Rise of the Quantum Theory

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Rise of the Quantum Theory

• Light particles or waves? Greeks answer
  particles
• 17th century, Christian Huygens, proposed light
  can be best described as a wave Isaac Newton
  vehemently opposed
• Mid-19th century, James Maxwell proposed that
  light is an electromagnetic wave consisting of
  magnetic and electric fields that can exert
  forces on an object (Classical Theory of light)

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The Wave Nature of Light
Electromagnetic waves originate from the movement
of electric charges
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Characterizing Waves
Electromagnetic radiation is characterized by its
wavelength, frequency, and amplitude
Wavelength (l) is the distance between any two
identical points in consecutive cycles
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Characterizing Waves
Frequency of a wave is the number of cycles of
the wave that pass through a point in a unit of
time
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The Electromagnetic Spectrum
The electromagnetic spectrum is largely invisible
to the eye
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The Electromagnetic Spectrum

• We can feel some radiation through other senses
  (infrared)
• Sunburned skin is a sign of too much ultraviolet
  radiation
• Materials vary in their ability to absorb or
  transmit different wavelengths
• Our bodies absorb visible light, but transmit
  most X rays
• Window glass transmits visible light, but absorbs
  ultraviolet radiation

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Bright Line Dark Line Spectra

• Robert Bunsen Gustav Kirchhoff invented the
  spectroscope (1859)
• They found that energized gases emit coloured
  light
• Different types of gases emit different colours
  of light
• Light from energized elements (gaseous form)
  produced specific bands of colour gt bright line
  or emission line spectrum
• What is a dark line or absorption spectrum?

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The Continuous Spectrum
The different colors of light correspond to
different wavelengths and frequencies
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Continuous Spectra
White light passed through a prism produces a
spectrum colors in continuous form.
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Line Spectra
Light passed through a prism from an element
produces a discontinuous spectrum of specific
colors
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Line Spectra
The pattern of lines emitted by excited atoms of
an element is unique atomic emission spectrum
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Key Evidence I Blackbody radiation

• Kirchhoff (1859) observed blackbody radiation.
• What is a black body? What is blackbody
  radiation?
• Spectrum of the intensity (brightness) of the
  radiation yielded a typical bell curve..SHOCKER

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Blackbody Radiation Curves

• Actual
  Predicted?

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Plancks Interpretation of Blackbody
Radiation Studies

• Planck (1900) proposed that the vibrating atoms
  in a heated solid could absorb or emit
  electromagnetic energy only in discrete amounts
  hypothesized that energy is not continuous but
  existed in discrete bundles called quanta

• The smallest amount of energy, a quantum, is
  given by
  E hv, where h is Plancks constant 6.626
  1034 J s

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Key Evidence II Photoelectric Effect

• Photoelectric Effect (discovered by Heinrich
  Hertz 1887) the release of electrons from a
  metal surface when struck by light of
  appropriate frequency
• According to classical theory, the intensity of
  the light shone on the metal impacts the KE of
  the liberated electrons the photoelectric effect
  disprove this however
• So what impacted the KE of the liberated
  electrons?

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Einsteins explanation of the Photoelectric
Effect

• Einstein hypothesized that light was bundled into
  little packets called photons
• The energy of a photon can be likened to the
  monetary value ascribed to coins
• A photon of red light contained less energy than
  a photon of UV light
• Electrons cannot break free unless they absorb a
  certain minimum quantity of energy from a single
  photon

