Jm honors pt 1 this one missing you

Jason Morris Honors Natural
Science Lectures Part 1
Copyright 2017

Pre-19th
Century Physics and Chemistry
The Birth of Science
From Natural Philosophy to Natural Science

How Science Works
Observation
(not relying on intuition or axioms or tradition or revelation):
Quantitation
Model building / Hypothesis generation:
Abstraction / Imagination
Generalizations vs Exceptional Cases
Experimental tests of models / hypotheses:
Quantitation
Refinement or rejection of models / hypotheses
Generalizations vs Exceptional Cases

Causes and Explanations
Aristotle posited four causes/explanations for phenomena: (e.g.
a paper airplane flies across a classroom…)
The airplane flew that way because:
1) of what is was made of
2) of its shape
3) of the momentum imparted to it by the student’s arm
4) the student wanted to hit someone with it
The first three causes are physical and are a part of scientific
discourse. The final cause is teleological or “the final cause.”
It deals with “purpose.”

Teleological Reasoning 1
Teleology made sense to Aristotle because of his premises that
a) the world is unchanging and comprised of eternal species.
b) Organisms appear perfectly designed and the environments
in which they live appear perfectly designed for the organisms’
flourishing.
Aristotle:
1) The patterns of rainfall is explained by the needs of crops.
2) The existence of all human organs is explained by the needs
of the human organism.
3) The fact that men are hairier on their chests than on their
backs is explained by the fact that nature devotes resources to
the nobler parts.

Teleological Reasoning 2
Teleology makes sense when discussing the actions of a being
with a psychology and desires (though even this is
controversial). Teleology is not part of the scientific discourse
for other phenomena.
1) Causes precede effects; they don’t work backwards in time
2) We have no plausible model for how teleological causes
could work
3) Ascribing telos to non-psychological entities is subjective and
retrospective
Francis Bacon (1620): teleological reasoning is unproductive:
Inquiry into final causes is sterile and “like a virgin consecrated
to God.”

What Is The Universe Made Of?
Empedocles: everything is made of four elements (Fire, Water,
Earth, Air). He might have received this indirectly from India.
Aristotle added a fifth element, “Ether,” to Empedocles’ list to
explain the circular motions of planets.
Space, Matter, Light, Heat, Moisture, Motion, Time…
What are these?
Why do things fall? What is lightning? Why does amber
attract other objects if you rub it with fur? Why do lodestones
attract iron?

What is Matter?
Matter: Substances of which a physical object consists
Substance: The material forming a thing
Object: A material thing
Material: Formed or consisting of matter. Corporeal
Matter has mass and takes up space

Ancient Theories of Motion
Aristotle taught that objects that tended to fall
to earth because of they were largely
composed of the element “Earth.” Other
objects tended to rise because they included
significant amount of the element “Fire” and
so were attracted to the “Realm of Fire.”
Aristotle taught that matter has an inherent
tendency to be at rest. He believed a moving
object will slow down unless a force acts on it.

Ancient Cosmologies: Aristotle
Geocentric
Circular orbits

Ancient Cosmologies: Ptolemy
“epicycles” make
model much more
complex, but the
model conforms
better to observations

Early Modern Astronomers
Galileo (died 1642): astronomer, physicist, performed
experiments, discovered some of the laws of motion
including that falling objects undergo a constant acceleration
(change in velocity over time) due to gravity.
Copernicus (died 1543): heliocentric model of the (known)
universe is simplest and probably true.
Kepler (died 1630): a) orbits are actually ellipses b) planets
move faster when orbit carries them closer to sun c) the time
to complete an orbit is mathematically related to the mean
distance between the planet and the sun.

Galileo, Newton, and Relativity
Principle of Relativity: the laws of physics
are the same everywhere whether observers
are moving or not.
Different observers legitimately have
different interpretations of events.
Example 1) observers in different locations
measure an object’s distance and direction
from them differently.
Example 2) observers moving with
different velocities ascribe different
velocities to the objects around them.

Describing Newton’s Universe
Mass Distance Time
Velocity (linear, angular)
Momentum (linear, angular)
Acceleration Force Energy
Following Galileo, Newton (1642-1727)
described the universe as following deterministic laws
that are best expressed mathematically. These laws
take measurable parameters as their inputs and give
very specific quantities as their outputs.

Symmetries and Invariance
A symmetry is an aspect of the system that does not
change even when some aspect of the system changes.
If the forces acting on an object are the same, Newtons’s
laws do not change if you move an object to a different
location, rotate it, move it at a constant velocity, or
allow time to pass.

Noether’s Theorem (1915)
Each type of symmetry (each type of change you can
make to a reference frame without altering the form of
physical laws) implies a specific conservation law.
Examples:
Doesn’t matter if you: so this is conserved:
relocate momentum
rotate angular momentum
come back another time energy

What is the absolute
reference for acceleration?
Why is this not
Newton: Not Everything Is Relative…

More Newton: Mass and Inertia
Objects have a tendency to move in a constant
direction at a constant speed: “inertia.”
Accelerating a massive object requires a force. Greater
masses or greater accelerations require more force.
F = ma
Change in direction or speed is acceleration.
Objects with more mass have more inertia
Published 1687

What is Space? 1
Democritus: Atoms are being. Space is non-being. But it
is a non-being that exists, through which atoms move.
Aristotle: If there is nothing between two objects, what
does it mean to say there is space between them? If space
is nothing, it doesn’t exist. If it is something, how can its
only property be to exist without doing anything?
Einstein: Spacetime is the gravitational field.

What is Space? 2
Newton called space “God’s sensorium.” No one has any
idea what this means. He thought space was “absolute”–
that empty space provides the true, objective reference
frame that tells us if we are accelerating.
Leibniz disagreed at first, claiming that space has no
meaning except as a way of describing the location of
objects. But Newton convinced him that somehow objects
do “know” if they are accelerating or not.
Mach thought it isn’t space that provides an objective
reference, it is all the collected matter in space…

Newton and Gravity 1
Newton thought of gravity as a force that acted
instantaneously over long distances to accelerate masses.
Newton combined kepler’s laws of orbital motion with
Galileo’s observation of constant acceleration due to
gravity. He calculated that an object orbiting the Earth at
the minimal possible distance (just above the mountain
tops) would take 1.5 hrs to complete its orbit. It’s
acceleration would be 9.8 m/s2, the same as the
acceleration of falling bodies in Galileo’s experiments!
He concluded that orbits are the same as falling!

Newton on Mass and Gravity
Newton was the first to understand and formulate his
law of gravity. Gravity causes all matter in the
universe to attract all other matter. The more matter
(“mass”), the stronger the attraction.
Gravity has an infinite range; the strength of
gravitational attraction decreases with the square of
the distance “inverse square law.”
Fg α
m1 m2
r2
Published 1687

Falling Bodies
Galileo claimed that, discounting air resistance, any
object dropped to earth from the same height would
fall in the same amount of time no matter how
different their masses. Newton’s laws express this
in terms of gravity and inertia:
Fg = G mobject mearth
r2
= mobject a
Acceleration due to gravity depends on the mass of
Earth and distance of object from center of the Earth,
but not on the mass of the object

Science as a Creative Process 2
1) Ancient physics: sun and planets orbit the earth in circles
and at constant speeds
2) Careful observation and measurement shows it is much
simpler to explain and predict astronomical events using a
model in which earth and other planets orbit the sun
( Copernicus) and that orbits are elliptical, with the orbital
speed related to the distance between the objects (Kepler)
3) Newton explained all orbital motion and the motion of
falling bodies in terms of one central concept: gravity!
4) Einstein and gravity (general relativity)
5) Quantum gravity?...

Newton and Gravity Illustrations
The Earth is falling toward (but not into) the sun!
The force pulling on the planet
depends on the distance to the
star and the gravity of the star.
A planet close to the star must
be traveling moving faster and
in a smaller radius. Its year will
therefore be shorter.

Newton and Gravity Illustrations
Satellite A and B have low velocity in the X
direction (vx)
Satellite C has exactly the vx needed so that
it curves with the curvature of the earth as it
falls (a circular orbit)
Satellite D has a slightly greater vx so that it
has an elliptical orbit
Satellite D has vx escape velocity.≥
If the kinetic energy of the satellite > potential energy, its path is
a hyperbola.
If the energies are equal, its path is an ellipse (orbit).
If the potential energy is greater, its path is a parabola.

