Transcript CHAPTER 1: The Birth of Modern Physics

Physics 334
Modern Physics
Credits: Material for this PowerPoint was adopted from Rick Trebino’s lectures from Georgia Tech which were based on
the textbook “Modern Physics” by Thornton and Rex. Many of the images have been used also from “Modern Physics” by
Tipler and Llewellyn, others from a variety of sources (PowerPoint clip art, Wikipedia encyclopedia etc), and contributions
are noted wherever possible in the PowerPoint file. The PDF handouts are intended for my Modern Physics class, as a
study aid only.
Class Overview and Chapter 1
The Birth of Modern Physics
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Discovery of Atoms
Classical Physics
Classical Electromagnetism
Thermodynamics
Particles and Waves
Nature of Light
Unsolved Problems in 19th Centaury
Discovery of Electron
Discovery of Nucleus
Mass and Binding Energy
Atoms of the Twentieth Centaury
Birth of Modern Physics
Atoms
“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.”
—Richard Feynman
The Atomic
Theory of Matter
Initiated by Democritus and Leucippus
(~450 B.C.), who were the first to
use the Greek atomos, meaning
“indivisible.”
Proust (1754 – 1826) proposed the Law of definite proportions
(combining of chemicals always occurred with the same
proportions by weight).
Dalton advanced the atomic theory to explain the law of definite
proportions.
Avogadro proposed that all gases at the same temperature, pressure,
and volume contain the same number of molecules (atoms):
6.02 × 1023 atoms.
Cannizzaro (1826 – 1910) made the distinction between atoms and
molecules advancing the ideas of Avogadro.
The Atomic Mass
Law of Multiple Proportions: Elements can combine in different
ways to form different substances, whose mass ratios are
small whole-numbers multiples of each other. (John Dalton,
1804)
CO2 has 32g of O and 12g of C 32 2


CO has 16g of O and 12g of C 16 1
This way each element was assigned an atomic mass number A
Molecule has more than one atom bound together. Molecular
mass number is the sum of atomic mass number of the atoms
that makeup the molecule.
The Periodic Table
First Classification of the
elements
Dimitri Mendeleev (1869)
What distinguished Mendeleev was not only genius, but a passion for the elements.
They became his personal friends; he knew every quirk and detail of their behavior.
- J. Bronowski
Periodic Table of the Elements
Periodic Table of the Elements
Periodic table
a chart (chemist’s road map) of elements arranged
by atomic number
classified by the number of protons in the nucleus
arranged from left to right
each having one more proton and electron than the
preceding element
on the far right, outer shells are filled to capacity, known
as noble gases
Brownian Motion
In 1827, Robert Brown, a botanist, observed
collisions between visible particles and invisible
atoms (Brownian motion)—later confirmed by
Einstein as evidence for the existence of atoms.
Avagadro’s Number
How many atoms there are in A (atomic mass) grams of any
element?
This is called the Avagadro’s Number NA
N A  6.02 1023
1g of H, 12g of C and 238g of U all contain the same number of
atoms.
The amount of matter that contains the Avagadro’s number of
atom is known as a mole
Example: Use Avagadro’s number to find
the mass and size of the Hydrogen atom
For H: A  1, N A  6.02  10 , Density of liquid H=71 kg/m
23
3
3
A
10 kg
27
mH 

 1.7  10 kg
23
N A 6.02  10
3
M
M 1  10 kg
Using  =  V  
V


V 1  103 kg
29 -3
Volume of One atom is Vatom 

 2.3  10 m
NA
NA
13
 d H  Vatom
 3  1010 m  0.3nm
Classical Physics of the 1890s
Mechanics →
Electromagnetism →
← Thermodynamics
Mechanics began with Galileo (1564-1642)
The first great experimentalist: he established experimental
foundations.
He described the Principle of Inertia.
Mechanics achieved maturity
with Isaac Newton
Three laws describing the relationship
between mass and acceleration.
