Transcript History of Quantum Theory

Niels Bohr
Learning Goals
 Students will be able to:
1) understand the Quantum Mechanical Model of the
Atom
2) understand how to describe the atom in terms of the
Quantum Mechanical Model (energy level, shapes of
orbits, sub-orbitals and quantum numbers)
Success Criteria
Students will:
1) record the important facts in an information chart.
2) understand the advancements of each new atomic
model.
3) identify the weakness of the model that lead to
further investigation.
Review – Rutherford’s Model
 Rutherford used the Gold Foil Experiment to theorize
that:
1) atoms contain a tiny, dense, positively charged
nucleus.
2) the nucleus was orbited by very light, negatively
charged electrons.
3) most of the volume of an atom was empty space.
Limitations of Rutherford’s Model
 An electron accelerating around the
nucleus would continuously emit
electromagnetic radiation and lose
energy
 Therefore, it would eventually fall
into the nucleus and the atom
would collapse
 However, this is not consistent with
real-world observations – atoms
are stable
Bohr and Quantum Theory
 Watch Structure of the Atom 4: The Bohr Model (9:08)
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http://www.youtube.com/watch?v=hpKhjKrBn9s
Bohr used recent work by Max Planck.
Planck and his teacher, Kirchhoff, studied the light
emitted from hot, dark objects (blackbodies).
Planck noticed that when radiation (light, UV, IR) is
emitted from a heated solid, the energy (blackbody
radiation) is not released at all wavelengths, but is released
at only specific wavelengths of energy
Energy is quantized. It comes in chunks.
Bohr and Spectroscopy
 A quanta is the amount of energy needed to move from
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one energy level to another.
Since the energy of an atom is never “in between” there
must be a quantum leap in energy.
Bohr looked at the spectra released by light produced by
an excited gas.
Bohr chose Hydrogen because it is the simplest element.
https://www.youtube.com/watch?v=LA9juHlyhKw (Mr.
Causey – Bohr’s Planetary Model)
http://www.youtube.com/watch?v=Nv1_YB1IedE
(Quantum Mechanics – The Fabric of the Cosmos – Brian
Greene)
A short Review on Spectroscopy –
remember grade 10! (neither do I)
 When white light is shone
through a prism, it is broken
into a spectrum.
 Each colour corresponds to a
different wavelength of light.
 Each wavelength corresponds
to a particular amount of
energy.
Comparing Spectra
 Absorption
spectra are
produced
when light is
shone through
a cooler gas.
 Emission
spectra are
produced
when light is
emitted by the
gas.
The Atomic Spectra of Hydrogen
 Bohr specifically
used the spectra of
hydrogen since it is
the simplest of
atoms.
Spectra of Other Atoms and
Luminous Objects
 Note that each element has
its own distinctive spectra.
 Bohr knew that he could
Bohr-ing Math
measure the wavelength of
the spectral lines.
 When hydrogen is
“excited” by the addition of
energy (electricity is used
in a gas discharge tube), an
electron jumps up from a
low orbit and moves into a
higher orbit.
 Eventually this electron
falls back down and
releases a specific amount
of energy (a quanta).
 When the electrons falls
back down it emits energy
that we can “see” as a
spectral line. (note some
lines appear in the infrared
and ultraviolet portions of
the spectrum)
Bohr-ing Math
 Bohr postulated that an
electron cannot exist between
orbits – electrons can only
exist in orbits and each orbit
occupies a specific energy
level.
 Each line in the spectrum is
produced by the quantum of
energy released when one
electron falls back down to a
lower orbit.
 Examples:
1. drop from 4th orbital to 2nd
orbital (blue line)
2. drop from the 3rd orbital to
1st orbital (ultraviolet line)
3. drop from 5th orbital to 3rd
orbital (infrared line)
Wavelength Equation
 Bohr knew that the wavelength of
light could be used to determine its
energy level and its velocity using
the equations below:
 Bohr eventually expanded his math to determine the
distance of each orbital from the nucleus and the
energy level of each permissible energy level for
hydrogen.
Successes and Weaknesses of
 Weaknesses
Bohr’s Model
 Successes
1)
2)
3)
Bohr’s mathematics
explained all the
observations for Hydrogen
perfectly
This is a major success for
Quantum Mechanics – to
this day it has never failed
He solved Rutherford’s
problem
1)
2)
Bohr’s method only worked for
Hydrogen
Although the quantum theory
of light was experimentally
proven, other experiments had
proven that light had also
continuous wavelike properties.
Einstein suggested that there
were "two contradictory pictures
of reality; separately neither of
them fully explains the
phenomena of light, but
together they do".
