Graphics courtesy of Science Joy Wagon Physics
Zone
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A high school teacher named Balmer found that
these wavelengths obeyed a 1/n2 rule
Shows visible portion of spectrum
Divide by 10 to get nanometers
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Infra-red
Visible
Shows Energy of emitted photons
UV
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One Formula Fits All(but no one knew why it
worked)

• Each observed wavelength described by
• 1/l R (1/n2 1/n2)
• n 1 for Lyman, n 2 for Balmer,
• n 3 for Paschen
• R Rydberg Constant 1.097 x 107 m-1

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Rutherford Model Could Not Explain

• Why atoms emit line spectra
• Why atom is stable. Accelerated electrons should
  emit radiation with increasing frequency as they
  spiral into atom.
• Spectra should be continuous.

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Bohr Model

• Atom has discrete energy levels - states
• Electrons move in orbits without radiating energy
• Light quanta (photons) emitted when electrons
  jump from state to state
• hf Eu - El

Eu
hf
El
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Bohr Balmer Connection

• Bohrs theory agrees with Balmer if electron
  angular momentum quantized
• L mvrn n h/2p
• n 1, 2, 3,
• rn is radius of nth possible orbit

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Bohr Theory for Hydrogen Atom

• Electron and Nucleus held together by Coulomb
  force
• Predicts r1 0.529 x 10-10 m as radius of
  smallest oribit in hydrogen (Bohr Radius)
• Leads to Lyman, Balmer, Paschen formulae
• En -13.6 eV/n2
• Ground state has most negative energy
• Excited states have higher(more positive) energy

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Bohrs Derivation

• F ma
• kZe2/ (rn) 2 mv2 /rn
• Mvrn nh/2p
• rn n2h2/(4p2mkZe2)
• En ½ mv2 kZe2/rn -2p2Z2e4mk2/n2h2
• En - 13.6/n2

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Bohr Radii

• Ground state has smallest radius
• Excited states have larger radii
• r n2 r1
• Changes in level are
• called atomic transitions

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Bohr Energy Levels for Hydrogen Atom
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Ionized atom, positive continuous energies,
electron free
E 0
E -1.5 eV
E -3.4 eV
E-13.6 eV
Ground state
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Emission vs. Absorption of Photon Energy

• Emission- atom drops to lower states
• Random and spontaneous process
• Absorption atom rises to higher states. Only
  photons of just the right energy can be absorbed

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Question If you shine a light on a gas do you
get

• Absorption?
• Emission?
• Both?

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Ionization Energy

• Minimum energy to kick electron out of ground
  state
• 13.6 eV for hydrogen atom
• Can supplied by heating or collision

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Find the Wavelength

• What is the wavelength in the transition from n2
  to n1?

hf E2 E1 13.6 eV 3.40 eV 10.2 eV
l c/f hc/(E2 E1) (6.63x10-34
J-S)(3.00x108 m/s)/(10.2 eV)(1.6 x 10-19 J/eV)
1.22 x 10-7 m or 122 nm
What kind of light is this?
Ans. Ultra Violet
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De Broglie Waves in Atoms

• Why should orbits be quantized a la Bohr?
• De Broglie wave is associated with electron l
  h/mv
• Only orbits that correspond to standing waves can
  persist
• Circumference must contain whole number of
  wavelengths

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Standing Circular Waves

• 2prn nl n 1, 2, 3
• But l h/mv
• 2prn nh/mv
• or mvrn nh/2p
• This was Bohrs quantization condition
• Implies wave-particle duality at root of atomic
  structure

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Limitations of Bohr Theory

• Could not explain spectra of other than hydrogen
  atoms
• Could not explain why emission lines are double,
  triple or more
• Could not explain why some lines brighter than
  others
• Could not explain how atoms bond
• Mixed classical and quantum ideas

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Quantum Mechanics

• Next step after Bohr in explaining atomic physics
• Explains details of spectra
• Gives classical(correct) results for larger
  objects
• Based on Wave functions, probability and
  Schrodinger equation
• Modern theory called quantum electrodynamics.

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Heisenberg Uncertainty Principle

• Accuracy of some measurements is inherently
  limited by nature
• To observe is to interfere
• We cannot measure the momentum and position of an
  object precisely at the same time
• The energy of an object may be uncertain(or even
  non-conserved) for a small time

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Probability vs Determinism

• On sub-atomic scale nature is probabilistic not
  deterministic
• Certain paths and events knowable only in terms
  of probability
• Electrons form cloud around atom called
  probability distribution

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Quantum Numbers Determine State of Atom

• Principle quantum number-from Bohr theory
• Orbital quantum number-related to angular
  momentum
• Magnetic quantum number-related to direction of
  electrons angular momentum
• Spin quantum number

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Pauli Exclusion Principle

• No two electrons in an atom can occupy the same
  state
• Cant have exactly the same quantum numbers
• Helps determine patterns of regularities in
  Periodic Table of Elements(explained by quantum
  mechanics)