Newton’s first law (Law of inertia):
An object with a constant velocity will
continue in motion unless acted upon
by some net external force.
Isaac
Newton
(16421727)
Newton’s second law: Introduces force
(F) as responsible for the change in
linear momentum (p = mv):
Newton’s third law (Law of action and
reaction): The force exerted by body 1 on body
2 is equal in magnitude and opposite in direction
to the force that body 2 exerts on body 1:
Classical Electromagnetism
Coulomb’s Law
Force on a static charge
kq1q2 ˆ
F  2 ir
r
Lorentz Force
F=q (E+v  B)
Force on a moving charge
Superposition Principle F=q(Enet +v  Bnet )
Vector sum of electric and magnetic fields
Electromagnetism culminated
with Maxwell’s Equations
Gauss’s law:
(electric field)
Gauss’s law:
(magnetic field)
  E  q / 0
B  0
Faraday’s law:
B
 E  
t
Ampère’s law:
E
  B  0 0
t
James Clerk Maxwell
(1831-1879)
in the presence of
only stationary
charges.
Particles and Waves
Two ways in which energy is transported:
Point mass interaction:
transfers of momentum
and kinetic energy:
particles.
Extended regions wherein
energy is transferred by
vibrations and rotations:
waves.
The Nature of Light
Newton promoted the corpuscular
(particle) theory
Particles of light travel in straight
lines or rays
Explained sharp shadows
Explained reflection and refraction
Newton in action
"I procured me a triangular glass prism to
try therewith the celebrated phenomena of
colours." (Newton, 1665)
The Nature of Light
Huygens promoted the wave theory.
He realized that light propagates as
a wave from the point of origin.
He realized that light slowed down
on entering dense media.
Christiaan Huygens
(1629-1695)
He explained polarization,
reflection, refraction, and double
refraction.
Double refraction
Diffraction confirmed light to be a wave.
While scientists of Newton’s time
thought shadows were sharp, Young’s
two-slit experiment could only be
explained by light behaving as a wave.
Fresnel developed an accurate theory
of diffraction in the early 19th century.
Diffraction patterns
One slit
Augustin Fresnel
Two slits
Light waves were found to be solutions to
Maxwell’s Equations.
microwave
2
1
106
10
10
radio
visible
The electromagnetic spectrum is vast.
infrared
0
105
10
-1
4
10
10
3
10
wavelength (nm)
UV
2
10
X-ray
1
10
0
10
-1
10
gamma-ray
All electromagnetic waves
travel in a vacuum with a
speed c given by:
where μ0 and ε0 are the permeability and permittivity of free space
Michelson & Morley
Waves typically occur in a medium.
So in 1887, Michelson and Morley
attempted to measure the earth's
velocity with respect to what was
then called the aether and found it
always to be zero. Yes, this was
disturbing. But no one knew what to
do about it.
Albert Michelson Edward Morley
(1852-1931)
(1838-1923)
Triumph of Classical Physics:
The Conservation Laws
Conservation of energy: The sum of energy
(in all its forms) is conserved (does not
change) in all interactions.
Conservation of linear momentum: In the
absence of external forces, linear
momentum is conserved in all interactions.
Conservation of angular momentum: In the
absence of external torque, angular
momentum is conserved in all interactions.
Conservation of charge: Electric charge is
conserved in all interactions.
These laws remain
the key to interpreting
even particle physics
experiments today.
Opposition to atomic theory
Ernst Mach was an extreme “logical
positivist,” and he opposed the theory on
the basis of logical positivism, i.e., atoms
being “unseen” place into question their
reality.
Wilhelm Ostwald (1853 – 1932) supported
Mach, but did so based on unexplained
experimental results of radioactivity,
discrete spectral lines, and the formation of
molecular structures. (These are good
points, but not against atomic theory, as it
turned out.)
Boltzmann committed suicide in 1905, and it’s
said that he did so because so many
people rejected his theory.
