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.

• 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

Chapter 1The Birth of Modern PhysicsThe 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)

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.

2CO has 32g of O and 12g of C 32 2

CO has 16g of O and 12g of C 16 1

First Classification of the elements

The Periodic Table

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

Dimitri Mendeleev (1869)

Periodic Table of the Elements

Periodic Table of the Elements

Periodic table

a chart (chemist’s road map) of elements arranged by atomic numberclassified by the number of protons in the nucleus

arranged from left to righteach 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

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

236.02 10AN

Example: Use Avagadro’s number to find the mass and size of the Hydrogen atom

23 3

327

23

3

329 -3

1 3 10

For H: 1, 6.02 10 , Density of liquid H=71 kg/m

10 kg1.7 10 kg

6.02 10

1 10 kgUsing =

1 10Volume of One atom is 2.3 10 m

3 10 m 0.3nm

A

HA

atomA A

H atom

A N

Am

N

M MV

V

V kgV

N N

d V

Classical Physics of the 1890s

Mechanics →

← Thermodynamics

Electromagnetism →

Mechanics began with Galileo (1564-1642)

The first great experimentalist: he established experimental foundations.

He described the Principle of Inertia.

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:

Mechanics achieved maturity with Isaac Newton

Isaac Newton (1642-1727)

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.

Newton’s second law: Introduces force (F) as responsible for the change in linear momentum (p = mv):

Classical Electromagnetism

Coulomb’s Law

Force on a static charge

Lorentz Force

Force on a moving charge

Superposition Principle

Vector sum of electric and magnetic fields

1 22

ˆF ir

kq q

r

F= (E+v B)q

net netF= (E +v B )q

0 0

EB

t

BE

t

0B

0/E q

Electromagnetism culminated with Maxwell’s Equations

Gauss’s law: (electric field)

Gauss’s law: (magnetic field)

Faraday’s law:

Ampère’s law:

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

"I procured me a triangular glass prism to try therewith the celebrated phenomena of colours." (Newton, 1665)

Newton in action

The Nature of Light

Huygens promoted the wave theory.

He explained polarization, reflection, refraction, and double refraction.

Double refraction

Christiaan Huygens (1629-1695)

He realized that light propagates as a wave from the point of origin.

He realized that light slowed down on entering dense media.

Diffraction confirmed light to be a wave.

Diffraction patterns

One slit

Two slits

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.

Augustin Fresnel

Light waves were found to be solutions to Maxwell’s Equations.

All electromagnetic waves travel in a vacuum with a speed c given by:

infrared X-rayUVvisi

ble

wavelength (nm)

microwave

radio

105106

gamma-ray

The electromagnetic spectrum is vast.

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.

Edward Morley (1838-1923)

Albert Michelson (1852-1931)

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

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.

J. J. Thomson (1856-1940)

Wilhelm Röntgen (1845-1923)

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

Exercise 1: An electron is moving under the influence of electric and magnetic fields. Show that the charge to mass ratio is given by;

Calculation of e/m

2

q E

m RB

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

11/ 0.7 10 /q m 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

Millikan’s oil-drop experiment

Determination of Electron Charge

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 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

Artist’s rendition of an electron (don’t take this too

seriously)

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

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

AtomsFrom the Greek for “indivisible”

Were once thought to the elementary particles

Atom constituentsProton, neutron, and electron

Were viewed as elementary because they are very stable

Quarks

Physicists recognize that most particles are made up of quarksExceptions 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 particlesBeginning 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 forcesStrong 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 forcesVery short-ranged

Less than 10-15 m

Electromagnetic Force

Is responsible for the binding of atoms and moleculesAbout 10-2 times the strength of the strong forceA 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 nucleiIs responsible for beta decay

A short-ranged forceIts strength is about 10-6 times that of the strong

forceScientists 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 forceWeakest of the four fundamental forces

Explanation of Forces

Forces between particles are often described in terms of the actions of field particles or quantaFor 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 forceTwo subclasses

MesonsDecay finally into electrons, positrons, neutrinos and

photonsInteger spins

BaryonsMasses equal to or greater than a protonNoninteger spin valuesDecay into end products that include a proton (except

for the proton)

Composed of quarks

Leptons

Interact through weak forceAll have spin of ½Leptons appear truly elementary

No substructurePoint-like particles

Scientists currently believe only six leptons exist, along with their antiparticlesElectron and electron neutrinoMuon and its neutrinoTau and its neutrino

Bubble ChamberExample

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 hadronsOriginally proposed independently by Gell-Mann and

Zweig

Original Quark Model

Three typesu – upd – downs – originally sideways, now strange

Associated with each quark is an antiquarkThe 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 rulesMesons consist of one quark and one antiquark

This gives them a baryon number of 0

Baryons consist of three quarksAntibaryons 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 quarkst – top (or truth)b – bottom (or beauty)

Added quantum numbers of topness and bottomness

Verificationb quark was found in a Y meson in 1977t quark was found in 1995 at Fermilab

Numbers of Particles

At the present, physicists believe the “building blocks” of matter are completeSix quarks with their antiparticles

Six leptons with their antiparticles

See table 30.5

The Standard Model – Chart