Measuring Mass
We can measure an object’s mass by determining its
gravitational attraction to the earth (e.g. on a scale)
OR
by determining its inertia (e.g. by finding how much a
given force can change the object’s speed or direction)
Why should inertia and gravitational attractiveness
correlate so well?
Mass is measured in grams (g) or kilograms (kg)

Pressure and Air
2) Flip the beaker and submerge it in a vat of
the same liquid
[liquid can flow in and out of the beaker]
3) Why doesn’t the liquid
“seek it’s own level?”
Pressure is caused by the force of gravity acting on an area
This indicated that air, or gas
is a form of matter. It has
mass and it exerts force.
1) Fill a tall beaker with a liquid (e.g Mercury)
[there is no air in the beaker now]
First Barometer (1643)

Gas Law 1: Boyle’s Law (1660)
Pressure α 1/Volume
open
trapped air
Pressure is measured
in weight/area
volume is
measured in
liters or cm3

Chemical Reactions and Elements
Alchemy began in the ancient world. It was a
mystical/religious/proto-scientific discipline concerned with the
transmutation of “base metals” into “noble metals,” with
purification of the soul, and with eternal life.
Modern chemistry begins with Boyle’s The Sceptical Chymist
(1661): attempted to use chemical reactions to distinguish
compounds from elements.
Chemical reactions: start with one type of substance or
collection of substances (reactants) and end with a different
substance or collection of substances

Chemistry and Air
Element: A substance that cannot be broken down (by
chemical means) to other types of substances
Compound: A substance that can be broken down (by
chemical means to other types of substances
Mixture: Different substances combined together that can be
purified from each other without changing them (chemically)
What is air, really? Is all “air” the same? Does air = gas?
(“Gas” comes from the Flemish spelling of “chaos”)

Fire and Some Common Reactions
Early on, chemists observed similarities in burning and rusting
(for example these common reactions require “air.”)
Some things burn or rust; others do not. Early chemists theorized
that materials containing a fire element, “phlogiston,” would burn
or rust. Once all the phlogiston was released, they would no
longer burn or rust.
But careful quantitation showed that when wood burns, it seems
to become lighter and when metals rust, they appear to get
heavier. Would phlogiston have a negative mass or a positive
mass? Was the rust the actual element and the metal a
compound?

Phlogiston
calx of mercury (HgO) mercury (Hg)
heat
Chemists discovered later that the weights only match if you
include an escaping gas. Flames burn more brightly in this gas!
heat

Michelangelo’s Frescoes (~1510)
“Air” does more than burn…

The Process
“limewater”
“slaked lime”
calcium hydroxide
Ca(OH)2
“quicklime”
calcium oxide
CaO
“Limestone”
calcium carbonate
CaCO3
Heat (500-1000 C)
water
sand

Carbon Dioxide Discovered (Black, 1756)
All the reactants were carefully weighed, including water,
base, etc.
Mass of reactants (e.g. limestone) equalled mass of
products (eg quicklime) IF AND ONLY IF the released
“air” was trapped and weighed!
The “air” that was released going from limestone to
quicklime is distinct from regular air:
fires won’t burn in it (Black)
mice can’t breath it (Rutherford, 1772)
Air is not an element! It contains small amounts of carbon
dioxide.

Hydrogen Discovered
Metal + Acid gives off a gas (Cavendish, 1766). We
will study this in lab!
If you collect this gas, you learn very quickly that it is
highly explosive if exposed to air. The gas is very
light.
Lavoisier named this gas
“hydrogen”-- “water
producer” after studying
this “combustion.”

Oxygen Discsovered
(Scheele, Priestley, Lavoisier, 1771-1775)
1) The gas released from calx of Mercury is utilized in
burning reactions (Scheele, 1772).
2) This gas is also required for mice to breathe. When
mice use the gas up, it can be restored by a sprig of
mint (Priestley, 1771, 1774).
1) Rust is metal oxide. That’s why it’s heavier than the
metal. Phlogiston doesn’t exist (Lavoisier)

Temperature and Charles’ Law (1787)
Temperature: temperature is measured in °C or K
Solids, liquids, and gases occur in the same substance
at different temperatures (e.g. water can freeze or
evaporate).
If you keep a gas at constant volume (e.g. in a
sealed container) T α P
If you keep a gas to at a constant pressure (e.g. under a
piston that can move) T α V

A Key Experiment (Lavoisier, 1784)
Weigh a particular volume of purified Hydrogen gas
Add the gases together in a sealed container
Set off an electric spark inside the chamber.
Weigh a particular volume of purified Oxygen gas
Heat and Light Escape, but nothing else does.
Pure water is produced!
The mass of the water = the mass of the gases!

Interpretations
What is water?
What are heat and light?
What is conserved in a chemical reaction?

Simple Proportions (Dalton, 1801)
The volume in a balloon at a particular temperature
and pressure is proportional to the amount of gas in
the balloon.
Gases react completely when you combine them in
simple ratios by volume (e.g. 1:1, 2:1, 3:2…).
These observations are consistent with the atomic
theory of matter and with the theory that molecules
are made up of simple, specific proportions of
particular types of atoms.

More on Simple Proportions
But 2 volumes of hydrogen react completely with 1 volume of
oxygen to produce water. That suggests water could be H2O.
2H + O H2O
1g 8g 9g
But when we combined 2 volumes of hydrogen with 1 volume of
oxygen, we got 2 volumes of water vapor, not 1!
This is part of the evidence that oxygen gas is O2 and hydrogen
gas is H2: 2H2 + O2 2H2O
If hydrogen gas were H and oxygen gas were O and water were
OH, then H + O OH

Kinetic Theory of Gases
Pressure: The pressure inside the balloon is caused by the
gas particles banging into it from the inside. Pressure outside
the balloon is caused by the air molecules banging into the
balloon from the outside.
Volume: If the pressure outside the balloon is lower than the
pressure inside, the balloon will expand. If the pressure is
higher outside, the balloon will contract,
Imagine a gas that is trapped inside a balloon. According to
the atomic theory of matter, the gas is made of tiny particles.
The particles constantly collide with the sides of the balloon
and with each other.

Atoms and Matter
“If, in some cataclysm, all of scientific knowledge were to be destroyed,
and only one sentence passed on to the next generations of creatures, what
statement would contain the most information in the fewest words? I
believe it is the atomic hypothesis (or the atomic fact, or whatever you
wish to call it) that all things are made of atoms—little particles that move
around in perpetual motion, attracting each other when they are a little
distance apart, but repelling upon being squeezed into one another. In that
one sentence, you will see, there is an enormous amount of information
about the world, if just a little imagination and thinking are applied.”
--Richard Feynman

Atoms, Elements, Molecules
Elements combine chemically in simple ratios to
produce molecules
Elements are made of atoms of a particular type
Atoms of different types have different masses
Not all elements combine to produce molecules.
Usually, elements combine in one or a few different ratios.

Balancing Chemical Equations
In chemical reactions, atoms are not created or destroyed.
The same numbers of each type of atom must be present in the
reactants (what you start with) and the products (what you end up
with) in the reaction.
Step 1: Write out the chemical reaction, keeping careful track of the
exact molecules (e.g. H2O is very different from H2O2).
Step 2: Starting with the most complex molecules, count the amount
of each type of atom on each side of the equation. To make the
numbers balance, you can change the amount of any product or
reactant molecule by using coefficients.
Step 3: Continue using coefficients until all atoms balance.
Example: potassium oxide (KO2) + carbon dioxide (CO2) + water (H2O)
produces oxygen (O2) + potassium hydrogen carbonate (KHCO3)

Atomic Mass and the Periodic Table
Atoms exhibit periodicity of chemical properties when
arranged in order of their atomic mass. But three
elements were “missing” to make the periodicity fit.
BUT: 1) Very different elements had similar masses
2) three elements are (slightly) out of order
These elements were soon discovered and had the
predicted chemical characteristics
Some chemical properties: reactivity, behavior of ions,
ratios in combination with Hydrogen and Oxygen, etc.

