Chapter 7 Beyond Rutherford to

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Chapter 7Beyond Rutherford toThe Most
Successful Theory of the 20th Century
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View Rutherfords experiment
http//www.learnerstv.com/animation/chemistry/ruth
er14.swf
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Rutherfords Atomic Model(planetary model)
e-
Orbiting electron (fixed radius)
Empty space
Nucleus Diameter 10-15 m
Diameter of atom 10-10 m
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Problem with Rutherfords Model !!

• It did not obey the classical laws of physics
• But atoms dont collapse, yet Rutherfords
  experiment showed that electrons can be located a
  distance away from the nucleus.
• So, the model of the _______ behavior is flawed.

According to Newtons classical laws, electrons
orbiting the nucleus should radiate energy, slow
down, and be pulled into the nucleus collapse
the atom
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Collision of Ideas
Matter
Dalton
Thomson
Rutherford
?
Bohr de Broglie
Einstein
Plank
Maxwell
Newton
Light
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What is the nature of light?
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Isaac Newton Light is a particle

• By the 17th century, light was found to
• travel in straight lines
• reflect refract
• transmit energy from one place to another

Newtons prism
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The WAVE THEORY, advocated by
Robert Hooke Christian Huygens argued
that light is a wave.
The PARTICLE THEORY, advocated by Isaac Newton
and Pierre Laplace, argued that light was made up
of a stream of tiny particles (corpuscles).
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Two Competing Theories

• The theory of light
• The theory of light

WAVE
Particle
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white light light energy composed of a
continuous spectrum of visible electromagnetic
radiation
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Basics of wave theory
Wavelength ? distance between wave crests (m)
Frequency ? cycles per second (Hz)
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Electromagnetic Wave Theory (1865)

• Based on experiments of
• Michael Faraday

• Theory developed by
• James Clerk Maxwell

Electromagnetic waves have a variety of
wavelengths, but all travel at the speed of
light, Based on conservation of energy,
Maxwell derived the wave equation,
c 2.998 108 m/s
c ? ?
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Electromagnetic Spectrum
1020 Hz
1014 Hz
1010 Hz
10-6 nm
108 nm
higher energy
lower energy
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• ROY G BIV
• low energy ? high energy

Colors in the visible spectrum Red, Orange,
Yellow, Green, Blue, Indigo Violet
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Problems with the Wave Theory of Light
By the mid-1800s, the wave theory became
predominant, but When light interacted with
matter, the wave theory failed. The important
examples are

1. Blackbody Radiation
2. The Photoelectric Effect
3. Emission Spectra of Atoms

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Problem 1. Blackbody Radiation

• blackbody
• object that absorbs all the
• colors in the spectrum

Blackbody Simulation
actual spectrum
When heated to a high enough temperature, the
blackbody radiates white light. The wave theory
predicts a continuous spectrum of emitted light,
but the theory fails to match experiment.
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Plancks Quantum Theory

• Measured blackbody radiation did not produce a
  continuous spectrum, as wave theory predicted
• In 1900, German Physicist Max Planck proposed a
  new quantum theory of light

Light is taken up and given off by a blackbody
not as a continuous wave, but in little packets
of light energy of specific values Planck called
these packets quanta (singular is quantum) of
energy
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Quantum Theory of Light and Quantum Physics

• Planks quantum theory of light was a historical
  turning point in physics, transitioning classical
  physics from the 18th and 19th centuries to the
  quantum physics of the 20th century.

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Problem 2Photoelectric Effect
Animation
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Problem 2. Photoelectric Effect

• Imagine shining light of various wavelengths
  (energies) on the surfaces of different metals
• Only light energies above a certain threshold
  cause electrons to be ejected from the metal
  surface
• This conflicts with predictions of the wave theory

Animation
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Einsteins Photons

• In 1905, a Swiss patent clerk proposed that light
  consists of particles called photons.
• As Planck proposed, Einsteins photons have a
  certain quanta of energy (based on wavelength)
• His model of light solved the problem of the
  photoelectric effect.

• Duality of Light
• Wave behavior
• Particle behavior

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Solar Sail (based on Einsteins photon theory)
- Light reflecting off a mirror imparts momentum
- Yet light has no mass (experiment by Compton
in 1923)
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Energy of Photons

• At a specific frequency (or wavelength) photons
  possess a specific quantity of energy (E )
• Plancks constant

E h ?
E h c/?
h 6.626 x 10-34 Js
Question Is 400 nm light (violet light) more
or less energetic than 750 nm light (red light)?
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Concept Check
The energy required to dislodge electrons from
sodium metal via the photoelectric effect is 275
kJ/mol. What wavelength (in nm) has sufficient
energy per photon to dislodge an electron from
the surface of sodium?
sodium
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Concept Check
Which photons have the highest energy? A) Cell
phone operating at 1900 MHz B) A laser
pointer using 635 nm light
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Problem 3. Atomic Line Spectra
Flame tests http//college.cengage.com/chemistry/
general/ebbing/general_chem/9e/assets/ instructors
/protected/videos.htmlChapter 7

• Periodic Table of Line Spectra

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Problem 3. Atomic Line Spectra
Fireworks
Emission spectra for pure elements

• Periodic Table of Line Spectra

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Niels Bohr (1885-1962)

• Danish physicist who worked with J.J. Thomson at
  Cambridge University in 1911. He didnt agree
  with Thomsons atomic model,
• so worked for Rutherford in 1912.

