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Superposition and Interference - Correct Answer - same wave + same wave = reinforcement - two opposite waves = cancellation - two similar waves = partial cancellation - interference patterns of overlapping waves from 2 vibrating sources - interference pattern = caused by interference b/w a pair of waves - constructive interference produces bright region where waves reinforce each other (waves arriving in phase) - destructive interference produces dark region where waves cancel each other (waves arriving half a wavelength out of phase) - a monochromatic light into double slits produces an interference pattern - the phenomenon of interference occurs for = sound waves + light waves --> interference is the property that characterizes waves in general Superposition and Interference part 2 - Correct Answer - single-color thin-film interference = reflection from the upper and lower surfaces of a wedge of air b/w 2 glass plates - interference colors by reflection from thin films = the thin film of gasoline is just the right thickness to result in the destructive interference of blue light - diffraction grating = composed of a large number of close, equally spaced slits for analyzing light source; produced by spectrometers that disperse white light into colors - if the thin film of gasoline was a bit thinner, the wavelength to be canceled would be = shorter than that of blue - if violet light were canceled by the double reflection of sunlight from gasoline on a wet surface, the resulting color would likely be = orange --> orange is the complementary color of violet - if you see the color blue reflected in the interference from gasoline on water, and you lower your head so a greater angle from the normal results, you'll likely see a color having a wavelength = shorter than that of blue --> the path through the gasoline would be longer, and a longer wavelength would be canceled; the result of a long wave being canceled is a shorter wave Superposition and interference part 3 - Correct Answer interference colors = that colors are subtractive primaries = magnetas, yellows, and cyans Double-slit experiment - Correct Answer - monochromatic light passing through 2 slits, a, forms an interference pattern, b, shown graphically in c - suppose we dim our light source so that, in effect, only 1 photon at a time reaches the barrier w/ the thin slits - if film behind the barrier is exposed to the light for a very short time, the film gets exposed = each spot represents the place where the film has been exposed by a photon; if the light is allowed to expose the film for a longer time, a pattern of fringes begins to emerge - if we cover one slit so that photons striking the photographic film can pass only through a single slit, the tiny spots on the film accumulate to form a single-slit diffraction pattern; we find that photons hit the film at places they would not hit if both slits were open How do photons traveling through one slit "know" that the other slit is open and avoid certain regions, proceeding only to areas that will ultimately fill to form an interference pattern? - Correct Answer - each single photon has wave properties as well as particle properties Spacetime - Correct Answer - space and time are initimately linked together; things exist in *spacetime* - each object, each person, each planet, each star, each galaxy exists in what physicists call "the spacetime continuum" - one observer's measurements of space and time differ from the measurements of another observer in some other realm of spacetime in such a way that each observer will always measure the same ratio of space and time for light: the greater the measured distance in space, the greater the measured interval of time Time dilation - Correct Answer - imagine that we are somehow able to observe a flash of light bouncing to and fro b/w a pair of parallel mirrors, like a ball bouncing to and fro b/w a floor and ceiling - if the distance b/w the mirrors is fixed, then the arrangement constitutes a light clock, bc the back-and-forth trips of the flash take equal time intervals - an observer moving w/ the spaceship observes the light flash moving vertically b/w the mirrors of the light clock - an observer who sees the moving ship pass by observes the flash moving along a diagonal path - suppose now that we are standing on things quite different from our reference frame, for we do not see the light path as being simple up-and-down motion - b/c each flash moves horizontally while it moves vertically b/w the 2 mirrors, we see the flash follow a diagonal path - b/c the spd of light is the same in all reference frames (Einstein's second postulate), the flash must travel for a correspondingly longer time b/w the mirrors in our frame than in the reference frame of the onboard observer - the relationship b/w time (proper time) in the frame of reference moving w/ the clock and the time t measured in another frame of reference (relative time) is y = 1/sqrt(1-(v42/c*2)) -> lorentz factor - as the spd of a spaceship increases, the Lorentz factor increases as per the graph shown -> clocks will tick slower and slower as the spaceship approaches the spd of light - when we see the rocket traveling at close to the maximum rate through space (the spd of light), we see its time practically standing still If you were moving in a spaceship at a high spd relative to earth, would you notice a difference in your pulse rate or the pulse rate of people on earth? - Correct Answer you would notice a