An Early Draft of the Periodic Table
Mendeleev (from a dream): completed 1870

What is Energy?
“we have no knowledge of what energy is”
--Richard Feynman
Energy is not matter. But Energy interacts with matter.
Energy is the capacity to do work: to accelerate a mass
for some distance.
Example: Rolling a ball uphill (against gravity)
Example: Separating opposite electric charges

Forms of Energy
Energy is conserved, but different types of energy can
interchange. Matter that could be lower in energy than it
is has “Potential Energy.” (e.g. due to gravity)
Total energy is conserved: e.g. when potential energy
decreases, the energy has to go somewhere. One
common outcome is directed movement (kinetic energy).
Another is increased temperature due to random
movement (heat energy).
Matter that is in motion has “Kinetic Energy.” Many
particles in random motion have “Heat Energy.”

Work: Transfer of Energy Using Directed Motion
Work against a gravitational force
Work against an electromagnetic force
Pressure-Volume work
Some Types of Potential Energy
Gravitational potential energy
Electrostatic or magnetic potential energy
Chemical bond energy or energy of excited electrons
Energy of unstable (high energy) nuclei
force
X
distance

Energy and Gravity
Moving an object against gravity is a type of work (it uses energy).
We can do work using an object moving with gravity.

Energy is energy
calorie: measures energy required to heat an object
joule: measures energy required to lift a weight
calories and joules can be converted into each other
We usually measure the energy contained in food
and the energy we spend in exercise in calories
Joule’s
Experiment
(1845)
Newton: Energy = Work
Heat and Work and Energy

The First Law of Thermodynamics
One type of energy can be exchanged for another.
Energy is not created or destroyed.
The change in the Internal Energy of a system =
Heat added to the system - Work done by the system
Internal Energy is the sum of ALL the kinetic and
potential energy of the system

Heat and Work and Energy 2
Change in internal energy (∆E) = heat - work
If you add heat to a system, internal energy goes up.
If you use a system to do work, internal energy goes down.
If you allow heat to leave a system, internal energy goes down.
If you do work on a system, internal energy goes up.

What Is Heat?
When you bore holes in cannons, the iron grows very
hot. Model: heat is released when you rub iron filings
off because the heat is matter that is stored in the iron.
Test: If you rub the cannon with a tool that does not
remove iron, even more heat is released. Heat is not
matter! It is a form of motion! (Thompson, 1798)
Heat is energy that is transferred from bodies at a
higher temperature to bodies at a lower temperature.
When the energy is transferred, it can break chemical
bonds, increase the kinetic energy of molecule, etc.

What Is Temperature?
Temperature is a measure of the average kinetic energy of
the atoms in a substance per accessible mode of motion.
According the the Equipartition Theorem, there is a
simple relationship between the modes of kinetic energy.
Kinetic energy of molecules can be:
translational
rotational
vibrational

The Equipartition Theorem and Heat
Capacity
At thermal equilibrium, energy is shared equally among all
“allowable modes.” These are the different ways that a molecule
can vibrate, rotate, and translate as well as the ways that potential
energy can be stored in interactions.
Heat capacity is the amount of energy it takes to change the
temperature of an object by a set amount. Specific heat capacity
is the amount of energy it takes to change the temperature of 1
gram of a substance by 1 degree Celsius.
Different substances have different specific heat capacities
because they differ in their allowable modes of motion. The
materials that distribute their kinetic energy among more modes,
have less energy per mode and register a lower temperature.

Atoms
Lone atoms have no bonds to vibrate. Rotation cannot use
significant energy because almost all the mass is concentrated in
a tiny nucleus. So all kinetic energy for lone atoms is
translational unless the energy is really high.
Except at very high energy, all energy is kinetic. At high
energy, electrons can become excited, and some potential
energy is stored.
At any temperature above absolute zero, the kinetic energy of
the single atoms in an ideal gas is partitioned equally into the
only three allowable modes: translation along the X, Y, and Z
axes. At absolute zero, all motion ceases.

Diatomic Gases
Most diatomic gases begin to rotate at <100 K.
Diatomic molecules can rotate in two dimensions.
Diatomic gases start to vibrate at > 1000 K. Larger
gases can vibrate at much lower temperatures.
Different phases of matter have other permissible
modes because they store energy in intermolecular
interactions.

Energy Distribution
At T = 0, molecules have no kinetic energy.
At low temperatures, almost all molecules have
low energy
At higher temperatures, more and more molecules
Adding a small amount of
energy to a cold system
changes the energy more
than adding that amount
of energy to a hot system.
The distribution of energy follows simple equations.
Energy is normally distributed.

Kinetic Theory of Gases and Temperature
In fact, temperature is the measure of the kinetic energy
per mole: the average kinetic energy within the sample!
Temperature: high temperature increases the speed and
frequency of collisions.

Ideal Gas Law
PV = nRT
What do we mean by an ideal gas?
Why isn’t everything a gas?
What is a non-ideal gas?
What theory can explain this law?
What do the units of the ideal gas constant, R, tell us?
A liter of an ideal gas at a particular temperature and
pressure will contain a particular number of atoms. An
ideal gas can expand or contract to any extent.

Absolute Zero and the Phases of Matter
At absolute zero, a substance has zero kinetic energy.
At higher temperatures, molecules move around very
freely, with very high kinetic energies. They tend to be
gaseous.
At lower temperatures, molecules have very low kinetic
energies-- when their kinetic energies are too low to
overcome intermolecular attractions, the molecules
associate in an ordered pattern to become liquids or solid
crystals.

The Ideal Gas Equation: All About Energy
Pressure = force per area: mass X acceleration / area
So pressure is measured in (kg m /s2
)(1/m2
) = kg /(s2
m)
Volume is measured in m3
So PV is measured in kg m2
/s2
: the same units as for
force X distance: [(kg m/s2
) X m], which is energy.
Inflating a balloon takes energy.
If PV = nRT then nRT must also equal energy
n is measured in moles of an ideal gas.
T is measured in degree
R is a constant: the amount energy changes in a mole of an
ideal gas for each degree of temperature change

Working With The Gas Law
P1V1 = P2V2
T1 T2
If the number of moles of gas does not change in a
reaction, then:
For simplicity, we often try to hold one of these
variables constant (by using a container that cannot
expand, or by carrying reactions out at a set
temperature or a set pressure).

When Gases Expand, They Cool!
Compressed gas expands when it is released. As it
expands, it does work on the atmosphere. As a result, the
gas loses internal energy: it cools!
Similarly, as air rises, it expands due to low pressure. As it
expands, it cools. This is really important in weather.
The concept that contraction of gases causes them to heat
up is essential in understanding the “life cycle” of stars.
The concept that expansion causes cooling is essential in
understanding the “life cycle” of the universe after the big
bang.

Other Phenomena For Your Consideration
The pre-modern world was familiar with the following
phenomena, all of which were assumed to be independent:
•Static electricity (from the Greek word for amber)
•Magnetism (lodestones in ancient Greece and China)
•Lightning
•Light
•Chemical reactions

Particles
Until the turn of the 20th century, natural phenomena
were conceived of as either particles or waves
Particles behave much like everyday objects, though
they can be much, much smaller (e.g. atoms).
Particles:
have mass and velocity, so they have momentum.
exist at a particular place
can move through empty space
affect each other via collisions

Waves
Waves are delocalized: they exist over a range of places.
Waves interfere constructively and destructively.
Waves are not matter: they transmit energy through
matter. Ex. ocean waves, sound waves. They were
thought to require a medium to travel through.
Amplitude: Wave height-- correlates with energy
Wavelength: distance it takes a wave to repeat
Frequency: 1/ time is takes a wave to repeat
Speed: wavelength X Frequency

Ancient Theories of Light 1
In ancient India and ancient Greece (~500 BCE), light
was described as made of high velocity particles.
According to Aristotle, white light is“simple” or pure.
Many following Aristotle thought prisms mixed
“darkness” into the light; the different colors of the
refracted light were due to different amounts of
darkness (red has some darkness, blue has a lot…)

Medieval and Cartesian Theories of Light
~1000 CE, scientists in the Muslim world (Iraq, Iran,
Afghanistan…) defined light as particles of pure
energy. They began working out the velocity of light
in different substances.
Descartes (died 1650) described light as made up of
waves, which enabled him to explain refraction (the
bending of light attributed to change of speed of
wave when it moves through different media).

