Transcript Quantum Mechanics

Quantum Mechanics
Chapters 27 and 28
The Beginning
 Thomson-Cathode


J. J. Thomson experimented with cathode
rays and discovered the charge to mass ratio
of the particles that were in there.
Thomson called these particles “electrons”
 Millikan-Oil

Ray Experiments
Drop Experiment
Millikan used a spray atomizer to determine
the charge of an electron. This is the smallest
charge known and is called the elementary
charge
Conclusions from Early
Experiments
 Combining
Millikan and Thomson’s
findings, we are able to determine the
mass and charge of an electron.
 The electron is very, very small-too small
to measure accurately
Quantized Energy
 Max
Planck measures black body
radiation so accurately that he is able to
see that it occurs in discrete intervals
 E = nhf, where h is Planck’s constant, n is
an integer, and f is the frequency of the
oscillation
 Discrete is the same as quantum or
quantized
Photoelectric Effect

It was noticed that some metals when incident
with certain colors of light would conduct
electricity.
 At the time, it was already widely accepted that
light was a wave (Newton thought it was a
particle, but Young disproved his theories)
 According to wave theory, it should not depend
on color of light, but rather the intensity
 Einstein determined that the photoelectric effect
is in fact proof that light is a photon (particle) and
has energy based on wavelength/frequency, not
intensity
Wave Nature of Matter
 De
Broglie (pronounce de broy) stated that
if light can be both a wave and a particle,
maybe all particles can also be waves
 He was laughed for the most part until the
acceptance of quantum mechanics
Atomic Spectra




Rarefied gases can be excited to emit light
Discharge tubes are used that contains very little gas at
low pressure
A high voltage is applied across the atoms, which cause
them to interact to create light (one of the four
interactions of photons)
For hydrogen, there is an equation for wavelength of
light emitted


It is able to predict what wavelengths of hydrogen can be found
No other element can be predicted as hydrogen can, as the
calculations are too complex due to the extra electrons and
protons
Bohr’s Model of the Atom

Niels Bohr had studied with Rutherford (who
determined that the nucleus was a concentration
of massive particles we now know to be protons
and neutrons) and from this made his own
model of the atom
 The Bohr model of the atom explains the
equations for the atomic spectrum of hydrogen,
but does not work for any other element
 Even though his theory was wrong, it provided
an excellent starting point for quantum
mechanics
Quantum Mechanics Theory

Since we know all of the laws already
established hold to be true, it was agreed upon
that any laws that are created on an atomic level
would correspond to their macroscopic laws
 The wave function, Y (psi) represents the
displacement as a function of time and position
 Thus, Y2 is the probability of finding a certain
electron at the given position and time
 The Y2 function gives us the shapes of the
orbitals
Heisenberg Uncertainty Principle

Heisenberg stated that it was impossible to
measure either the energy of anything at the
same instant as time or the momentum at the
same instant of position
 This means that if something is moving, there is
a real possibility that you do not know where it
actually is
 This is typically a very small number (10-30) for
ordinary objects, but for electrons and other tiny
objects it is on the order at which they exist
Quantum Numbers

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
Principal-n-energy level, anywhere from 1 to
infinity
Orbital-l- gives us the shape, can be 0 to n-1
Magnetic-ml-gives us the orientation, can be –l
to +l
Spin-ms –gives the sign of the angular
momentum, can be +1/2 or -1/2
Pauli Exclusion Principle states that no two
electrons can have the same set of quantum
numbers
Equations
h
p x 
2
E t 
h
2
1240 eV  nm
E  pc  hf 


 (nm)
hc
K max  hf   
h
h
 
p mv
c  f
hc


Heisenberg Uncertainty Principle
Energy of a Photon
Photoelectric Effect,  = work function
 = hf0, f0 = threshold/cutoff frequency
Matter Waves
True for all electromagnetic radiation
Problems
 Chapter
27: pp 782-785
 Questions: 5, 6, 7, 25, 26
 Problems: 15, 17, 21, 23, 27
 Demonstrate: Ex 27-10 on page 766, Ex
27-11 on page 767, P #14 on page 783,
Review Graph on page 760, Ex 27-3 and
27-4 on page 761, P #20, 22, 26 on page
783 and GP#84 on page 785
Problems
 Chapter
28
 Questions: 7
 Problems: none
 Demonstrate: none