Phys104 - How Things Work - Fall 2009 - Prof. T. Jacobson - Exam3 Crib Sheet - Chapters 13, 14, 15.2, 16

Electromagnetic (em) wave: oscillating pattern of electron and magnetic fields that travels through vacuum at the speed of light c = 3 x 10⁸ m/s = 30 cm/ns. Electromagnetic waves are generated by accelerating charges, and they travel perpendicular to the acceleration. They carry energy.

Polarization of em wave: direction of electric field vector. Can be linear or circular, or, generically, ellipsoiodal. It points in the direction of the charge's acceleration. Far from the source, the wave front is planar, the electric and magnetic fields are perpendicular to each other and to the direction the wave is traveling, which is the one your right hand palm faces when your thumb points along E and your fingers point along B. In such a wave E = cB.

wave speed = wavelength x frequency

AM: amplitude modulation, 550-1600 kHz (wavelength 300 m @ 1MHz), 10 kHz bandwidth
FM: frequency modulation, 87-106 MHz (wavelength 3 m @ 100MHz), 200 kHz bandwidth
Cell phones: digital (today), 870-895 MHz (wavelength 30 cm @ 1GHz), 30 kHz bandwidth

Microwave oven: uses 2.45 GHz, 12 cm waves, generated by a magnetron. Heats by shaking (mainly) water molecules.

Visible light: wavelength 450-700 nm = 0.45 - 0.7 microns. Different frequencies appear  to a human eye as different colors.

Infrared (IR) light has longer wavelength than visible, and ultraviolet  (UV) has shorter wavelength.

Rayleigh scattering: scattering of light by molecules or small particles. More effective for shorter wavelengths closer to the size of the particle.

Index of refraction: factor by which light slowed down in a material. If this depends on frequency there is dispersion.

Reflection: light (or other waves) partially reflect (reverse direction) and partially transmit at an interface between two media in which the wave speed is different.

Refraction: bending of light (or other waves) at an interface between two media in which the wave speed is different.

Total internal reflection: If the wave speed is faster on the far side of an interface between two media, waves incident from a sufficiently shallow angle will totally reflect.

Rainbows: arise from refraction, reflection, and dispersion of light in spherical water droplets.

Colors from interference: Light reflecting from a double layer, like a soap film or oil on water, combines from the two reflections to a greater or lesser extent in phase depending on the viewing angle and the wavelength of the light. So different colors have different brightness at different viewing angles.

Polarizing filter: blocks or reflects one linear polarization and transmits the perpendicular one. Polarized sunglasses block horizontally polarized light, which is more pronounced in glare that has reflected off horizontal surfaces.

Color perception: Three types of cone cell receptors in retina, with different sensitivities to different wavelengths of light. Almost any color we can perceive can be generated by mixing three primary colors of light, or  primary additive colors, red, blue and green. For example, yellow light can be made from a combination of red and green light. Pigments absorb colors, for example  yellow pigment absorbs blue light, leaving the red and green in the incident light to reflect and combine to make yellow. Almost any color we can perceive can also be made by mixing three primary colors of pigment, or primary subtractive colors, cyan, magenta, and yellow.

Atomic structure and spectra: each type of atom has particular energy level structure. The ground state is the lowest energy state. The electrons don't collapse into the nucleus because of Heisenberg's uncertainty principle: the uncertainty in the position times the uncertainty in the velocity must be at least as big as Planck's constant divided by the mass. The electrons don't all pile up in the same lowest energy state because of the Pauli exclusion principle: no two electrons can be in the same state. In a radiative transition of electrons from a higher to an available lower energy state, a photon is emitted, in a process called luminescence. Each type of atom has a characteristic set of radiative transition energies, hence a particular spectrum. The photon is a "packet" of light whose frequency is related to the energy difference by

energy difference = frequency x Planck's constant, and Planck's constant is h = 6.626 x 10^-34 J-s.

Gas discharge lamps accelerate electrons that collide with and excite atoms, which then emit light in radiative transitions. Fluorescent lamps are gas discharge lamps with mercury vapor that emits ultraviolet light. The UV light strikes a phosphorescent coating that absorbs UV and re-emits much of the energy as visible light. This process is called fluoresence.

Laser light: all the photons have nearly (i) the same wavelength, (ii) the same direction of propagation, (iii) the same phase (oscillating in step with each other). The photons are produced by stimulated emission from a laser medium with electrons "pumped" into excited states, and mirrors on the ends of a cavity so the emitted light will return and stimulate more emission.