Newton’s Prism Experiments (1670)
White light is not “simple” as
Aristotle taught.
Light can be focused with a lens
and the various colors can be
mixed to produce white light
again.
Light can be refracted through a
prism into many different
colors. These colors are
“simple.”

Waves and Interference
Interference: The cumulative effect of waves depends on
their phase, amplitude, wavelength, and frequency,

Single Slit Diffraction
Diffraction: Waves can
expand around obstacles
of about the same size as
their wavelength
Different wavelengths
are diffracted to different
extents.

Waves vs Particles and 2-Slit Diffraction

Newton: Light is Made of Particles
1) Newton could explain and predict the reflection behavior of
light with his particle theory.
2) Waves need a medium-- light travels through empty space
3) Waves should bend around obstacles, but light was not
(yet) observed to do so.
4) Waves have interference patterns. Light not known to.
5) Newton thought he could explain refraction with his
particle theory, but his explanation was incorrect.
6) Newton explained diffractions as particles that somehow
made waves in the “ether.”

Huygens: Light is Made of Waves (1690)
1) Wave theory also explains reflection and refraction
2) Wave theory explains colors of light (based on
wavelengths)
3) Could particles really move as fast as light?
4) Nothing happens when light beams “collide”
5) Predictions of wave theory include interference

Diffraction occurs when waves
encounter openings of about the
same size as their wavelengths
The 2-Slit Experiment: Young, 1801

Young’s Result:
Light Diffracts!
By 1850, Newton’s
particle theory was
largely displaced by
the wave theory

Static Electricity and Induction
Ancient Greece 18th
Century: wool-rubbed amber
attracts small objects. The wool and amber will attract.
Pieces of rubbed amber will repel. The pieces of rubbed
wool will repel. “Triboelectric series” established.
1650: Allowing a spinning sulfer ball to rub against
your hand builds up a charge on the ball.
1745: Leydon Jar: glass jar coated on the inside and
outside with tin. A metal rod is pushed through the
stopper and this is connected by a chain to the inner foil.
Charge can flow from a charged object to the rod, and
opposite charges are stored in the outer and inner foils. Leyden jar

How Do We Know What Lightning Is?
In Ben Franklin’s kite experiment, lightning was used to
charge up an empty Leyden jar, demonstrating that
lightning was electricity.

Lightning and Electricity
Lightning manifests as a flash of light and a clap of thunder. (There
is also a very strong, very transient magnetic field).
We now know that the flash of light occurs because of a flow of
electric current from cloud to ground that heats the air until it glows!
The thunderclap is caused by the hot air rapidly expanding into slow-
moving cool air, causing a shockwave.
The cause of lighting: clouds build up negative charge close to the
ground and positive charge above. The mechanism for this is
controversial. The underside of the cloud induces a positive charge in
the surface of the Earth. The resulting electric field ionizes air in a
path leading from cloud to ground. The lightning is a discharge of
electrons along that path to balance the charge. Lightning can also
occur within clouds and between clouds.

Electrical Phenomena To Explain 1
Static Electricity (plus and minus charges)
Both the glass and the wool will attract neutral objects!
Attraction and repulsion: If you rub pieces of
glass with different bits of wool, the wool
will repel the other wool. The glass will
repel the other glass. The wool and the glass
will attract each other.

Electrical Phenomena To Explain 2
Volta (1800) showed that the source of the
electricity was the interaction of two
different electrodes. He made a pile of zinc
and copper electrodes in an acidic brine.
Current flowed from the zinc to protons in
the brine. Vitalism is wrong.
Current (1791): Galvani made an electric circuit
using two different metals and a frog’s leg! He
called this “animal electricity” At the time,
vitalism, the notion that living things required
their own physical laws, was in vogue.

Chemistry and Electricity
Electrolysis: If you melt Sodium Chloride crystals and
pass a current through the liquid salt, Sodium metal
forms at the cathode and Chlorine gas forms at the anode
This experiment provided important evidence that
electricity and chemistry are somehow linked.
The difference between the element, Sodium, and the
Sodium ions in salt is provided by some component of
electricity
1807

Magnetic Phenomena To Explain
Magnetic Dipoles
Magnets will attract certain non-
magnets. Strong magnets can even
induce certain materials to act as
magnets.
Every magnet has two poles (north and
south). These will align with the
magnetic field of the Earth. North poles
and south poles attract each other. North
repels north and south repels south.

Faraday: Forces and Fields
In some cases, we impart force through contact. In other cases,
forces are communicated by the exchange of particles through
space.
Physicists sometimes discuss “fields” that
appear to transmit force over a distance:
Masses via gravitational fields, magnets via
magnetic fields, etc.
Faraday (died 1867) used the concept of
fields to explain observations of magnetic
and electrical behavior: Electric charges
produce electric fields

More Interesting Parallels
Moving magnets generate electric current: This is
the principle behind dynamos
Moving electric charges (currents) generate magnetic
fields: This is the principle behind electromagnets
and electric motors

Currents or Changes in Electric Fields
Create Magnetic Fields
As charges move through a wire
(current), a magnetic field is
generated. More current creates
a stronger field.
Coiling a wire around a piece of
iron and running a current
through the wire can magnetize
the iron very strongly!
electromagnet

Electric Motor Illustration
If the battery wires
were switched, the
electromagnet
would spin 1/2 turn
(180°)
If you design an alternating current (AC) that
switches direction at the right rate, you can spin the
magnet to turn a blade on a lawnmower or a fan

Dynamos generate electric
power: They operate like electric
motors in reverse.
Mechanical energy spins a coil of
wires inside a permanent magnet.
This causes current to flow
through a wire. The current
constantly changes direction
(alternating current).
A Changing Magnetic Feld
Generates Electric Current

James Maxwell (1873) and Electromagnetism
Electric fields generate forces on charged objects:
F = Eq (force = field strength X charge on object)
Magnetic fields generate forces on charged objects in
motion:
F = Bqv (force = field strength X charge X velocity)
Maxwell followed up the work of Faraday and others,
synthesizing all that was known about electricity and
magnetism into four equations. These equations showed
that electricity and magnetism are really one phenomenon.

Maxwell and Electromagnetic Constants
If two electric charges of strength, q, are separated by a
distance, r, the charges will exert an electric force on
each other:
ε0 is a constant: it relates the amount of charge present
to the strength of the electric field it generates.
If two parallel wires are separated by distance, r, and each has a
current, I, running through it, the wires will exert magnetic
forces on each other:
µ0 is a constant: it relates the current flowing through
the wires to the strength of the magnetic field.

Maxwell and The Speed of Light
In manipulating his equations, Maxwell realized that they
described a wave (which he called an electromagnetic wave).
Maxwell calculated the speed of the wave as it propagates
through space to be a constant, c = 1 / ε0µ0
Scientists a generation earlier calculated the speed of light
fairly precisely using rotating mirrors that reflected light onto
stationary mirrors 20 miles away. Maxwell realized that the
“c” he calculated was very close to the speed of light measured
in experiments. He intuited that light must itself be an
electromagnetic wave and he predicted that light of many
different wavelengths (larger and smaller than visible light’s)
would exist and possess different energies.

The Electromagnetic Spectrum
Maxwell correctly predicted that electromagnetic radiation of
many wavelengths (smaller and larger than visible light)
would behave like visible light, but with different energies.
After that, almost no one doubted that light is a wave.

Electromagnetic Waves
Electromagnetic
radiation (e.g. visible
light) is generated by
mutually-reinforcing
oscillations in electric
and magnetic fields

Newton, Maxwell, and Relativity
Newton’s laws obey principle of relativity: observers
moving relative to each other will agree on the forces
that are acting around them.
Maxwell’s laws do not obey the principle of relativity:
magnetic and electric forces are typically perpendicular
to each other. Magnetic fields depend on the velocity
of moving charges.
Observers moving relative to each other should
disagree on the forces acting around them! Who is
right? Which is the “valid” frame of reference?

