Modern Physics For Scientists And Engineers
2nd Edition
ISBN: 9781938787751
Author: Taylor, John R. (john Robert), Zafiratos, Chris D., Dubson, Michael Andrew
Publisher: University Science Books,
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Chapter 1, Problem 1.17P
To determine
To find:
The expected shift
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Muons are unstable subatomic particles that decay to electrons with a mean lifetime of 2.2 µs. They are produced when cosmic rays bombard the upper atmosphere about 10 km above the earth’s surface, and they travel very close to the speed of light. The problem we want to address is why we see any of them at the earth’s surface. (a) What is the greatest distance a muon could travel during its 2.2 µs lifetime? (b) According to your answer in part (a), it would seem that muons could never make it to the ground. But the 2.2 µs lifetime is measured in the frame of the muon, and muons are moving very fast. At a speed of 0.999c, what is the mean lifetime of a muon as measured by an observer at rest on the earth? How far would the muon travel in this time? Does this result explain why we find muons in cosmic rays? (c) From the point of view of the muon, it still lives for only 2.2 µs, so how does it make it to the ground? What is the thickness of the 10 km of atmosphere through which the muon…
Chapter 1 Solutions
Modern Physics For Scientists And Engineers
Ch. 1 - Prob. 1.1PCh. 1 - Prob. 1.2PCh. 1 - Prob. 1.3PCh. 1 - Prob. 1.4PCh. 1 - Prob. 1.5PCh. 1 - Prob. 1.6PCh. 1 - Prob. 1.7PCh. 1 - Prob. 1.8PCh. 1 - Prob. 1.9PCh. 1 - Prob. 1.10P
Ch. 1 - Prob. 1.11PCh. 1 - Prob. 1.12PCh. 1 - Prob. 1.13PCh. 1 - Prob. 1.14PCh. 1 - Prob. 1.15PCh. 1 - Prob. 1.16PCh. 1 - Prob. 1.17PCh. 1 - Prob. 1.18PCh. 1 - Prob. 1.19PCh. 1 - Prob. 1.20PCh. 1 - Prob. 1.21PCh. 1 - Prob. 1.22PCh. 1 - Prob. 1.23PCh. 1 - Prob. 1.24PCh. 1 - Prob. 1.25PCh. 1 - Prob. 1.26PCh. 1 - Prob. 1.27PCh. 1 - Prob. 1.28PCh. 1 - Prob. 1.29PCh. 1 - Prob. 1.30PCh. 1 - Prob. 1.31PCh. 1 - Prob. 1.32PCh. 1 - Prob. 1.33PCh. 1 - Prob. 1.34PCh. 1 - Prob. 1.35PCh. 1 - Prob. 1.36PCh. 1 - Prob. 1.37PCh. 1 - Prob. 1.38PCh. 1 - Prob. 1.39PCh. 1 - Prob. 1.40PCh. 1 - Prob. 1.41PCh. 1 - Prob. 1.42PCh. 1 - Prob. 1.43PCh. 1 - Prob. 1.44PCh. 1 - Prob. 1.45PCh. 1 - Prob. 1.46PCh. 1 - Prob. 1.47PCh. 1 - Prob. 1.48PCh. 1 - Prob. 1.49PCh. 1 - Prob. 1.50PCh. 1 - Prob. 1.51PCh. 1 - Prob. 1.52PCh. 1 - Prob. 1.53P
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- Two astronomical events are observed to occur at a time of 0.30 s apart and a distance separation of 2.0109m from each other. How fast must a spacecraft travel from the site of one event toward the other to make the events occur at the same time when measured in the frame of reference of the spacecraft?arrow_forwardIf a galaxy moving away from the Earth has a speed of 1000 km/s and emits 656 nm light characteristic of hydrogen (the most common element in the universe). (a) What wavelength would we observe on the Earth? (b) Whattype of electromagnetic radiation is this? (c) Why is the speedof the Earth in its orbit negligible here?arrow_forwardOne of the difficulties with the Michelson Morley experiment is that several extraneous effects (mechanical vibrations, variations of temperature, etc) can produce unwanted shifts in the interference pattern, masking the expected shift of interest. Suppose, for example, that during the experiment the temperature of one arm of the interferometer were to rise by deltaT. This would increase the arm’s length (L) by delta(L) =aLdeltaT, where a=10-5 is the arm’s coefficient of expansion. a) Symbolically, express the shift delta(N) that this temperature change would cause (in terms of a, L, deltaT, and lamda).b) Calculate deltaN for lamda=590nm, L=50cm, and deltaT=0.01 C. c) Make a conclusion about the importance of careful temperature control in the experiment by comparing result in b) with the expected shift deltaN (without temperature correction). Hint: we calculated the expected shift in class for different dimensions of the Michelson Interferometer.arrow_forward
- (a) How long in seconds does it take a radio signal to travel 180 km from a transmitter to a receiving antenna? (b) We see a full Moon by reflected sunlight. How much earlier did the light that enters our eye leave the Sun? The Earth – Moon and Earth – Sun distances are 3.8x105 km and 1.5 × 108 km, respectively. (c) What is the round-trip travel time in seconds for light between Earth and a spaceship at a 6.8 × 107 km distance from Earth? (d) Suppose astronomers observe a supernova about 7300 light-years (ly) distant. How long ago in years did the explosion actually occur?arrow_forwardMichelson-Morley Experiment. A shift of one fringe in the Michelson-Morley experiment corresponds to a change in the round-trip travel time along one arm of the interferometer by one period of vibration of light (about 2 X 10-15 s) when the apparatus is rotated by 90. Based on the results of such experiment, what velocity through the ether would be deduced from a shift of one fringe? (Take the length of the interferometer arm to be 11 m.)arrow_forwardIn the 1887 experiment by Michelson and Morley, the length of each arm was 11 m. The experimental limit for the fringe shift was 0.005 fringes. If sodium light was used with the interferometer ( λ=589 nm), what upper limit did the null experiment place on the speed of the Earth through the expected ether?arrow_forward
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- A galaxy G is moving away radially with speed with respect to an observer O. The relation between X, the wavelength of light emitted at G, and λo, the wavelength observed at O, is 入。 λ = λe λε 1+B 1- B' = where ẞ v/c (c is the speed of light). For ẞ < 1 find a power series expansion of the above formula up to and including terms of order ẞ³.arrow_forwardSuppose a satellite has a mass of 1950 kg and is orbiting at 7.9 km/s. Use the approximation that y 1+(1/2)(c) at low velocities. Randomized Variables m = 1950 kg v = 7.9 km/s Part (a) What is the relativistic momentum of the satellite in kilogram meters per second? Part (b) Find the fractional difference between the relativistic and non-relativistic momenta, (p - Pnr)/Pnr (p-Par Por= Gra Dedi Potearrow_forwardcalculate: (a) the real andimaginary part of fı2)= 32-i (b) the real andimaginary part of f(zl=22²-2 c() the abselute va lw of fiz) =z²arrow_forward
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