LED - light emitting diode:  Made from a junction of two materials, works like a waterfall: the ground state of the conduction electrons on one side of the junction has higher energy than that on the other side, so when a current flows across the junction, the downstream electrons can drop to a lower level and emit the energy difference in the form of a photon. A laser diode is an LED whose downstream electrons survive long enough in the excited state to play the role of the pumped laser medium. Also mirrors or reflective crystal boundaries confine the radiation into a resonant cavity to allow the laser amplification process.

Photo diode: LED run backward, so when it absorbs a photon it contributes to an electric current. Used in photo detectors.

CCD (charge coupled device): A planar array of "buckets" each of which uses a photo diode to collect an amount of charge proportional to the amount of light that it absorbed. The charge is read out by shifting the charges from one row to the next by manipulating the voltages on the buckets, and shifting sideways to read out the last row. Used in digital cameras.

Binary numbers  use only the digits 0 and 1, and have digit places that are powers of 2 (from right to left, 1, 2, 4, 8, 16, etc).  For example, the binary number 1101 means (in the decimal system) 8+4+1 = 13. One bit of information is one choice between 0 and 1. One byte is eight bits.

CD's and DVD's: Digital (binary) data stored on a spiral track,  0 vs. 1 coded in change of reflected light intensity, due to manufactured pits or, for CD's & DVD's that are burned, spots of dye that are transformed from transparent to cloudy by heat of a laser beam.  Pit/spot size is limited by the diffraction effects of the laser light, which are due to the wave nature of the light and determined by the wavelength. A smaller wavelength can make a smaller spot. The wavelength in the plastic of the CD is shorter than in air because the speed of light in the plastic is slower (by a factor equal to the index of refraction). DVD's have two readable layers, and use shorter wavelength laser light, so they can store more information. The readout system focuses laser light on the spots, and detects the reflection with a photodiode, turning the pattern of spots into an electrical signal. Feedback from the light detector controls the lense to keep the light focused sharply in the correct location and track the spirals.

Diffraction maxima: When light reflects from or transmits through a large number of closely spaced grooves or lines, the light from each groove that emerges at a given angle combines with different phases. These cancel out almost completely, except if the length difference for paths from adjacent grooves is a whole number of wavelengths, in which case they are all in phase and a bright "diffraction maximum" occurs. The angle for this depends on wavelength, so the diffraction maxima for different colors lie at different angles. This is how the surface of a CD or DVD, and the diffraction gratings we used in class, separate white light into colors.

Optical fiber: Total internal reflection in a glass fiber with graded index of refraction makes a "light pipe". Minimal absorption and dispersion occur at the infrared wavelength around 1550 nm. Pulses can travel 50 km without loss of the signal. Amplification is done by passing the light through an EDFA, an optically pumped medium with excited atoms that are stimulated  by the incoming pulse of light to emit more light.

X-rays: produced e.g by accelerating electrons, and colliding them with heavy atoms. Used medically for imaging and for "therapy", i.e. to kill cancer cells. Imaging with 87 keV X-rays exploits the photoelectric effect: a tighly bound core electron absorbs an X-ray photon and gets ejected from the atom. Higher energy photons are needed for therapy, in order not to be absorbed too much, e.g. around 1 MeV. These can be obtained by accelerating electrons to higher energies, or from nuclear decays. In the latter case they are called gamma rays. They deposit energy in cells mostly by Compton scattering: colliding with an atomic electron  and knocking out the electron, while continuing on as a lower energy photon. The electron has a lot of energy and This can damage molecular bonds in DNA. The Compton scattering is a relatively rare event, and most of the photons pass through. To target the cancer beams are directed from many angles, with the beams intersecting at the cancer.

1 eV = 1 electron-volt: the energy acquired by an electron accelerated across a potential difference of one volt. Visible light photon energies are in the neighborhood of 2 eV, depending on frequency. 1 keV = 1000 eV, 1 MeV = 1,000,000 eV.

Proton therapy: radiation therapy with proton beam, whose initial energy can be adjusted so the protons slow and deliver the punch at a pre-selected location.

MRI - magnetic resonance imaging: With body in a strong magnetic field, radio frequency radiation flips proton spins in hydrogen atoms. The spins flip back into alignment with the magnetic field at a rate that depends on the chemical/tissue environment. This relaxation is monitored with the radio frequency radiation that the flipping spins emit. Plane to be imaged is selected by tuning magnetic field with gradient coils.