Speed of Light and “The Ether”
The success of Maxwell’s equations along with Young’s 2-
slit experiment led to the triumph of the wave theory of light.
But:
What is the medium through which EM waves propagate?
The magnetic and electric constants reveal “the” speed of
light. But for what frame of reference (whose point of view)?
Maxwell’s equations describe magnetic forces as differing
from electric forces because they depend on a charged
particle’s velocity; velocity from whose perspective?“The Ether” was posited as a potential answer…

Michelson-Morley Experiment (1887)
X and Y are reflective mirrors
in the center is a half-
transparent mirror.
Half the laser’s light goes to
X, half goes to Y. When the
light is reflected back to the
screen, you see an interference
pattern.
X
Y
Michelson and Morley were trying to find the velocity of the
ether relative to the earth. By rotating their experiment
relative to the earth and measuring at different seasons, they
hoped to find changes in the interference pattern that would
indicate the velocity. They found no change!

∆H
If you do not allow a system to do any work, then change in
energy = heat transferred. In a chemical reaction, work is
generally pressure-volume work (P∆V + V∆P).
If a chemical reaction releases heat, it is exothermic. ∆H is
negative. If it absorbs heat, it is endothermic. ∆H is
positive.
If the beginning of the chemical reaction has the same same
volume and pressure as the end, then work = 0. In that case,
you can measure the change in energy of the chemical
reaction just by measuring the heat exchange. The heat of
the reaction in this case is called the enthalpy, ∆H.

How Can A Reaction Release Heat?
How can a Reaction Absorb Heat?
In a chemical reaction, some bonds are broken and some
bonds are formed. Different types of chemical bonds store
different amounts of chemical potential energy.
If the total potential energy stored in bonds is lower in the
products of a reaction than in the reactants, heat is released.
We say in this case that ∆H < 0. The reaction is exothermic
(gives off heat).
If the total potential energy stored in the bonds is higher in
the products, the reaction absorbs heat from the
surroundings: it is endothermic.

Example
If the ∆H for A + B C = X joules/mole
and the ∆H for C D +E = Y joules/mole
then the ∆H for A + B D+E = X+Y joules/mole
You can use this method to calculate the energies of different
types of bonds (e.g. C-H bonds, C=O bonds)
CaO + CO2 CaCO3 ∆H = X
CaCO3 + H2O Ca(OH)2 + CO2 ∆H = Y
What is ∆H for CaO + H2O Ca(OH)2
∆H are additive:

Entropy
Entropy is a measure of disorder.
Entropy is higher for:
large molecules
gases
solutions
metallic bonds
Entropy is a measure of the likelihood of an arrangement of
molecules. For example, crystals are unlikely when other
states are achievable (i.e. at high energy).
As energy increases, molecules can be arranged in more states.

Information and Entropy
Shannon (a telephone company employee) : information is a function
of the number of possible alternatives for something. If we specify
that one of the alternatives is the right one, we’ve ruled out the
others, giving us information. For example, if I know you rolled a 3
on a die, that gives me an amount of information N=6, because there
had been 6 possibilities.
S (Shannon Information) = log2N.
When N = 2 (a binary decision), S = 1.
Boltzmann showed that S = k loge W: The information we lack is the
log of the number of alternatives in which a system can be arranged.
Entropy is missing information! The total amount of entropy can
only increase because we can’t learn information for free.

Entropy 2
Entropy is the amount of information needed to exactly
specify the state of a system. A more ordered system can be
specified with relatively little information and has low
entropy. A less ordered system requires more information to
specify it and has high entropy.
Entropy, S, is mathematically related to the number of
different states in which the system can possibly be without
changing the energy: this value is “W:”
S = K logeW (K is a constant).
At high entropy, the components of a system are equally likely
to be found in many different states. At low entropy, the
components are much more likely to be in just a few states.

Entropy Examples
Pages of a telephone book
Molecules in a crystal
Molecules in a gas

The Second Law of Thermodynamics
Transforming one form of energy to another is not
perfectly efficient (unless you are converting to heat)
If you try to convert any form of energy to work, some of
the energy is”lost.” This energy heats the universe and
increases the disorder of the universe.
The entropy of the universe can never decrease!
∆S > 0 for a closed system

Spontaneity of Reactions
Intrinsically, a reversible reaction can go in both directions:
A B or B A
We can write this as A B
Under a given set of conditions, a reaction may be more likely
to go in one direction than the other. This is the “spontaneous”
reaction. It may be fast or slow, but this is what will happen if
no energy is put into the system and if no other conditions
change.
Interestingly, a reaction can be spontaneous even if it generates
products with higher potential energy stored in their chemical
bonds (i.e. endothermic reactions can be spontaneous).

Equilibrium
In a spontaneous reaction, the reactions happen
more frequently in one direction than in the other.
A B
At equilibrium, A B is exactly as frequent as B A
The proportions of A and B at equilibrium depend on
experimental conditions (e.g. pressure, temperature)
At equilibrium, the system has no capacity for overall
change. e.g. it cannot be used to do work.
All systems tend toward equilibrium.

“Favorable” Reactions
The spontaneous or “favorable” reaction is the one
that increases the entropy of the entire universe.
There are two main components to the entropy of the
universe: the disorder of the the chemicals undergoing
the chemical reaction (the system) and the disorder of
everything else. The disorder of the system = S.
In many cases, order can be created in a chemical
reaction, but only at the expense of even more disorder
being created elsewhere.

Free Energy and ∆G
Τhe Gibbs Free Energy, ∆G, of a reaction is the determinant
of whether a reaction will be “spontaneous.”
In other words, ∆G measures the change in entropy of the
entire universe (system and everything else)!
∆G also measures how much work a reaction can do!
If ∆G is negative, a reaction is spontaneous
If ∆G is positive, the reverse of the reaction is
spontaneous
If ∆G = 0 then the reaction is at equilibrium
∆G = ∆H -T∆S

More on ∆G
∆G0
is the Gibbs free energy at standard temperature and
pressure when reactants and products are 1 mole/liter. This is
important because under different conditions, reactions may have
a tendency to proceed in different directions.
Exothermic reactions release heat into the universe, increasing
entropy outside the system; more exothermic reactions (∆H
more negative) have a greater tendency to be spontaneous.
Reactions in which ∆S increases also have a tendency to be
spontaneous (because the system is part of the universe too).
If ∆S is high enough, even endothermic reactions can be
spontaneous.

Comparing ∆G and ∆G0
A B
If A and B are in equilibrium, and you add more B or
remove some A, what would happen? Explain.
If A and B are in equilibrium and B is a gas and A is a
solid, what would happen if you increased the
temperature? Explain?

Le Chatelier’s Principle
If you “stress” a system at equilibrium, the equilibrium
shifts to accomadate the stress.
Adding more heat favors endothermy
Adding more pressure favors solids over gases
Adding more products favors reactants
We can take advantage of this to “drive reactions”
--if you can constantly remove products as they form, you
will never reach equilibrium. Many biological processes
work this way.

Life and Spontaneity
All living things grow, repair damage, and reproduce.
These processes all reduce the disorder of the organism: how
can these chemical reactions go forward?
The spontaneity of a reaction relies on increasing entropy in
the universe, not just in a part of the universe. In spontaneous
reactions that decrease entropy locally, Heat is produced. This
increases the disorder of the universe because it increases the
random motion of particles. (Bonds break, gases expand, etc).
In addition, the sun provides energy (directly or indirectly) for
most biochemistry. Sunlight is emitted in a process that
increases the entropy of the sun.

Cathode Ray Tubes
(Discovery of Electrons: 1854-1876)
A cathode ray tube is a glass container holding gas at very
low pressure (near vacuum) with an electric current running
into wires at either end
The tube glows when the current is running, and light appears
to move in straight lines from the cathode: you can detect
fluorescence where the ray hit the glass
If you put a paddle wheel in the tube, the wheel will spin.
If you put an object in the tube, it will cast a shadow.
Objects in the ray’s path become
negatively charged. Cathode
(-)

Illustration
-
cathode
+
anode
pressure valve
Cathode ray
*
*
. . . . . .
In magnetic field or electric field: For a given strength
field, the radius of
curvature of the
electron will be
proportional to its
charge/momentum.

