Quantum MechanicsQuantum Mechanics

Chapters 27 and 28Chapters 27 and 28

The BeginningThe Beginning

Thomson-Cathode Ray ExperimentsThomson-Cathode Ray Experiments J. J. Thomson experimented with cathode J. J. Thomson experimented with cathode

rays and discovered the charge to mass ratio rays and discovered the charge to mass ratio of the particles that were in there.of the particles that were in there.

Thomson called these particles “electrons”Thomson called these particles “electrons” Millikan-Oil Drop ExperimentMillikan-Oil Drop Experiment

Millikan used a spray atomizer to determine Millikan used a spray atomizer to determine the charge of an electron. This is the smallest the charge of an electron. This is the smallest charge known and is called the elementary charge known and is called the elementary chargecharge

Conclusions from Early Conclusions from Early ExperimentsExperiments

Combining Millikan and Thomson’s Combining Millikan and Thomson’s findings, we are able to determine the findings, we are able to determine the mass and charge of an electron. mass and charge of an electron.

The electron is very, very small-too small The electron is very, very small-too small to measure accuratelyto measure accurately

Quantized EnergyQuantized Energy

Max Planck measures black body Max Planck measures black body radiation so accurately that he is able to radiation so accurately that he is able to see that it occurs in discrete intervalssee that it occurs in discrete intervals

E = nhf, where h is Planck’s constant, n is E = nhf, where h is Planck’s constant, n is an integer, and f is the frequency of the an integer, and f is the frequency of the oscillationoscillation

Discrete is the same as quantum or Discrete is the same as quantum or quantizedquantized

Photoelectric EffectPhotoelectric Effect It was noticed that some metals when incident It was noticed that some metals when incident

with certain colors of light would conduct with certain colors of light would conduct electricity.electricity.

At the time, it was already widely accepted that At the time, it was already widely accepted that light was a wave (Newton thought it was a light was a wave (Newton thought it was a particle, but Young disproved his theories)particle, but Young disproved his theories)

According to wave theory, it should not depend According to wave theory, it should not depend on color of light, but rather the intensityon color of light, but rather the intensity

Einstein determined that the photoelectric effect Einstein determined that the photoelectric effect is in fact proof that light is a photon (particle) and is in fact proof that light is a photon (particle) and has energy based on wavelength/frequency, not has energy based on wavelength/frequency, not intensityintensity

Wave Nature of MatterWave Nature of Matter

De Broglie (pronounce De Broglie (pronounce de broyde broy) stated that ) stated that if light can be both a wave and a particle, if light can be both a wave and a particle, maybe all particles can also be wavesmaybe all particles can also be waves

He was laughed for the most part until the He was laughed for the most part until the acceptance of quantum mechanicsacceptance of quantum mechanics

Atomic SpectraAtomic Spectra

Rarefied gases can be excited to emit lightRarefied gases can be excited to emit light Discharge tubes are used that contains very little gas at Discharge tubes are used that contains very little gas at

low pressurelow pressure A high voltage is applied across the atoms, which cause A high voltage is applied across the atoms, which cause

them to interact to create light (one of the four them to interact to create light (one of the four interactions of photons)interactions of photons)

For hydrogen, there is an equation for wavelength of For hydrogen, there is an equation for wavelength of light emittedlight emitted

It is able to predict what wavelengths of hydrogen can be foundIt is able to predict what wavelengths of hydrogen can be found No other element can be predicted as hydrogen can, as the No other element can be predicted as hydrogen can, as the

calculations are too complex due to the extra electrons and calculations are too complex due to the extra electrons and protonsprotons

Bohr’s Model of the AtomBohr’s Model of the Atom

Niels Bohr had studied with Rutherford (who Niels Bohr had studied with Rutherford (who determined that the nucleus was a concentration determined that the nucleus was a concentration of massive particles we now know to be protons of massive particles we now know to be protons and neutrons) and from this made his own and neutrons) and from this made his own model of the atommodel of the atom

The Bohr model of the atom explains the The Bohr model of the atom explains the equations for the atomic spectrum of hydrogen, equations for the atomic spectrum of hydrogen, but does not work for any other elementbut does not work for any other element

Even though his theory was wrong, it provided Even though his theory was wrong, it provided an excellent starting point for quantum an excellent starting point for quantum mechanicsmechanics

Quantum Mechanics TheoryQuantum Mechanics Theory

Since we know all of the laws already Since we know all of the laws already established hold to be true, it was agreed upon established hold to be true, it was agreed upon that any laws that are created on an atomic level that any laws that are created on an atomic level would correspond to their macroscopic lawswould correspond to their macroscopic laws

The wave function, The wave function, (psi) represents the (psi) represents the displacement as a function of time and positiondisplacement as a function of time and position

Thus, Thus, is the probability of finding a certain is the probability of finding a certain electron at the given position and timeelectron at the given position and time

The The function gives us the shapes of the function gives us the shapes of the orbitalsorbitals

Heisenberg Uncertainty PrincipleHeisenberg Uncertainty Principle

Heisenberg stated that it was impossible to Heisenberg stated that it was impossible to measure either the energy of anything at the measure either the energy of anything at the same instant as time or the momentum at the same instant as time or the momentum at the same instant of positionsame instant of position

This means that if something is moving, there is This means that if something is moving, there is a real possibility that you do not know where it a real possibility that you do not know where it actually isactually is

This is typically a very small number (10This is typically a very small number (10 -30-30) for ) for ordinary objects, but for electrons and other tiny ordinary objects, but for electrons and other tiny objects it is on the order at which they existobjects it is on the order at which they exist

Quantum NumbersQuantum Numbers

Principal-n-energy level, anywhere from 1 to Principal-n-energy level, anywhere from 1 to infinityinfinity

Orbital-Orbital-ll- gives us the shape, can be 0 to n-1- gives us the shape, can be 0 to n-1 Magnetic-mMagnetic-mll-gives us the orientation, can be –-gives us the orientation, can be –ll

to +to +ll Spin-mSpin-ms s –gives the sign of the angular –gives the sign of the angular

momentum, can be +1/2 or -1/2 momentum, can be +1/2 or -1/2 Pauli Exclusion Principle states that no two Pauli Exclusion Principle states that no two

electrons can have the same set of quantum electrons can have the same set of quantum numbersnumbers

EquationsEquations

2

hxp

2

htE Heisenberg Uncertainty Principle

)(

1240

nm

nmeVhchfpcE

Energy of a Photon

hc

hfKmaxPhotoelectric Effect, = work function

= hf0, f0 = threshold/cutoff frequency

mv

h

p

h Matter Waves

fc True for all electromagnetic radiation

ProblemsProblems

Chapter 27: pp 782-785Chapter 27: pp 782-785 Questions: 5, 6, 7, 25, 26Questions: 5, 6, 7, 25, 26 Problems: 15, 17, 21, 23, 27Problems: 15, 17, 21, 23, 27 Demonstrate: Ex 27-10 on page 766, Ex Demonstrate: Ex 27-10 on page 766, Ex

27-11 on page 767, P #14 on page 783, 27-11 on page 767, P #14 on page 783, Review Graph on page 760, Ex 27-3 and Review Graph on page 760, Ex 27-3 and 27-4 on page 761, P #20, 22, 26 on page 27-4 on page 761, P #20, 22, 26 on page 783 and GP#84 on page 785783 and GP#84 on page 785

ProblemsProblems

Chapter 28Chapter 28 Questions: 7Questions: 7 Problems: noneProblems: none Demonstrate: noneDemonstrate: none