PHYS 1260 Exam 4
will observers A and B agree on measurements of time if A moves at 1/2 the spd of light relative to B?
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
the radioactive decay of nature's elements occurs in the: A.soil we walk on. B.air we breathe. C.interior of Earth. D.All of the above.
all of the above
Any atom that emits an alpha particle or beta particle
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
The origins of radioactivity go back to
before humans emerged on Earth.
excitation is the process in which
electrons are boosted to higher energy levels in an atom
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
half.
Explanation of Quantized Energy Levels: Electron Waves
- 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 on a 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
x-rays and radioactivity
- Roentgen discovered X-rays produced by a beam of e- striking the glass surface of a gas-discharge tube - He found that X-rays could pass through solid materials, could ionize the air, showed no refraction in glass, and were undeflected by magnetic fields - X-rays are high-frequency electromagnetic waves, usually emitted by de-excitation of the innermost orbital e- of atoms - an energetic beam of e- striking a solid surface excites the innermost e- and produces higher-frequency photons of X-radiations - X-ray photons have high energy and can penetrate many layers of atoms before being absorbed or scattered - X-rays do this when they pass through your soft tissue to produce an image of the bones inside your body - radioactivity = the process of nuclear decay; nothing new in the environment; it's going on since time zero; it warms Earth's interior, is in the air we breathe, and is present in all rocks (some in trace amounts); it is natural
addition of velocities
- 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 + (v1v2)/c^2) - 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
spacetime
- 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
Which of these is the nucleus of the helium atom?
Alpha
Which of these is actually a high-speed electron?
Beta
superposition and interference part 3
interference colors = that colors are subtractive primaries = magnetas, yellows, and cyans
most of what we know about atoms is gained by investigating the
light they emit --> light emitted by atoms, their atomic spectra are considered to be the fingerprints of atoms
Atoms can transmute into completely different atoms in
nature + labs --> Atomic transmutation occurs in nature, in laboratories, and as far as we know, throughout the cosmos
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?
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
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.
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
The half-life of carbon-14 is about 5730 years, which means that the present amount in your bones will reduce to zero A.when you die. B.in about 5730 years. C.in about twice 5730 years. D.None of the above
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
The strong force is a force in the
nucleus that holds nucleons together.
which has less energy per photon?
red light --> in accord w/ E ~ f, the lowest-frequency light has the lowest energy per photon
When an element ejects an alpha particle and a beta particle, the atomic number of that element
reduces by 1 --> Alpha emission reduces atomic number by 2, and beta emission increases atomic number by 1, so net result is -1.
When an element ejects an alpha particle and a beta particle, the atomic number of the resulting element
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
In the nucleus of an atom, the strong force is a relatively
short-range force.
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?
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
does time dilation mean that time really passes more slowly in moving systems or only that it seems to pass more slowly?
time really passes more slowly in moving systems -> the slowing of time in moving systems is not merely an illusion resulting from motion; time really does pass more slowly in a moving system relative to one at relative rest
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?
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
michelson interferometer
- a beam of light from a monochromatic source was separated into 2 beams w/ paths at right angles to each other; these were reflected and recombined to show whether there was any difference in avg spd over the 2 back-and-forth paths - the interferometer was set w/ one path parallel to the motion of earth in its orbit - either michelson or morley carefully watched for any changes in avg spd as the apparatus was rotated to put the other path parallel to the motion of earth - but no changes were observed
mass, energy, and E = mc^2
- 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 = mc^2 - 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
uncertainty principle
- 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) ΔpΔx ≥ ħ - the Δ is "uncertainty in measurement of": Δp is uncertainty in measurement of p and Δx the uncertainty in position. the product of uncertainties must be equal to or greater than (≥) the size of ħ - applies to uncertainties of measurements of energy and time. the uncertainty in knowledge of energy, ΔE, and the duration taken to measure the energy, Δt, are related by the expression: ΔEΔt ≥ ħ. - 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
postulates of special theory of relativity
- all laws of nature are the same in all uniformly moving frames of reference - the spd of light in free space has the same measured value for all observers, regardless of the motion of the source or the motion of the observer; that is, the speed of light is constant
length contraction
- 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 = L0 * sqrt (1 - (v^2/c^2)) - length contraction takes place only in the direction of travel = if an object is traveling horizontally, no contraction takes place vertically
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?