Nuclei - made of protons and neutrons (nucleons), held together by the nuclear force (a.k.a. strong interaction), while the protons repel electrically. Nuclei with the same number of protons but different numbers of neutrons are isotopes. A nucleus is around 100,000 times smaller than the atom built by electrons around it,  and its mass is around 4000 times greater than the mass of the electrons.

Radioactive decay: With too few or too many neutrons a nucleus with a given number of protons is unstable to spontaneous decay, a random event that has a certain probability of happening in any given time interval.  The half-life is the time it takes half of the nuclei in a sample to decay, on average. Radioactive nuclei can emit either alpha particles (helium-4 nuclei), beta rays (electrons or their anti-particle, positrons), or gamma rays, or a combination thereof. A lone neutron decays, with a half-life of 10 minutes, to a proton, an electron and a neutrino. This is called beta decay. Neutrons in nuclei can be stable, if there are not too many, since creating the proton near the other protons costs too much energy. But otherwise neutrons in nuclei can decay, which is also called beta decay. Example: Cobalt-60 beta decays with a half-life of 5.3 years to nickel-60 in an excited state, which then decays emitting two gamma rays, of energies 1.33 MeV and 1.17 MeV, which are used (for example) in medical radiation therapy. Another example is americium-241, which decays, with a half-life of 432 years, to neptunium-237, emitting an alpha particle and a 60 keV gamma ray. Americium is used (for example) in smoke detectors.

Binding energy of a nucleus is the energy required to separate the nucleons. Iron and nickel have the most binding energy per nucleon. Nuclei can undergo fusion (joining) or fission (splitting), which releases energy if the end product(s) are more tighly bound than the starting ones.

Uranium is made in supernova explosions of stars. That found on earth is mostly U-238 (99.3%, half-life 4.5 billion years) and U-235 (0.7%, half-life 710 million years). U-238 absorbs neutrons, whereas U-235 fissions into smaller nuclei when hit by a neutron, emitting on average 2.5 neutrons, so a chain reaction is possible. For a reactor, enrichment to 3-4% U-235 is needed, and for a bomb 90%. Since the two isotopes are chemically equivalent, enrichment must be based on the small mass difference of around 1%. The common method is with centrifuges, cylinders that spin with uranium hexafluoride gas, the U-238 preferentially going to the outside on account of its greater mass.

Plutonium-239:  made from U-238 in reactors, half-life 24,400 years, fissions when hit by a neutron, emitting 3 neutrons, so a chain reaction is possible.

Critical mass: minimum mass of material needed so that on average at least one neutron from any fission event induces another fission event before escaping from the material. For U-235 the critical mass is 52 kg, a sphere 17 cm in diameter. For Pu-239 critical mass is 10 kg, a sphere 10 cm in diameter.

Fission bomb: A uranium-235 bomb can be made by firing a plug to complete a sphere of critical mass, a relatively simple design. A plutonium-239 bomb is trickier since the reaction goes so fast. A sub-critical plutonium-239 core is surrounded by U-238 tamper that (partially) reflects neutrons, which in turn is surrounded by chemical explosives that compress the plutonium. A neutron source in the center is a trigger.

Fusion bomb, a.k.a hydrogen bomb or thermonuclear bomb: Fusion of H-2 (deuterium, stable) and H-3 (tritium, half-life 12.3 years, made in reactors) to make helium-4 + neutron. Alternatively, use lithium deuteride (Li-6 H-2), since when Li-6 absorbs a neutron it fissions to He-4 and H-3. To set off the fusion reaction the fuel is enclosed with a fission bomb. The whole is encased in a U-238 tamper, which confines the hydrogen, and itself ignites because the released neutrons have high enough energy to fission U-238.

Fallout: Besides the destructive power of a nuclear bomb explosion, the reactions create a large number of radioactive nuclei with excess neutrons, because the proportion of neutrons needed for stability of smaller nuclei is less than for the original uranium or plutonium.

SI (Systeme International) units                             quantity SI unit name length m meter time s second mass kg kilogram velocity m/s acceleration  m/s2 force N = kg m/s2 newton energy J = Nm = kg m2/s2 joule power W = J/s watt pressure Pa = N/m2 pascal temperature K kelvin entropy J/K volume m3 particle density 1/m3 mass density kg/m3 frequency Hz = 1/s hertz electric charge C coulomb voltage V = J/C volt electric field N/C = V/m electric current A = C/s ampere electrical resistance Ω = V/A ohm magnetic pole A-m magnetic field T = N/A-m tesla