Ernst Mach
(1838-1916)
Discovery of Electron
Wilhelm Röntgen
(1845-1923)
J. J. Thomson
(1856-1940)
In the 1890s scientists and
engineers were familiar
with “cathode rays.” These
rays were generated from
one of the metal plates in
an evacuated tube with a
large electric potential
across it.
It was surmised that cathode rays had something to do with atoms.
It was known that cathode rays could penetrate matter and were deflected
by magnetic and electric fields.
Observation of X Rays
Wilhelm Röntgen studied the effects
of cathode rays passing through
various materials. He noticed that a
phosphorescent screen near the tube
glowed during some of these
experiments. These new rays were
unaffected by magnetic fields and
penetrated materials more than
cathode rays.
He called them x rays and deduced
that they were produced by the
cathode rays bombarding the glass
walls of his vacuum tube.
Wilhelm Röntgen
Röntgen’s
X-Ray Tube
Röntgen constructed an x-ray tube by
allowing cathode rays to impact the
glass wall of the tube and produced x
rays. He used x rays to make a
shadowgram the bones of a hand on a
phosphorescent screen.
Quantization of Electric Charge
Thomson used an evacuated cathode-ray tube to show that
the cathode rays were negatively charged particles
(electrons) by deflecting them in electric and magnetic fields.
Thomson’s method (1897) of measuring the ratio of the electron’s charge to
mass was to send electrons through a region containing a magnetic field
perpendicular to an electric field. This experiment also proved that cathode
rays had particle behavior
Calculation of e/m
Exercise 1: An electron is moving under the influence of electric and
magnetic fields. Show that the charge to mass ratio is given by;
q
E

m RB 2
The B filed can be computed by
measuring the current using an
ammeter, the electric field can be
computed by measuring the voltage
and the radius R can be measured
experimentally by a rod
q / m  0.7 1011 C / kg
This is independent of the nature of gas or metal for the Cathode. Lorentz
called the charge electron e as one unit of negative charge
Determination of
Electron Charge
Millikan’s oil-drop
experiment
Robert Andrews Millikan
(1868 – 1953)
Millikan was able to
show that electrons
had a particular
charge.
Calculation of the oil drop charge
Exercise 2: For Millikan’s experiment derive an expression for
the charge of an electron as a function of mdrop, acceleration
due to gravity g, plate separation d and voltage V. Then using
Stoke’s law to determine the terminal velocity and thus the
mass of the drop, calculate the charge of an electron.
e = 1.602 x 10-19 C
The Electron Volt (eV)
The work done in accelerating a charge
through a potential difference is given by
W = qV. For a proton, with the charge
e = 1.602 × 10−19 C and a potential
difference of 1 V, the work done is:
W = (1.602 × 10−19 C)(1 V) = 1.602 × 10−19 J
Artist’s rendition of an
electron (don’t take this too
seriously)
The work done to accelerate the proton across a potential
difference of 1 V could also be written as:
W = (1 e)(1 V) = 1 eV
Thus eV, pronounced “electron volt,” is also a unit of energy.
It’s related to the SI (Système International) unit joule by:
1 eV = 1.602 × 10−19 J
Binding Energy
The equivalence of mass and
energy becomes apparent when
we study the binding energy of
systems like atoms and nuclei that
are formed from individual
particles.
The potential energy associated
with the force keeping the system
together is called the binding
energy EB.
The binding energy is the difference between the rest energy of the individual
particles and the rest energy of the combined bound system.
