Grading Homework: 4 quizzes + 2 tests x 20 pts each; will drop the lowest Tests: in-class midterm, multiple choice, closed book in-class final, multiple choice, closed book All are equal @ 20% of score, so 5 x 20 points = 100 pts possible (plus any bonus) Some extra points available on HW3, 4, Final
Mass The Metric System (used by scientists and foreigners) 1 kilogram (kg) = 1000 grams (g) 100 kg = 220 lbs We tend to use mass and weight interchangeably, but weight depends on gravity. Distance 1 meter (m) = 100 centimeters (cm) 1 m = 1.1 yards (approx.) 1 cm = 0.4 inches (approx.) Volume 1 cubic centimeter or 1 cm 3 (about the size of a sugar cube)
Scientific Notation Powers, or exponents, of 10: 100 = 10 2 (= 10 x 10) 1000 = 10 3 (= 10 x 10 x 10) 10 = 10 1 1 = 10 0 0.1 = 10-1 0.007 = 7 x 10-3 Add the exponents 4000 x 0.002 = (4 x 10 3 ) x (2 x 10-3 ) = 8 x 10 0 = 8
Atomic Structure example: Helium Nucleus Protons Neutrons Electrons Nucleons = protons, and neutrons Helium entry in the Periodic Table (see text, page 203): 2 He Helium 4.003 Electric charge: Protons = charged positively (+) Neutrons = neutral, no charge Electrons = charged negatively (-) Atomic Number = number of protons Atomic mass (rounded to nearest integer) = number of protons + neutrons If number of electrons does not equal number of protons, the atom has a net charge, and is said to be ionized.
Waves are vibrations in space and time; something vibrates up and down, or back and forth, and also moves away from its source Examples are: sound, a mechanical wave; and light, an electromagnetic wave; and, radio, also an electromagnetic wave Waves are depicted by sine curves (also often called sine waves) Waves have the following properties: Amplitude (height or magnitude) Wavelength (distance from peak to peak) Speed Frequency (number of waves passing you in one second) Frequency and wavelength are inversely related, i.e., the higher the frequency, the shorter the wavelength, and viceversa Sound waves heard by humans have frequencies of 20 Hz to 20000 Hz 1 Hz (Hertz) = 1 cycle (wave) passing by per second
Period = time to complete one wave Period = 1/frequency, and frequency = 1/period Types of waves Transverse waves: the wave amplitude is perpendicular to the direction of travel of the wave Example: water waves; also, electromagnetic waves Longitudinal waves: the wave amplitude is along the same axis as the direction of travel; example = sound waves For sound waves, the wave is actually an alternate compression and expansion of the density of air along the direction of motion You can feel this as pressure changes from a loud sound (jackhammer, nearby thunder, explosion)
Waves can interfere: two (or more waves) can add their amplitudes But, the amplitudes go first positive, then negative, so they add up in either a constructive sense (resulting net amplitude is larger), or in a destructive sense (resulting net amplitude is smaller) Constructive and destructive interference Example: two musicians, one slightly out of tune with the other; we hear a slight warble when they play simultaneously You can also see this effect in water waves in a small pond or tub Standing waves are produced by constructive interference that reinforces a wave Example: waves on a guitar or violin string This is an example of resonance
Doppler effect: a wave phenomenon; applies to sound and also to light An increase in frequency as the wave source approaches you A decrease in frequency as the wave source moves away from you Example: the pitch of an approaching train whistle or truck horn changes as it approaches you, passes by, then moves away from you With light, this effect causes the color of the light to shift to the red when the object recedes, or to the blue when it approaches Widely used in astronomy
Electric charge Like charges repel Unlike charges attract Electrons have negative charge, protons have positive charge Electric force Is an inverse-square law force (like gravity) Difference: gravity is only attractive, electric force can be either attractive or replusive Electrons are not created or destroyed in charging; they are simply moved from one place to another Conductors allow electric charge to flow easily; most metals are good conductors Insulators do not allow electric charge to flow; glass, rubber, and sand are examples of insulators Semiconductors can be made to behave either way, and are therefore used in all modern electronic components Superconductors allow electric charge to flow with little or no resistance
The Electric Field describes the electric force; it points from a positive charge to a negative charge It is defined as the force per unit of charge; its strength falls off as 1/distance 2, i.e., it is an inverse-square law Electric potential refers to the potential energy a charge has due to its location in an electric field. Electric potential is sometimes referred to as voltage because it is measured in units of Volts. When an electric potential (a voltage) is applied to the opposite ends of a conductor, such as a wire, it will cause a current of electrons to flow Electric potential is the amount of electric potential energy per unit charge Since energy is measured in Joules, and charge in Coulombs, the electric potential (Volt) has a value of 1 joule per coulomb.