• In 1912, in a bold step, he suggested that the
  classical laws of physics cannot be applied to
  matter as small as atoms and electrons. Instead,
  new laws are needed
• Bohr sought to solve the problem with
  Rutherfords atomic model and explain the
  phenomenon of atomic spectra, by applying the
  quantum theory of light to atoms and electrons

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Bohrs Quantum Atomic Model

• Postulated that the energy of the electron must
  be quantized. Only certain electron energies are
  possible.
• Orbit radii (energy levels) correspond to
  definite energies
• Energy is emitted or absorbed by the electron
  only as the electron changes from one allowed
  energy level to another

n energy level number or principal
quantum number
Why does an electron possess energy? 1) 2)
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How do quantized energy levels explain spectral
lines?

• Atoms place electrons in lowest possible energy
  levels (ground state)
• When electrons are provided with enough energy,
  they jump to higher energy levels, where they
  are unstable (excited state)
• The electrons then fall back down to the lower
  possible energy levels, releasing absorbed energy
  as a photon of light
• We see these photons as the spectral lines
  emitted by excited atoms

Energy of H electron E -RH/n2 n 1, 2, 3,
8 RH 2.179 x 10-18 J
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energy levels
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H emission spectrum
quantum jump ?E4?2 ?E2 - E4? h?4?2
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A quantum jump
Emission ?E ?E2 - E4? h?4?2
Absorption ?E ?E4 E2? h?2?4
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Simulations of Bohr Model

• Visible emission spectral lines of hydrogen

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Success Limitation of Bohrs Quantum Model

• Explained the existence of spectral lines
• Solved the problem with Rutherfords model of the
  hydrogen atom
• But, the mathematics only worked for atoms with 1
  electron!

How can this model be made to work for all
elements?
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de Broglies Novel Notion
1923

• Light was known (thought) to be a wave, but
• Einstein showed that it also acts particle-like.
• Electrons were known to be particles mass
  charge.
• French physicist
• What if

electrons behaved as waves also
Diffraction pattern obtained by firing a beam of
electrons through a crystal.
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• Dr. Quantum video

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Werner Heisenberg
The Uncertainty Principle
speed
position

• In 1927, German physicist, proposed that the dual
  nature of the electron places limitations on how
  precisely we can know both the location and speed
  of the electron
• Instead, we can only describe electron behavior
  in terms of probability

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HeisenbergsUncertainty Principle

• Wave behavior limits what can be known!
• What if the particle has a small mass?
• What if the electrons position is known very
  precisely?
• What if the electrons speed is known very
  precisely?

(x)(vx) ?
Can the electrons orbit be precisely defined?
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Erwin Schrodinger
Wave Equation Wave Mechanics

• In 1926, Austrian physicist, proposed an equation
  that incorporates both the wave and particle
  behavior of the electron
• When applied to hydrogens 1 electron atom,
  solutions provide the most probable location of
  finding the electron in the first energy level
• Can be applied to more complex atoms too!

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Electron Characteristics

• Extremely small mass
• Located outside the nucleus
• Moving at very high speeds
• Have specific energy levels
• Standing wave behavior

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Baseball v. Electron
A baseball behaves as a particle and follows a
predictable path. BUT An electron behaves as a
wave, and its path cannot be predicted. All we
can do is to calculate the probability of the
electron following a specific path.
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What if a baseball behaved like an electron?
? h /(mu)
speed
mass

• Characteristic wavelength (?)
• baseball ? 10-34 m
• electron ? 0.1 nm

So, all we can predict is..
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deterministic
probabilistic
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Bohr Model v. Quantum Mechanics
Bohr Quantum Mechanics
Energy Electron Position/Path Elements
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Quantum Mechanics Model
The electron's movement cannot be known
precisely. We can only map the probability of
finding the electron at various locations outside
the nucleus. The probability map is called an
orbital. The orbital is calculated to confine 99
of electrons range. Energy of the electron is
quantized into sublevels.
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Quantum Mechanics ModelDescribes the energy,
arrangement and space occupied by electrons in
atoms
Electrons energy is quantized
Quantum Mechanics
Mathematics of waves to define orbitals (wave
mechanics)
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Most Successful Theory of the 20th Century
Matter
Dalton
Thomson
Rutherford
Quantum Mechanics
Bohr de Broglie
Heisenberg
Einstein
Plank
Schrödinger
Maxwell
Wave Mechanics
Newton
Light