Elementary Particles
Atoms
From the Greek for “indivisible”
Were once thought to the elementary particles
Atom constituents
Proton, neutron, and electron
Were viewed as elementary because they are very stable
Quarks
Physicists recognize that most particles are made
up of quarks
Exceptions include photons, electrons and a few others
The quark model has reduced the array of
particles to a manageable few
The quark model has successfully predicted new
quark combinations that were subsequently
found in many experiments
Discovery of New Particles
New particles
Beginning in 1937, many new particles were discovered
in experiments involving high-energy collisions
Characteristically unstable with short lifetimes
Over 300 have been cataloged
A pattern was needed to understand all these new
particles
Fundamental Forces
All particles in nature are subject to four fundamental forces
Strong force
Electromagnetic force
Weak force
Gravitational force
Strong Force
Is responsible for the tight binding of the quarks to
form neutrons and protons
Also responsible for the nuclear force binding the
neutrons and the protons together in the nucleus
Strongest of all the fundamental forces
Very short-ranged
Less than 10-15 m
Electromagnetic Force
Is responsible for the binding of atoms and molecules
About 10-2 times the strength of the strong force
A long-range force that decreases in strength as the inverse
square of the separation between interacting particles
Weak Force
Is responsible for instability in certain nuclei
Is responsible for beta decay
A short-ranged force
Its strength is about 10-6 times that of the strong
force
Scientists now believe the weak and
electromagnetic forces are two manifestations of
a single force, the electroweak force
Gravitational Force
A familiar force that holds the planets, stars and
galaxies together
Its effect on elementary particles is negligible
A long-range force
It is about 10-43 times the strength of the strong
force
Weakest of the four fundamental forces
Explanation of Forces
Forces between particles are often described in terms of the
actions of field particles or quanta
For electromagnetic force, the photon is the field particle
The electromagnetic force is mediated, or carried, by photons
Forces and Mediating Particles
(also see table 30.1)
Interaction (force)
Mediating Field
Particle
Strong
Gluon
Electromagnetic
Photon
Weak
W and Z0
Gravitational
Gravitons
Hadrons
Interact through the strong force
Two subclasses
Mesons
Decay finally into electrons, positrons, neutrinos and photons
Integer spins
Baryons
Masses equal to or greater than a proton
Noninteger spin values
Decay into end products that include a proton (except for the
proton)
Composed of quarks
Leptons
Interact through weak force
All have spin of ½
Leptons appear truly elementary
No substructure
Point-like particles
Scientists currently believe only six leptons exist,
along with their antiparticles
Electron and electron neutrino
Muon and its neutrino
Tau and its neutrino
Bubble Chamber
Example
The dashed lines
represent neutral
particles
At the bottom,
- + p  Λ0 + K0
Then Λ0  - + p and
K0   + µ- + µ
Quarks
Hadrons are complex particles with size and
structure
Hadrons decay into other hadrons
There are many different hadrons
Quarks are proposed as the elementary particles
that constitute the hadrons
Originally proposed independently by Gell-Mann and
Zweig
Original Quark Model
Three types
u – up
d – down
s – originally sideways, now strange
Associated with each quark is an antiquark
The antiquark has opposite charge, baryon number and strangeness
Original Quark Model, cont
Quarks have fractional electrical charges
+1/3 e and –2/3 e
All ordinary matter consists of just u and d quarks
Original Quark Model – Rules
All the hadrons at the time of the original proposal were
explained by three rules
Mesons consist of one quark and one antiquark
This gives them a baryon number of 0
Baryons consist of three quarks
Antibaryons consist of three antiquarks
Additions to the Original Quark Model –
Charm
Another quark was needed to account for some
discrepancies between predictions of the model
and experimental results
Charm would be conserved in strong and
electromagnetic interactions, but not in weak
interactions
In 1974, a new meson, the J/Ψ was discovered
that was shown to be a charm quark and charm
antiquark pair
More Additions – Top and Bottom
Discovery led to the need for a more elaborate
quark model
This need led to the proposal of two new quarks
t – top (or truth)
b – bottom (or beauty)
Added quantum numbers of topness and
bottomness
Verification
b quark was found in a Y meson in 1977
t quark was found in 1995 at Fermilab
Numbers of Particles
At the present, physicists believe the “building blocks” of matter
are complete
Six quarks with their antiparticles
Six leptons with their antiparticles
See table 30.5
The Standard Model – Chart