Electricity: units Charge: Coulomb Current (flow of charge): Coulombs per second = Amps Potential: Volt = 1 Joule / Coulomb
Electric current can be Direct Current (D.C.), or Alternating Current (A.C.) Commercial electricity in North America (i.e., what you get from the wall socket) is A.C. Batteries are D.C. Standard house voltage in the U.S. is 117 Volts AC (VAC); you sometimes see this written as 120 VAC It alternates at 60 Hz The amount of current that will flow in a circuit is determined by the resistance (Ohm s Law, V = I*R, V = voltage, I = current, R = resistance) The electric power used is Current x Voltage, in units of Watts
Magnets have North and South poles Every magnet has a North pole at one end, and a south pole at the other No isolated magnetic poles (monopoles) exist Like electric charge, likes repel and unlikes attract North poles attract South poles, and repel other North poles Magnetism is caused by the spin or motion of electrons Therefore, electricity and magnetism are linked An electric charge (such as an electron) moving near a magnetic field will feel a force that is mutually perpendicular to the direction of the magentic field and its own direction of travel So, magnetic fields cause charged particles to bend their trajectories
Light is an electromagnetic wave It has an electric field and a magnetic field, vibrating at right angles to each other and to its direction of motion The Electromagnetic Spectrum, from shortest to longest waves: Gamma rays X-rays Ultraviolet (UV) Visible light Infrared (IR) Microwaves Radio There is no sharp boundary between these regions In the visible the colors we see (in the rainbow) are [shortest to longest] Violet, Indigo, Blue, Green, Yellow, Orange, Red
Light waves move at the speed of light, called c, when in a vacuum; and at a speed very close to this in the air Inside glass or water or other transparent objects, the speed of light is slower than c
Since light is a wave, it has wave properties Amplitude of the wave = height of the Electric field vibration Wavelength = distance between two successive peaks This defines the color of the light wave Direction of wave travel Most light we see with our eyes has a spread of many colors mixed Generally, some colors stronger than others, so we see objects in different colors White light is a nearly uniform mix of all the colors that we can see with our eyes There are many other colors (= wavelengths) that we can t see But, electronic detectors and telescopes can see them
So, almost all light reaches us with a spectrum Spectrum = spread of light wavelengths, mixed in varying strengths,that reaches our eye / telescope / camera (plural = spectra) Spectra can be continuous (like this) or discrete (like this) Continuous spectra come from warm objects (everything in the Universe, almost). The color extent and intensity of the spectrum depends on the temperature of the object. This is known as thermal or blackbody radiation. Even you are emitting thermal radiation, right now.
The visible spectrum 400 nm 700 nm The human eye is sensitive only to the range 400 700 nanometers. (1 nanometer = 10-9 meter = one-billionth of a meter.) Blue wavelengths are shorter than red wavelengths. The visible spectrum is only a small part of the overall possible electromagnetic spectrum. Other regions of the spectrum correspond to gamma rays (very short) x-rays (pretty short wavelengths) UV (ultraviolet, shorter than visible blue light) infrared or IR (long wavelengths, beyond the visible) radio waves (longer than infrared)
Light of a certain color also has a characteristic frequency Frequency = number of waves passing an arbitrary location (any convenient reference point) per second. Frequency and wavelength are inversely related: Longer wavelength = lower frequency = slower vibrations Shorter wavelength = higher frequency = faster vibrations Often in physics we will talk about wavelength rather than frequency. But if you specify one, you know the other.
Light can undergo: Reflection, and Refraction (bending of light when it enters or leaves a transparent material Refraction is used in lenses to create magnification In the sky, light is scattered by molecules Scattering is a redirection of incoming light into many directions But, blue wavelengths are scattered more strongly than red wavelengths This is why the clear sky is blue, and sunset skies are reddishorange In a raindrop, refraction occurs as light enters and leaves the drop, and reflection when the light bounces off the inside back wall of the drop The amount of refraction (bending) depends on the wavelength, so when the light comes back out of the raindrop the colors are spread out This accounts for the spread of colors in the rainbow A similar effect occurs in glass prisms that are used in the lab
The law of reflection states that the angle of reflection = the angle of incidence Both are measured from the normal, an imaginary line perpendicular to the surface where the reflection occurs Total internal reflection can occur in some cases; this is how fiber optics work, and also the types of prisms used inside of binoculars We speak of the refractive index (or, index of refraction) which means (The speed of light in a vacuum) / (speed in a transparent medium) Refraction is responsible for many common illusions, e.g., mirages, magnification and bending of light when looking into water
Light, like other waves, also undergoes a phenomenon called diffraction, which causes the spreading of waves after passing through an aperture with solid edges This is what ultimately limits the resolution of optical systems, including your eye, microscopes, binoculars, and telescopes The larger the aperture, the less the diffraction, so the better we can resolve fine details, and thus, the higher the amount of magnification we can use Light, like sound, also undergoes interference, both constructive and destructive Reflected and scattered light is usually polarized Polarization means that the transverse vibrations of light are not evenly distributed or transmitted, but light with vibrations in a certain axis are preferentially emitted or transmitted Polarizing materials only transmit light that vibrates in a given axis Example: polarizing sunglasses Scattered skylight and light reflected from water are usually polarized