Hence light and photons display
wave and particle properties
deBroglie (1924) & Schrödinger (1925)
 Responding to the
difficulties in the Bohr
model, Louis deBroglie ,
from France, suggested
that matter like light, has
the properties of both
particles and waves.
This particle-wave
duality -derived from the
work of Einstein and
Planck - was
experimentally confirmed,
for the electron, in 1927.
 Austrian physicist Erwin
Schrodinger formed a
model of a complete atom
as interacting waves.
 The particles became like
vibrations on a violin
string, only they were
closed in circles.
 His partial differential
equation seemed to bear a
similar relation to the
mechanics of the atom as
Newton's equations of
motion bear to planetary
astronomy.
deBroglie (1924) & Schrödinger (1925)
 A representation of energy levels and sub-levels as
waves instead of particles in circular orbits. Note the
math – Schrodinger’s wave function being applied.
Heisenberg (1926)
 German physicist Werner
Heisenberg formulated
his Uncertainty Principle which says
that you cannot know by measurement
the position and momentum of a
particle simultaneously.
 The better you know one, the worse
you know the other.
 Particles and fields undulate and jump
between all possible values consistent
with the quantum uncertainty.
 Atoms were now visualized as a
nucleus surrounded by a cloud of
electrons distributed according to a
wave pattern by the Schrodinger
equation.
Clouds of electrons determined
by Heisenberg and Schrodinger’s
mathematical models and borne
out by X-ray studies.
Dirac (1926)
 Paul Dirac devised a form of
quantum mechanics (developed
by Schrodinger and Heisenberg),
which provides the laws of motion
that govern atomic particles.
 The electron could now be
described by four wave functions,  It followed from Dirac's
satisfying four simultaneous
equations that the electron
differential equations. As before
must rotate, or spin, on its
the electrons still cannot be
axis, and also that there must
pinpointed but exist as a sort
be states of negative energy.
of cloud of probability outside
the nucleus.
Quantum Numbers
 Using high resolution spectra,
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Michelson noticed that the
main lines found in spectra were
often split into smaller lines.
Sommerfeld (1915) was able to
explain these small lines using
elliptical orbits.
deBroglie and schrodinger’s
work clarifies this
He explained that each level has
sub-levels or subshells.
Therefore each one of Bohr’s
energy levels can be divided into
smaller levels.
Secondary Quantum Number
 BOHR – his energy levels (orbitals) were labeled the
Primary Quantum Number (n)
 SOMMERFELD – Secondary Quantum Number (l)
 l = 0 to n-1,
 therefore if l = 3, n can equal 0, 1, 2
 Therefore the 3rd energy level contains 3 sublevels.
 The secondary quantum number caused orbitals to take
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on different shapes
l = 0 (speherical orbital)
l = 1 (dumb-bell shaped 2-lobed orbitals)
l = 2 (4-lobed orbitals)
l = 3 (6 and 8-lobed orbitals)
Magnetic Quantum Number
 Zeeman (1896) noticed that the spectral lines could also be
split if placed in a magnetic field.
 Sommerfeld and DeBye used this information to produce
another Quantum number, the Magnetic Quantum
Number (ml)
 ml = -l to +l
 Therefore if l = 1; ml can be -1, 0, +1
 This means that each sublevel can have further
sublevels.
 This causes the orbitals to have different orientations in
space
Spin Quantum Number
 Work by Pauli (1925) determine that two electrons
could occupy each orbital.
 These electrons have opposite spins given the values
+1/2 and -1/2.
 The Spin Quantum Number (ms)
 ms = -l/2 and +l/2
 This means that each sublevel can be occupied by
two electrons!
Summary
 This time line draws
nice comparisons
between the Quantum
view of the Atom with
the Bohr-Rutherford
model and the Lewis
Structures we have used
in the past.
Senior Physics – TVO programs
 Structure of the Atom 1: The Earliest Models (9:04)
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http://www.youtube.com/watch?v=BhWgv0STLZs
Structure of the Atom 2: Smaller than the Smallest (8:47)
http://www.youtube.com/watch?v=WmmglVNl9OQ
Structure of the Atom 3: The Rutherford Model (9:10)
http://www.youtube.com/watch?v=FfY4R5mkMY8
Structure of the Atom 4: The Bohr Model (9:08)
http://www.youtube.com/watch?v=hpKhjKrBn9s
Structure of the Atom 5: Spectra (9:28)
http://www.youtube.com/watch?v=5z2ZfYVzefs
Structure of the Atom 6: The Wave Mechanical Model (9:08)
http://www.youtube.com/watch?v=IsA_oIXdF_8
These programs provide excellent review of the History of the
Atomic Model and how Quantum Mechanics is important!