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Bohrs Hydrogen Atom
Niels Bohr found that the electron energy (En)
was quantized, that is, that it can have only
certain specified values
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The Bohr Model
En B/n2 where B is a constant 2.179 1018
J and n is an integer
The negative sign represents the forces of
attraction
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Energy Levels and Spectral Lines for Hydrogen
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Bohr Explains Line Spectra
Bohrs equation is most useful in determining the
energy change (?Elevel) that accompanies the leap
of an electron from one energy level to another
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Ground States and Excited States
Electrons in their lowest possible energy levels
are in the ground state
Electrons promoted to any level n gt 1 are in an
excited state
Electrons are promoted by absorbing energy e.g.,
electric discharge, heat, lasers (photons)
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• The Quantum (Wave) Mechanics Model
• In 1924, a French physicist named Louis de
  Broglie suggested that, like light, electrons
  could act as both particles and waves.
• De Broglie's hypothesis was soon confirmed in
  experiments that showed electron beams could be
  diffracted or bent as they passed through a slit
  much like light could.
• The waves produced by an electron confined in its
  orbit about the nucleus sets up a standing wave
  of specific wavelength, energy and frequency
  (i.e., Bohr's energy levels) much like a guitar
  string sets up a standing wave when plucked.
• De Broglie's vision of Bohr's atom  
•    

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Quantum (Wave) Mechanics
Quantum mechanics, or wave mechanics, is the
treatment of atomic structure through the
wavelike properties of the electron
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Wave Mechanics Probability
Wave mechanics provides a probability of where an
electron will be in certain regions of an atom
This region of space where theres a high
probability of finding an electron is called an
orbital
Wave mechanics led to the idea of a cloud of
electron density rather than a discrete location
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Quantum Numbers and Atomic Orbitals
A wave function with a given set of these three
quantum numbers is called an atomic orbital In
quantum mechanics the atomic orbitals require
three integer quantum numbers to completely
describe the energy and the shape of the 3-D
space occupied by the electron (n, l, and ml)
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Principal Quantum Number (n)

• Is independent of the other two quantum numbers

• Can only be a positive integer

• indicates the size of an orbital (distance from
  the nucleus) and its electron energy
• n can be 1, 2, 3, 4,

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Orbital Angular Momentum Quantum Number (l)(aka
Azimuthal quantum number)

• Determines the shape of the orbital s, p, d, f
  , which corresponds to values l values of 0,
  1, 2, 3
• Possible values of l 0 to n 1 e.g. if n
  2, l can only be 0 or 1
• Each of these orbitals is in a different region
  of space and has a different shape
• All the l quantum values represent different
  sublevels or subshells
• When n 1, there is only one l value meaning
  there is only one sublevel in the first energy
  level when n 2 there are two values for l
  indicating two sublevels in the second energy
  level

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Magnetic Quantum Number (ml)
Determines the orientation in space of the
orbital so named because in a magnetic field,
these different orientations have different
energies
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Taken together the three quantum numbers specific
the orbital the electron occupies.
Namelythe energy of the orbital, the shape of
the orbital, and the orientation of the orbital
.
Quantum Numbers Summary
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• writing 3 quantum numbers to indicate every
  possible orbital an electron can occupy is
  cumbersome instead do we do the following
• retain the numeric value of the principal quantum
  number and use a letter to indicate the azimuthal
  quantum number
• l 0 ? s l 1? p l 2 ? d l 3 ? d
• - When combined, they indicate an a specific
  orbital e.g. 1s orbital 2s orbital 2p orbital

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Radial Distributions
Electrons are most likely to reside nearest the
nucleus because of electrostatic attraction
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Electron Probabilitiesand the 1s Orbital
The 1s orbital looks very much like a fuzzy ball,
that is, the orbital has spherical symmetry (the
probability of finding an electron is the same in
direction)
The electrons are more concentrated near the
center
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Electron Probabilitiesand the 2s Orbital
The 2s orbital has two regions of high electron
probability, both being spherical
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The Three p Orbitals-There are three p orbital
each orbital is cylindrically symmetrical with
respect to rotation around one of the 3 axes, x,
y, or zEach p orbital has two lobes of high
probability density separated by a node (region
of zero probability)
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The Five d Orbitals
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Electron Spin (ms)
The electron spin quantum number explains some of
the finer features of atomic emission spectra