difference in the pulse rate of people on earth, but not your own pulse rate -> there would be no relative spd b/w you and your pulse bc the 2 share the same frame of reference; therefore, you would notice no relativistic effects in your pulse; there would be, however, a relativistic effect b/w you and people back on earth; you would find their pulse rate to be slower than normal Will observers A and B agree on measurements of time if A moves at 1/2 the spd of light relative to B? - Correct Answer No -> when A and B move relative to each other, each observes a slowing of time in the other's frame of reference, so they do not agree on measurements of time Will observers A and B agree on measurements of time if both A and B move together at 1/2 the speed of light relative to earth? - Correct Answer yes -> when they are moving in unison, they share the same frame of reference and agree on measurements of time; they see each other's time as passing normally, and they see events on earth in the same slow motion - earth frame of reference: 10 flashes @ 12 min = 120 mins; 10 flashes @ 3 min = 30 mins; 120+30 = 150 mins --> 2.5 hours - spaceship frame of reference: 20 flashes @ 6 min = 120 min = 2 hr The ship sends equally spaced flashes every 6 min while approaching the receiver at constant spd. How will these flashes be spaced when they encounter the receiver? - Correct Answer they will be equally spaced less than 6 min apart - > as long as the ship moves at constant spd, the equally spaced flashes will be seen equally spaced but more frequently Since motion is relative, can't we say as well that the spaceship is at rest and the earth moves, in which case the twin on the spaceship ages more? - Correct Answer no -> the situation is not symmetrical, for one twin remains in a single reference frame in spacetime during the trip while the other makes a distinct change of reference frame, as evidenced by the acceleration in turning around Addition of velocities - Correct Answer - for everyday objects: V = v1 + v2 - strictly speaking, the above rule is an approx. Of the relativistic rule for adding velocities. We'll not treat the long derivation but simple state the rule: V = v1 + v2/ (1 + (v1Vv2)/c42) - no matter what the relative velocities b/w 2 frames, light moving at c in one frame will be seen to be moving at c in any other frame. If you try chasing light, you can never catch it Length contraction - Correct Answer - as objects move through spacetime, space as well as time changes - space is contracted, making the objects look shorter when they move by us at relativistic spds -L=LO* sqrt (1 - (v42/c42)) - length contraction takes place only in the direction of travel = if an object is traveling horizontally, no contraction takes place vertically Mass, energy, and E = mc42 - Correct Answer - a piece of matter, even at rest and not interacting w/ anything else, has an "energy of being" = rest energy - Einstein concluded that it takes energy to make mass and that energy is released if mass disappears - the amount of energy E is related to the amount of mass m by: E = mc42 - saying that a power plant delivers 90 mil megajoules of energy to its consumers is equivalent to saying that it delivers 1 gram of energy to its consumers, bc mass and energy are equivalent - in 1 sec, 4.5 mil tons of mass are converted to radiant energy in the sun; the sun is so massive, however, that in 1 mil years only 1 ten-millionth of the sun's mass will have been converted to radiant energy Correspondence principle - Correct Answer - it states that any new theory or any new description of nature must agree w/ the old where the old gives correct results - if the equations of special relativity are valid, they must correspond to those of classical mechanics when spds much less than the spd of light are considered - when spds are very low, compared to the spd of light v is much smaller than c, then: Y = 1/sqrt(1-(v42/c42)) = 1/sqrt(1-0) = 1 Light emission - Correct Answer - light emission is understood in terms of familiar planetary model of the atom - just as each element is characterized by the # of e- that occupy the shells surrounding its atomic nucleus, each element also possess its own characteristics pattern of electron shells, or energy states Most of what we know about atoms is gained by investigating the - Correct Answer light they emit --> light emitted by atoms, their atomic spectra are considered to be the fingerprints of atoms Uncertainty principle - Correct Answer - act of observing something as tiny as an electron probes the e- and, in doing so, produces a considerable uncertainty in either its position or its motion - german physicists Werner Heisenberg called this the uncertainty principle - when the uncertainties the measurements of momentum p and position x for a particle are multiplied together, the product must be equal to or greater than Planck's constant, h, divided by 2pi, which is represented as h (called h-bar) dpdx 2h - the Ais "uncertainty in measurement of": Ap is uncertainty in measurement of p and Ax the uncertainty in position. The product of uncertainties must be equal to or greater than (2) the size of h - applies to uncertainties of measurements of energy and time. The uncertainty in knowledge of energy, AE, and the duration taken to measure the energy, At, are related by the expression: dedt 2 h. - Heisenberg's uncertainty principle applies only to quantum mechanics; does not apply to: uncertainties of macroscopic lab measurements; a shield of nature's secrets; the notion