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Chapter 7
Atomic Structure
• Waves
wavelength,  (peak to peak distance)
amplitude, A (peak height)
frequency,  (number of waves that pass a point per
unit time)
• speed, v (frequency x wavelength)
v  
• Light speed (constant) = c = 2.99792458  108 m/s
Energy--frequency relationship:
E  h
where h = Planck’s constant = 6.626  10-34 J-s
Long wavelength --> small frequency--> low energy
Short wavelength --> high frequency -->high energy
• Planck & Einstein: Energy is quantized.
Energy can only be absorbed or released from
atoms in certain amounts called quanta.
Light is quantized in packets called photons.
Light and matter have both wave and particle properties.
Wave-Particle Duality
• Quantization example: Ramp vs. stairs
• Ramp - continuous change in height
• Any value is of potential energy is allowed.
• Stairs – only certain heights allowed (quantization)
• Each stair step represents an allowed potential
Evidence for Quantization of Energy
Photoelectric Effect
• Evidence for the particle nature of light
• Light shines on a metal surface
• If above a threshold frequency---electrons ejected
• If below the threshold frequency---no electrons
ejected (no matter how intense the light)
• Number of electrons ejected depends on light intensity
• Recall light comes in photons (particle like nature)
Light must have enough energy to knock an electron
off of the metal surface.
E  h
Line Spectra
• Radiation spanning an array of wavelengths is called
continuous (e.g. sunlight).
• Prisms separate white light a spectrum of colors.
• Spectrum is continuous --- no dark spots (no missing
• Elements in gas discharge tubes have line spectra
• Not continuous
• Only certain colors present
• Monochromatic lines = one 
• Each color has a unique  and energy E
Bohr correlated lines with electron transitions between
energy levels
• Bohr model –
• Energy of electrons is quantized
• Energy states correspond to orbits
• Orbits are numbered: principal quantum number (n)
• n = 1, is closest to nucleus (lowest energy)
• Electrons can only move between orbits by absorbing
and emitting energy in quanta (h).
• Ground State –electron is in its lowest energy orbit.
• Excited State – An outside energy source promotes
electron to a higher energy orbit.
• Unstable – electrons transition to lower states and
give off excess energy as light
• Each line (monochromatic color) is from one transition
excited state  lower state
• Energy of light = energy difference between electron
E  h 
 1
1 
  2.18 10 18 J  2  2 
 f ni 
• When ni > nf, energy is emitted.
• When nf > ni, energy is absorbed
Limitations of the Bohr Model
• Only adequately explains hydrogen’s line spectrum.
• Electrons are not completely described as small
• Knowing that light has a particle nature, it seems
reasonable to ask if matter has a wave nature.
• Using Einstein’s and Planck’s equations, de Broglie
• The momentum, mv, is a particle property, whereas 
is a wave property.
• de Broglie summarized the concepts of waves and
particles, with noticeable effects if the objects are
The Uncertainty Principle
• Heisenberg’s Uncertainty Principle: on the mass scale
of atomic particles, we cannot determine exactly the
position, direction of motion, and speed
• For electrons: we cannot determine their momentum
and position simultaneously.
• If Δx is the uncertainty in position and Δmv is the
uncertainty in momentum, then
x·mv 
• Schrödinger proposed an equation that contains both
wave and particle terms (duality).
• Solving the equation leads to wave functions, .
• The wave function gives the shape of the electronic
• The square of the wave function, 2, gives the
probability of finding the electron,
• that is, gives the electron density for the atom.
See fig 6.16