Physics 334 Modern Physics

1. 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.

2. Class Overview and Chapter 1The Birth of Modern Physics • 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

3. 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

4. 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.

5. 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.

6. 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

7. Periodic Table of the Elements

8. 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

9. 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.

10. 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

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

12. Classical Physics of the 1890s • Mechanics → Electromagnetism → ← Thermodynamics

13. Mechanics began with Galileo (1564-1642) The first great experimentalist: he established experimental foundations. He described the Principle of Inertia.

14. 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. 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: Isaac Newton (1642-1727)

15. 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

16. 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.

17. 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.

18. 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)

19. Double refraction 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.

20. 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 Two slits Augustin Fresnel

21. visible microwave infrared UV X-ray 106 105 radio gamma-ray wavelength (nm) Light waves were found to be solutions to Maxwell’s Equations. • All electromagnetic waves travel in a vacuum with a speed c given by: The electromagnetic spectrum is vast. where μ0 and ε0 are the permeability and permittivity of free space

22. 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 (1852-1931) Edward Morley (1838-1923)

23. 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.

24. 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)

25. 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. Wilhelm Röntgen (1845-1923) J. J. Thomson (1856-1940) 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.

26. 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

27. 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.

28. 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

29. 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; 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 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

30. 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.

31. e = 1.602 x 10-19 C 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.

32. 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 • 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)

33. 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 energyEB. The binding energy is the difference between the rest energy of the individual particles and the rest energy of the combined bound system.

34. 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

35. 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

36. 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

37. Fundamental Forces • All particles in nature are subject to four fundamental forces • Strong force • Electromagnetic force • Weak force • Gravitational force

38. 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

39. 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

40. 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

41. 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

42. 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

43. Forces and Mediating Particles (also see table 30.1)

44. 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

45. 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

46. Bubble ChamberExample • The dashed lines represent neutral particles • At the bottom, • - + p  Λ0 + K0 • Then Λ0  - + p and • K0   + µ- + µ

47. 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

48. 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

49. 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

50. 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