that science is basically uncertain The which of these does Heisenberg's uncertainty principle apply? A. Measuring room temperature with a thermometer B. Momentum and distances of a high-speed bullet C. A public opinion survey D. None of the above. - Correct Answer none of the above --> Heinsenberg's uncertainty principle involves the unavoidable interaction b/w nature at the atomic level and the means by which we probe it Explanation of Quantized Energy Levels: Electron Waves - Correct Answer - Louis de Broglie hypothesized that a wave is associated with every particle = The wavelength of a matter wave is inversely related to a particle's momentum - de Broglie showed that a Bohr orbit exists where an electron wave closes on itself constructively = The electron wave becomes a standing wave, like a wave ona musical string - In this view, the electron is thought of not as a particle located at some point in the atom but as if its mass and charge were spread out into a standing wave surrounding the atomic nucleus with an integral number of wavelengths fitting evenly into the circumferences of the orbits - a) An orbiting electron forms a standing wave only when the circumference of its orbit is equal to a whole- number multiple of the wavelength. - b) When the wave does not close in on itself in phase, it undergoes destructive interference. Hence, orbits exist only where waves close in on themselves in phase - the circumference of the innermost orbit, according to this picture, is equal to one wavelength = the 2nd has a circumference of two electron wavelength; 3rd orbit has a circumference of 3 electron wavelengths, and so forth - The electron orbits in an atom have discrete radii because the circumferences of the orbits are whole-number multiples of the electron wavelength - This results in a discrete energy state for each orbit - This model explains why electrons don't spiral closer and closer to the nucleus, causing atoms to shrink to the size of the tiny nucleus - If each electron orbit is described by a standing wave, the circumference of the smallest orbit can be no smaller than one wavelength = No fraction of a wavelength is possible in a circular (or elliptical) standing wave - As long as an electron carries the momentum necessary for wave behavior, atoms don't shrink in on themselves - food irradiation kills microbes = doesn't make the food radioactive; there is no diarrhea w/ astronauts in space (their food is first irradiated) The origins of radioactivity go back to - Correct Answer before humans emerged on Earth. Any atom that emits an alpha particle or beta particle - Correct Answer becomes an atom of a different element, always --> Contrary to the failures of alchemists of old to change elements from one to another, this was going on all around them—unnoticed Which of these is the nucleus of the helium atom? - Correct Answer Alpha Which of these is actually a high-speed electron? - Correct Answer Beta The atomic nucleus and the strong force - Correct Answer - the strong force holds nucleons together - the strong force is more effective w/ smaller nuclei - a lone neutron is radioactive and spontaneously transforms to a proton and an e- = a neutron needs protons around to keep this from happening - alpha emission = new proton formed from neutron --> electron (beta particle) ejected from neutron) --> alpha particle emitted The strong force is a force in the - Correct Answer nucleus that holds nucleons together. In the nucleus of an atom, the strong force is a relatively - Correct Answer short- range force. Radioactive half-life - Correct Answer - the rate of decay for a radioactive isotope is measured in terms of a characteristic time, the half-life, the time for half of an original quantity of an element to decay - uranium-238 to lead-206 through a series of alpha and beta decays; in 4.5 billions years, half of uranium presently in earth will be lead A certain isotope has a half-life of 10 years. This means the amount of that isotope remaining at the end of 10 years will be - Correct Answer half. Suppose the number of neutrons in a reactor that is starting up doubles each minute, reaching 1 billion neutrons in 10 minutes. When did the number of neutrons reach half a billion? - Correct Answer 9 minutes --> Can you see that working backward, each minute has half the number of neutrons? Transmutation of the elements - Correct Answer - w/ alpha or beta particles, a diff element is formed; this is transmutation, which occurs in natural events and is also initiated artificially in the lab - uranium naturally transmutes to thorium when an alpha particle is emitted - natural transmutation = thorium naturally transmutes to protactinium when a beta particle is emitted - an e- = e0/-1 --> 0 indicates e-'s mass is insignificant compared w/ nucleons; -1 = electric charge of the electron - artificial transmutation = An alpha particle fired at and impacting on a nitrogen atom, which transmutes to oxygen and hydrogen When an element ejects an alpha particle and a beta particle, the atomic number of the resulting element - Correct Answer reduces by 2 --> An alpha particle (a helium nucleus) has atomic number 2. Ejection of an alpha particle means a loss of 2 protons, so the atomic number of the element is lowered by 2 B.in about 5730 years. C.in about twice 5730 years. D.None of the above - Correct Answer none of the above --> In theory, the amount never reaches zero. In eons to come, trace amounts of the carbon-14 in your bones, even if completely dissolved, will still exist 