Mass and Charge of electron: 1
Set up a cathode ray tube in opposing electric and magnetic
field. Adjust the strengths of the fields so that electrons travel
in straight lines: Fm = Fe
Eq = Bqv so velocity of electrons (v) = E/B
Electric force (Fe) = strength of the electric field (E) X the
charge of the electron (q) Fe = Eq
Scientists used cathode ray tubes to determine q/m (the charge
to mass ratio) of the electron! They exploited the relationship
between the forces the electron would experience in magnetic
and electric fields (from Maxwell’s equations):
Magnetic force (Fm) = strength of the magnetic field (B) X
charge of electron (q) X velocity of the electron (v) Fm = Bqv

Mass and Charge of electron 2
Now that we know the velocity of the electrons as the they
leave the emitter, note the voltage of the electric field and
leave it unchanged. Turn off magnetic field to measure
deflection caused by electric field.
A simple formula taking into account the voltage and shape of
the tube and electric plates generating the field gives a result
for q/m (charge per mass) of the electron proportional to tanθ
(the angle of deflection).
V = voltage
v = velocity from first
calculation
d and h relate to the
geometry of the setup.
tanθ = q Vd
m hv2

Mass and Charge of Electron 3 (1913)
Oil droplets were given electric charge (they were collided
with ions). An electric field of known strength was used to
counteract the gravity pulling the oil droplets down (electric
force and gravitational forces were equal and opposite).
Since strength of gravity on the droplets was known, this
allowed calculation of charge. Once charge was known,
knowing q/m permitted calculation of mass of electron.
9.10938188 × 10-31
kilograms

The Triumphs of Pre-Quantum Physics
Complete description of the mechanical and gravitational laws
Complete description of laws regulating energy transfers
Unification of electricity and chemical behavior
Unification of magnetism and electricity into electromagnetism
Unification of electromagnetism and optics

The End of Physics
The most important fundamental laws and facts of physical
science have all been discovered… Our future discoveries
must be looked for in the sixth place of decimals
--Albert Michelson, 1894
"There is nothing new to be discovered in physics now. All
that remains is more and more precise measurement.”
--Lord Kelvin, 1900

Some Flies in the Ointment
How does radioactivity (Nuclear Fission) work?
What are atoms made of?
Why does chemistry work the way it does?
How does black body radiation work?
What explains absorption and emission spectra?
Is light a wave or a particle?
How does the sun radiate so much energy?
Why do Maxwell’s laws disobey principle of relativity?
Why do accelerating bodies disobey principle of relativity?

Radioactivity
alpha radiation: deflected with electric and magnetic fields and
found to have mass = 4 amu (~ 4 protons), charge = +2
gamma radiation: very high frequency
EM radiation similar to X-rays
Radioactive elements are very hot and “radiate” energy (Marie and
Pierre Cure, Henri Bequerel 1896-1898). There are three principal
types of radiation:
beta radiation: later found to be the same
as cathode rays-- mass ~1/1800 proton
mass, charge = -1
The radiation is not due to a chemical
change. The amount of energy released per
second depends on the mass of the material.

Half Lives
A particular fraction of radioactive material will undergo
fission in a particular amount of time. In one “half-life” half
the remaining material will undergo fission.
Marie Curie
(Died 1934)

Nuclear Fission
Nuclear Fission is the process by which a radioactive
isotope breaks down into lighter isotopes.
238
U Decay

Properties of α Particles
alpha
emitter
α particles bend in electric field in the
opposite direction from electrons
the α particles are deflected less than electrons--
the charge:mass ratio is much lower than it is for
electrons.
α particles can be stopped by a very thin sheet of
aluminum. β radiation (electrons) and γ radiation
(high energy EM radiation) cannot.

Rutherford and the Nucleus (1909-1911)
Gold foil: 20,000 atoms
thick (almost transparent)
The atoms are almost entirely empty space.

Atomic Nuclei
The protons were shown to have mass = 1 amu and
charge = +1. This is the same as the H nucleus.
Rutherford bombarded nitrogen with alpha particles and
isolated protons (he named them) and oxygen
14
N + 4
He 17
O + 1
H

There Must Be More Than Protons and Electrons
Atoms are much more massive than would be
predicted from the sum of protons and electrons.
Atomic nuclei have a “spin” (related to angular
momentum) that affects magnetic fields. Electrons
also have spin. The total spin of atoms ≠ spin of
electrons plus protons. Observation and theory
suggested spin should be conserved; where was the
missing spin?
Rutherford first thought of neutral particles
(“neutrons”as electrons orbiting protons within the
nucleus (1920). This was incorrect.

Discovering Isotopes
Isotopes were originally identified in cathode ray tubes:
the cathode rays would knock electrons off of atoms in the
low-pressure gas; the positive ions would then move
toward the cathode. They moved comparatively slowly,
because they all had a +1 charge, but were much more
massive than electrons: q/m ratio was low.
Even when the gas was made of a pure element, several
different velocities of ion resulted! Not all atoms of a
given element have the same mass!
Now we can isolate isotopes with a mass spectrometer.

Discovery of the Neutron
(Chadwick, Joliet-Curie)
1930: When Be is bombarded with alpha particles, it emits
radiation that is not deflected by magnetic or electric fields. These
“neutrons” could eject protons from wax in a manner that
suggested the particles had approximately the same mass as
protons (1932).
alpha particle = 2 protons + 2 neutrons. This is a He nucleus.
Atoms with the same number of protons belong to the same element
and have the same chemical properties. These atoms atoms will
have different masses if their number of neutrons differ. These
atoms with similar chemical properties but different masses are
called “isotopes.” Not all isotopes are equally stable.
Joliet-Curie (1934): 27
Al + alpha particles  30
P + 1
n.

The Atom Before Quantum Mechanics
Protons and Neutrons in the nucleus (positive charge)
Electrons are negative particles that orbit the nucleus
Electrons further from the nucleus have a higher energy

Atoms
Atoms are very tiny. One molecule of water contains three atoms. In one drop of water (0.05
ml), there are approximately 5,100,000,000,000,000,000,000 atoms.
One molecule of table sugar contains 45 atoms. In one sugar cube, there are approximately
315,000,000,000,000,000,000,000 atoms.
The nucleus of an atom is positively charged. It has almost all of the mass of the atom, but it
is much much tinier than the whole atom. If Lowenstein were the size of an atom, the nucleus
would be about the size of a grain of rice.
The rest of the atom is made up of negatively charged, very light, fast moving electrons.
When we refer to the size of the whole atom, we take into account that the fast moving,
negative electrons from one atom can only get so close to those of another before they repel
each other.
In a neutral atom, the charges in the nucleus balance out the charge of the electrons, so there is
no net electrical charge.

Mass Spectrometry and Isotopes

Nuclear Fission Chain Reactions
A critical mass of 235
U can cause
a chain reaction of rapid nuclear
decay. This is what occurs in an
atomic bomb explosion.
420,000 times more energy is
released in the fission of a gram of
uranium than in the combustion of
a gram of gasoline!
But why are some nuclei stable and other nuclei are unstable???
Why does radiation consist of alpha particles, beta particles, and
gamma radiation?

Nuclear Fusion
Nuclear fusion also relies on the conversion of mass to
energy. The Hydrogen Bomb relies on the reaction:
2
H + 2
H 4
He2+
This reaction relies on the strong force. It is highly favorable
but requires high heat and pressure to overcome the electric
repulsion of the deuterium nuclei.
The sun relies on fusion as well, but it uses ordinary
Hydrogen (1
H) and converts some protons to neutrons with the
weak force. This limits the rate of reaction.
There is enough deuterium in a liter of water (1/7000
hydrogens) to get the energy equivalent of burning 300 liters
of gasoline.

Fusion
in the
sun
There is ten-fold more energy released in fusion of a
gram of hydrogen than in fission of a gram of uranium.

Fusion Reactors
2
H + 2
H 3
He +1
n
and (both happen equally)
2
H + 2
H 3
H +1
p
In the second case:
3
H + 2
H 4
He + 1
n
Overall reaction:
5 2
H 3
He + 4
He + 1
p + 2 1
n
If we carried out nuclear fusion on all the 2
H in the oceans, we
would get as much energy as burning gasoline = to 450 times the
volume of the earth!