We often speak of light as a wave, but it also has properties of a particle A particle of light is called a photon Photons of a certain color have a particle amount of energy The energy of a photon is given by: E = h*ν, where h = Planck s constant and ν = frequency of the light Higher energy = higher frequency = shorter wavelengths And, vice-versa
Example wavelengths, temperatures, and frequencies Object Temperature Wavelength or frequency Dental X-rays narrow line near 5 nm Sun 5700 K Peak at about 500 nm Your skin about 70F Peak at about 10000 nm = 10 microns WiFi signal narrow signals at 2.4 GHz or 5 GHz (approx.) 1 GHz = 10 9 waves/sec. AM Radio 530 1070 khz wavelength 280 560 m
Atomic and Nuclear Physics A little history 1865 Maxwell: Electromagnetic theory of light 1890s Radioactivity, X-rays discovered 1897 J.J. Thomson discovers the electron 1900 Idea of the quantum introduced by Planck 1905 Einstein explains the photoelectric effect 1911 Rutherford detects the nucleus 1913 Bohr proposes quantum theory of the atom 1920s Quantum theory fully developed for atoms 1923 Existence of the photon confirmed 1932 Positron (anti-electron) and neutron discovered
Some Nobel Prizes for Physics 1901 Roentgen: discovery of X-rays 1903 Bequerel, Pierre & Marie Curie: Radioactivity 1906 J.J. Thomson: discovery of the electron 1908 Max Planck: discovery of energy quanta 1921 Albert Einstein: explanation of the photoelectric effect 1922 Niels Bohr: atomic theory 1923 Robert Millikan: studies of the electron 1929 Louis de Broglie: wave nature of the electron 1932 Werner Heisenberg: creation of quantum mechanics 1933 Erwin Schroedinger, P.A.M. Dirac: quantum theory
Nuclear forces: the strong nuclear force binds the nucleus together Otherwise it would fly apart since protons are all positively charged and would repel each other Radioactive elements decay into other elements by emitting particles: Alpha particle = Helium nucleus Beta particle = an electron (emitted from the nucleus, not from the electron orbits that surround the nucleus) Gamma particle = electromagnetic particle, i.e., a gamma ray
Nuclear transmutation rules: example 234 Th! 234 Pa + 0 e 90 91 "1 Top numbers (superscripts) = atomic mass Bottom numbers (subscripts) = atomic number [type of element] Both sets of numbers must balance from one side of the equation to the other The above is read and interpreted as follows: Thorium-234 decays ( ) to Protactinium-234 plus a Beta particle (the electron) This would be an example of spontaneous (radioactive) decay. Verify that the atomic numbers and atomic masses balance.
Another example: an induced nuclear reaction: 14 N + 4 He! 17 O + 1 H 7 2 8 1 This one is read as: Nitrogen-14 is bombarded by an alpha particle (Helium nucleus) and produces (or is transmuted into) an Oxygen-17 atom plus a proton (the Hydrogen nucleus). Verify that the atomic numbers and atomic masses balance.
Fission = splitting of a parent atom into two smaller, usually roughly equal-mass, daughter atoms via a nuclear event The most important example is the fissioning of U-235, after it is hit with a neutron, which splits it into two atoms of lighter elements plus several excess neutrons Each of these neutrons could go on to split more U-235 if it is present So the number of neutrons and the number of fissionings would multiply very quickly chain reaction: [atomic bomb] A nuclear reactor uses moderator materials to absorb and slow some of the excess neutrons to control this reaction so that it produces some energy but is not explosive Other elements can fission, for example, Plutonium Fusion = the joining of two light elements into a heavier element via a nuclear reaction Requires very intense temperatures and densities; not yet successfully demonstrated as a reactor technology
Environmental Radiation Units of radiation Particle Radiation Dosage Factor Health effect alpha 1 rad 10 = 10 rems beta 10 rad 1 = 10 rems Doses of radiation Lethal doses of radiation begin at 500 rems.
Environmental Radiation Source received annually Typical dose Natural origin Cosmic radiation 26 mrem =.026 rem Ground 33 mrem =.033 rem Air (Radon-222) 198 mrem =.198 rem Human tissues (K-40; Ra-226) 35 mrem =.035 rem 1 mrem = 1 millirem = 0.001 rem
The Quark Theory of Matter Developed in early 1960s to help explain a proliferation of mysterious subatomic particles found in atom smashers [particle accelerators] Further developed up to present day Proton and neutron are no longer fundamental particles They are composed of quarks Free quarks are not stable, they quickly recombine Quarks are bound together by gluons
Size Scales a Comparison Virus 10-7 m Molecule 10-9 m Atom 10-10 m Nucleus 10-14 m Proton 10-15 m Electron 10-18 m Quark 10-19 m
The Quarks Name Charge Up (u) +2/3 Down (d) -1/3 Charm (c) +2/3 Strange (s) -1/3 Top (t) +2/3 Bottom (b) -1/3
Proton Neutron u u d d d u Some particles are composed of 3 quarks (above) Some particles (mesons, found in cosmic rays) are made of 2 quarks No single quarks are observed in nature
What we don t know. Why quarks can have fractional charge when the electron (still thought to be fundamental ) has a charge of -1? Whether any of the exotic particles we know about now can account for dark matter that we believe is in most galaxies Whether there really is a graviton How to reconcile gravity and quantum/subatomic physics and lots more besides stay tuned.