- each single photon has wave properties as well as particle properties - the photon displays different aspects at different time - a photon behaves as a particle when it is being emitted by an atom or absorbed by photographic film or other detectors, and behaves as a wave in traveling from a source to the place where it is detected - so the photon strikes the film as a particle but travels to its position as a wave that interferes constructively
radiometric dating
- earth's atmosphere is continuously bombarded by cosmic rays, which causes many atoms in the upper atmosphere to transmute; these transmutations result in many protons - a nitrogen that captures a neutron and becomes an isotope of carbon by emitting a proton - Carbon-14 is a beta emitter and decays back to nitrogen - b/c living plants take in CO2, any C-14 lost by decay is immediately replenished w/ fresh C-14 from the atmosphere - dead plants continue emitting C-14 w/o replenishment - relative amounts of C-12 to C-14 enable dating of organic materials
the twin trip
- identical twins, one an astronaut who takes a high-speed round-trip journey in the galaxy while the other stays home on earth - when the traveling twin returns, he is younger than the stay-at-home twin - how much younger depends on the relative speeds involved - since motion is relative, why doesn't the effect work equally well the other way around? why wouldn't the traveling twin return to find his stay at home twin younger than himself? - when no motion is involved, the light flashes are received as frequently as the spaceship sends them - when the sender moves towards the receiver, the flashes are seen more frequently - when the sender moves away from the receiver, the flashes are spaced farther apart and are seen less frequently - suppose the traveling twin recedes from the earthbound twin at the same high speed for 1 hr and then quickly turns around and returns in 1 hr - the traveling twin takes a round-trip for 2 hr, according to all clocks aboard the spaceship - this trip will not be seen to take 2 hrs from the earth frame of reference - as the ship recedes from earth, it emits a flash of light every 6 mins; these flashes are received on earth every 12 mins - during the hr of going away from earth, a total of 10 flashes are emitted; if the ship departs from earth at noon, clocks aboard the ship read 1 PM when the tenth flash is emitted - 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
time dilation
- 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-(v^2/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
correspondence principle
- 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-(v^2/c^2)) = 1/sqrt(1-0) = 1
light emission
- 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
double-slit experiment
- 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
alpha, beta, and gamma rays
- radioactive elements emit 3 distinct types of radiation: 1. alpha = positively charged (helium nuclei) 2. beta = negatively charged (e-) 3. gamma (electromagnetic radiation) - food irradiation kills microbes = doesn't make the food radioactive; there is no diarrhea w/ astronauts in space (their food is first irradiated)
Superposition and Interference
- 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
- 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
emission spectra
- spectroscope = arrangment of slit, focusing lenses, and prism or diffraction grating; to see emission spectrum of light from glowing element; when an electron is at a higher energy level, atom is excited and temporarily loses the acquired energy when it returns to a lower level and emits radiant energy - spectral lines = forms an image of the slit on the screen using a spectroscope; each component of color is focused at a definite position according to frequency - spectral lines of hydrogen - more orderly than other elements; successive lines get closer until the lines merge; swedish physicist and mathematician Johannes Rydberg discovered that the sum of the frequencies of 2 lines often equals the frequency of a 3rd line - Ritz combination principle = Rydberg's discovery called the Ritz combination principle = the spectral lines of any element include frequencies that are either the sum or the difference of the frequencies of 2 other lines
motion is relative
- the place from which motion is observed and measured is a *frame of reference* - *an object may have different velocities* relative to different frames of reference - to measure the spd of an object, we first choose a frame of reference and pretend that we are in that frame of reference standing still = then we measure the spd w/ which the object moves relative to us - that is, relative to the frame of reference
radioactive half-life
- 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
the atomic nucleus and the strong force
- 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
transmutation of the elements
- 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
excitation
- when energy is imparted to an element, an electron may be boosted to a higher energy level --> this atom is said to be excited - the frequency of an emitted photon ~ energy level difference in de-exciting --> E = hf
An element emits 1 beta particle, and its product then emits 1 alpha particle. The atomic number of the resulting element is changed by
-1 --> Beta emission increases atomic number by 1, then alpha emission decreases atomic number by 2, so the net change is -1
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?
9 minutes --> Can you see that working backward, each minute has half the number of neutrons?
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?
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