Relativity and Maxwell
Newton’s laws obey principle of relativity: observers
moving relative to each other will agree on the forces
that are acting around them.
Maxwell’s laws do not obey the principle of relativity:
magnetic and electric forces do not have to operate in
the same direction.
For example: magnetic force depends on the velocity of
the charged particle, but relative to what?
Electric force does not depend on velocity; what if you
are moving relative to an electric field?
In what reference frame does the “speed of light” = c?

Special Relativity (Einstein
1905)
Spacetime (to any observer at any constant velocity) is not
relative! Different observers perceive space and time
differently, but they all agree on “spacetime.”
Speed of light in a vacuum is constant-- all observers
measure the same speed of light regardless of their relative
velocities! This is why Maxwell’s equations Laws of physics
also independent of velocity of observer!
For the speed of light to be constant, other parameters must
be relative: distance is relative (contracts at high speed); time
is relative (slows at high speed), mass is relative (increases at
high speed)

Movement in Spacetime!
We are all moving through spacetime at the speed of light!
Most objects we encounter are moving slowly relative to
us: we perceive them as moving mostly along the time
axis (they age fast and go from place to place slowly).
Some objects move very rapidly relative to us in space.
We perceive them as aging slowly. Photons move
entirely along the space axis and do not “experience”
time at all.

Disagreeing on Timing
Scenario: A train car is speeding through a station.
One person is inside the train car. Another is on the
platform. A light goes off in the center of the train car.
When does the light reach the front and back of the car?
The observer in the train says: it reaches both ends at
the same time.
The observer on the platform says: the back end is
reached first (because it is moving toward the light
source).

Illustration
Observer on train Observer on platform

Illustration 2
Observer on train Observer on platform

X
distance
time
Showing Motion With Relativity
To graph motion through spacetime, we need to use one
dimension for time. In a two dimensional graph, we only
depict movement in one space dimension. In a three
dimensional graph, we can depict movement in two space
dimensions.

An observer is at A, at the nexus of the
cones. The borders of the cones
represent objects traveling at the speed
of light Any point is an event in space
and time.
B lies within the “future” cone: all
observers anywhere, traveling at any
velocity. will agree that A occurs before
B. At least some objects could travel
from A to B so A can influence B.Spacetime
C lies outside the cone in the “extended present.” The greater the
distance from the observer, the longer the duration of the extended
present. According to some frames of reference, A and C occur
simultaneously. Nothing can travel from A to C (there isn’t
enough time to move through that much space), so A cannot

Einstein: Maxwell is Relative!
Observers moving relative to each other will not disagree
on the outcomes of the forces acting on them, though
they may credit electric and magnetic forces differently.
If an observer is not moving relative to a charge, only an
electric force is observed. If an observer is moving
relative to a charge, electric and magnetic forces are
observed.
Observers moving at different velocities will predict the
same final result, though they will attribute that result to
different contributions of magnetic and electric forces

Energy and Mass: E = mc2
(Einstein 1905)
The energy of a system contributes to the mass we
observe it to have! Faster objects, hotter objects,
interacting electrical charges, all have more energy and
so are more massive! They attract other masses more
strongly and they have more inertia.
Mass and energy can be
interconverted!
velocity
mass

Problem With The Classical Approach
Why are there discrete frequencies in absorption and
emission spectra?
Classical physics would predict that EM energy can be
absorbed or emitted at any frequency.
As an orbiting electron moves in a circle, it should produce
changing electric and magnetic fields. It should continuously
emit electromagnetic radiation and spiral into the nucleus!
emit electromagnetic radiation.

But certain frequencies are missing from sunlight
refracted through a prism!
If you look at star light from outer space, different
frequencies are missing depending on the star!
If you refract light through
a prism, you get a rainbow
Absorption Spectra

Emission Spectra
If you heat a a gas at low pressure, and look through a
spectroscope, you see that the color of the gas is made up
of very discrete frequencies! These frequencies are
different for different gases.

Black Body Radiation
A “black body” is an object that can absorb and emit
all frequencies of electromagnetic radiation.
If you heat a black body, it
emits EM energy in a pattern
dependent on its temperature:
Each temperature has a
characteristic color.
Higher temperature objects
radiate more energy of all
frequencies, but especially
more at higher frequencies.

Problem With The Classical Approach:
Black Bodies
According to classical theory, a black body, which emits and absorbs
light of all frequencies, should radiate energy mostly at high
frequency (low wavelength) because:
According to the equipartition theorem,
most of the possible modes of vibration are
at high frequency, so most of the energy
should be there, too.
This discrepancy between what is predicted
and what we observe is called:
“The Ultraviolet Catastrophe.”
According to Classical EM theory: the number of modes of vibration
at any frequency should be proportional to the frequency squared.

The Photoelectric Effect:
Light is Made of Particles
If you shine a light on a metal, it will emit rays
These rays are similar to cathode rays: same charge: mass
For some metals, any visible light will do this, for others,
blue is sufficient, but red is not. For others, you need
ultraviolet or X-rays.
More intense light increases the intensity of the cathode
rays, but the frequency of the light determines whether
you get rays and how fast they move.

Problem With The Classical Approach
The number of electrons emitted by the photoelectric effect
depends only on the intensity of light!
This can only make sense if light is made of particles whose
energy depends on their frequency!??!!?!
Intense light has more energy.
High frequency light also has more energy.
The energy of the emitted electrons (or whether they are emitted
at all) depends only on the wavelength (or frequency) of the light
used!
A light’s intensity α number of photons.
A light’s energy per photon α frequency of light.
(Einstein 1905)

More 2-Slit Experiments with Light
(particles or waves?)
source
A
B
detector
If the slits are narrow enough,
light travels by both paths
(wave behavior).
The light detector clicks in response to light. Dimmer
light makes fewer clicks, but each click is just as loud
(particle behavior)!
If you close B, ~1% of the light emitted by the source
reaches the detector. If you close A, ~1% of the light
will reach the detector.

Even More 2-Slit Experiments With Light
source
If you put special detectors at A and B and use a very
dim light, light is only ever detected at A or B, not both.
But if you do this, 2% of the light will always reach the
final detector (no interference)!
You can put “inefficient” detectors at A and B that only
A
B
detector

Philosophy of Science
I'm going to describe to you how Nature is - and if
you don't like it, that's going to get in the way of
your understanding it… [Scientists] learned to
realize that whether they like a theory or they
don't like a theory is not the essential question.
Rather, it is whether or not the theory gives
predictions that agree with experiment…
[Quantum mechanics] describes Nature as absurd
from the point of view of common sense. And it
agrees fully with experiment. So I hope you can
accept Nature as She is - absurd... Please don't
turn yourself off because you can't believe Nature

New Concepts in Quantum Mechanics
•Energy is quantized
•Light is only partly described as wave or particle
•Matter is only partly described as wave or particle
•Particle behavior can only be described in terms of
probability; behavior of single particles is unpredictable
(the clockwork universe concept is dead!)
•Certain pairs of information about a particle cannot be
precisely known at the same time.

Energy is Quantized (Planck, 1900)
Therefore the electron of a hydrogen atom does not slowly emit
EM radiation and spiral to the nucleus-- it simply cannot
continuously emit energy. It only emits or absorbs energy in
bursts.
The ultraviolet catastrophe is avoided because the energy
contained in one quantum of high frequency light is much
higher than the energy in one quantum of low frequency light.
This amount of energy will accumulate less frequently (usually
released first as low energy light).
Posited:Nature is discontinuous (quantized): energy occurs in
discrete packets with a minimum size (quanta).

Equal Partition and Cold Temperatures
At high temperatures, the equal partition theory works well, but at
cold temperatures it breaks down.
This is because at low energy, it is very
inaccurate to assume that all energy
levels form a smooth continuum, which
is an assumption built in to the equal
partition theorem.
That Planck’s theory that energy is quantized not only eliminates
the problem of the ultraviolet catastrophe, it also explains low-
temperature behavior.

Matter Waves
Light is both a particle and a wave, though we cannot perceive
both characters at the same time. Matter likewise has wave and
particle properties! Wavelength is inversely proportional to mass!
Electrons are small enough to have a
significant wave character. A “free”
electron has a wavelength = h/mv.
(inversely proportional to
momentum).
The wave character of the electron
helps to explain much of chemistry.
2-slit experiment with e-

More on the Particle and Waves
All particles (photons, e-, …) can be described as waves.
For photons, energy, frequency, and wavelength are all interrelated.
c = wavelength X frequency. Energy α frequency. Very high
energy photons have small wavelengths, so they interact with a
smaller region of space. In this sense, they are more localized.
For massive particles (e.g. electrons) the wavelength is inversely
proportional to the particle’s momentum. More massive and faster
moving particles have smaller wavelengths. Consequently, they are
more localized (behave more like particles).
Atomic nuclei are large enough that they are very localized. Their
wavelength is usually not significant enough to bother treating them
as waves at all. Electrons are small enough to have a significant
wave character.

Heisenberg Uncertainty Principle
Position and Momentum
Energy and Time
Strength of a field and Rate of change of field strength
The product of our uncertainty in our knowledge of
each member of these pairs is equal to a constant, h.
Certain pairs of data cannot be known to arbitrary precision at
the same time.
This is not a technical problem. Quantum “jitters” fuzz out the
answers to one member of a pair when you lock in the value for
the other!

Example: Position and Momentum
A wave’s momentum is proportional
to its frequency and inversely
proportional to its wavelength.
A single wave spreads uniformly
through space. As you add more
waves with different wavelengths
(momentums) the wave is localized.
If you are adding waves that are
more restricted in wavelength
(better resolution of momentum),
there is less localization

Borrowed Energy and Tunneling
Because a particle’s position is uncertain, there is a
non-zero probability that the particle could be
observed on the “other side” of an energy barrier
that, classically, it does not have enough energy to
overcome.

Conventional and Electron Microscopes
Conventional Light Microscopy cannot resolve objects
closer together than the wavelength of visible light (several
thousand atoms).
Electron Microscopy has greater resolution due to tiny
wavelength of electrons.
Transmission: electrons penetrate thin slices. “Electron
dense” regions appear black. The great resolution of the
microscope is determined by the electron’s wavelength!
Scanning-tunneling: relies on detecting changes in the
strength of electric current between a 1-atom diameter needle and
the electrons on the surface of an object. Electrons actually tunnel
between the needle and the surface!

More on the Quantum World
All particles (photons, e-, etc) can be described as waves,
though we cannot perceive both wave and particle character at
the same time. The wavelength is inversely proportional to
momentum. More massive and fast moving particles have
small wavelengths, so they are more localized and behave
more like particles.
For photons, c = wavelength X frequency.
Energy α frequency. Very high energy photons
have small wavelengths, so they interact with a
smaller region of space. In this sense, they are
more localized.

Diffraction and Resolution by Light
Diffraction from nearby sources of light can create
overlapping patterns. When the two primary maxima overlap,
it is impossible to distinguish the two sources. This is the
resolution limit.
Increasing the wavelength of light increases the resolving
power. This is why visible light microscopes are limited in
what they can resolve regardless of how much magnification
you use.

Diffraction and Resolution by Light
Resolving two points that are:
Far apart
Near Rayleigh Limit
Closer than Rayleigh Limit
For visible light, maximum resolution
under a microscope ~200 nm.

More on the Particle and Waves
Atomic nuclei are large enough that they are very localized. Their
wavelength is usually not significant enough to bother treating them
as waves at all. Electrons are small enough to have a significant
wave character.
Bohr postulated that the electron CANNOT be in the nucleus. We
now know that if an electron’s location were restricted to a location
as small as the nucleus, it’s momentum would be extremely
uncertain and its energy would be enormous.
An e- can possess many different discrete energies that place it
different average distances from the nucleus with different angular
momenta. Electrons in an atom are associated with standing waves
that cannot destructively interfere. The smallest energy (longest
wavelength) permitted is outside the nucleus!

The Schroedinger Equation Gives a
Complete Description of an e-
-h2
8π2
m
d2
dx2
ψ(x) + V(x) ψ(x) = Eψ(x)
Kinetic energy Potential energy Total energy
Physicists use Shroedinger’s equation to solve for the function,
ψ. We can use ψ to tell us everything about a particle (it’s energy, its
velocity, the likelihood it is in a location).
Outside of an atom, an electron is “free.” In this case, the electron’s
energy = its kinetic energy and is simply a function of the electron’s
wavelength.
An electron interacting with other electrons or the nucleus of an atom
can have a very complex potential energy function [V(x)]

The e- in an Atom
When the function, ψ, is very complex. Shroedinger’s equation
has very few solutions because most functions would be
internally inconsistent: they “destructively interfere” with
themselves. The electron’s wavefunction is like a standing wave
that can only take on certain energies (certain wavelengths)!
Wavelength, energy, probability of being in a certain position, etc
are all determined by ψ. In an atom, certain values are permitted,
others are forbidden.
For example, The probability of an e- being in a certain place is a
function of ψ2
. The e- cannot be at a node, though it can be on
either side of a node.

Orbitals
When you solve the Shroedinger equation for the electron
in a hydrogen atom, you find that it can exist in only a few
physical states that occur at discrete (quantized) energies.
ψ2
gives the probability of finding the electron in a location
for a particular solution of the Shroedinger equation.
These 3 dimensional “locations” of the electron are called
“orbitals” and the electrons can be described completely by
the quantum numbers N, l, m, s.
The equation has been solved exactly only for hydrogen!

Absorption and Emission Spectra Explained

Absorption and Emission Spectra Explained 2
(UV)
(visible)
(infra-red)

N, l, m
Each spectral line corresponds to the energy jump
between orbitals (different energy states of the electrons)
Preliminary observation shows that electrons can “jump”
between “shells” that were each assigned a number, N
Many of these emission lines contain several closely
spaced lines. These lines corresponded to sub-divisions
within each “N” that are assigned the identity, “l”
In a magnetic field, these closely spaced lines resolve
into sets of lines defined by the magnetic quantum
number “m”

l, m continued
l values determine the shape of the wave function:
the 3D space that is likely to contain the electrons.
l values range from 0 to N-1
1st “shell” N=1. l = 0; there is 1 shape of orbital
2nd shell N= 2. l = 0 or 1; 2 shapes of orbitals…
m values determine the orientation of the orbital in 3D
m values range from - l to + l
if l =0, there is one orientation (m = 0)
if l =1 there are three orientations (m = -1, 0, +1)
if l =2 there are 5 orientations etc. (m = -2, -1, 0, +1, +2)

“Atomic orbitals” are 3 dimensional depictions of the
shape of the wave function for different energies
Atomic Orbitals
s orbitals have l = 0. m = 0; only one way to orient the
orbital in space. This is the lowest allowable energy state
for an electron in any given N.

f orbitals
p, d, and f Atomic Orbitals!
l = 1
l = 2 l = 3

Quantum Numbers and Orbital Characteristics
Potential energy is related
to the first quantum
number, N.
EN = E1/N2
Angular momentum, L, is
related to the second
quantum number, l:
L2
ψ = h2
(l(l+1) ψ
Orbitals in Scandium

Pauli Exclusion Principle And Filling Orbitals
Each set of quantum numbers: n, m, l, s describes at most
one electron per atom
Only two electrons can “occupy” each orbital: one with
s = 1/2 and one with s = -1/2
When you assign electrons to orbitals, electrons are placed in
the lowest available N and the lowest available l.
Electrons only share an m orbital if the next lowest orbital is
in a new l.

Explaining The Periodic Table
1s
2s 2p
3s 3p 3d
4s 4p 4d 4f
5s 5p 5d 5f

Magnetic Materials
Atoms with unpaired electrons respond
to magnetic fields.
Some substances can crystallize so that
their electrons spins are aligned to give
them permanent magnetic properties.
If these objects are heated, the
atoms in the crystal re-align
randomly so that they can still
respond to magnetic fields but
they have no permanent
magnetic properties.

Jm honors pt 1 this one missing you

Recommended

Recommended

More Related Content

What's hot

What's hot (18)

Similar to Jm honors pt 1 this one missing you

Similar to Jm honors pt 1 this one missing you (20)

More from Dr Robert Craig PhD

More from Dr Robert Craig PhD (20)

Recently uploaded

Recently uploaded (20)

Jm honors pt 1 this one missing you