Modern Physics for Scientists and Engineers
4th Edition
ISBN: 9781133103721
Author: Stephen T. Thornton, Andrew Rex
Publisher: Cengage Learning
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Chapter 2, Problem 37P
To determine
The rough figure of classical and relativistic number of muons at sea level and reason behind taking 104 muons instead of only 103.
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Mu mesons are subatomic particles which are created when cosmic rays strike the top of the
atmosphere. The travel downward at 99.5% of the speed of light. Mu meson counters were placed
at the top and bottom of Mt. Washington, which is 6265 feet (1909.6 m) tall. Mu mesons are
unstable particles with a half-life of 1.53 x 106 s.
3.
a.
How long does it take the mu mesons to go from the top to the bottom of the mountain? How many
half-lives is this?
6.40x10 s, 4.18 half-lives
If the counter at the top of the mountain detects 560 mu mesons per second, how many should be
detected after 4 half-lives?
b.
ou
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35 per second
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Mass of a proton: 1.007825 u; Mass of a neutron: 1.008665 u
1 The lifetime of a free neutron is 887 s. If a neutron moves with a speed 2.9 × 108
m/s relative to an observer in the lab, what does the observer measure the neutron's
lifetime to be? What is this an example of?
2. (a) What is the rest energy (in joules) of a subatomic particle whose (rest) mass is
6.7 x 10-3¹ kg? (b) How many MeV's of energy is this?
3. The rest energy of a particular subatomic particle is 1200 MeV. If this particle is
traveling at 90% the speed of light, what is its total relativistic energy?
You have a machine that produces a beam of π(pi) mesons moving at a speed of 0.9938c. In your lab, you aim this beam at a target that is 278.70 m away from your machine. The half‑life for π(pi) meson decays is 26.0 ns.
Calculate the time it takes in ns, in the lab frame, for particles to travel from your machine to the target.
Find the classically expected fraction of particles that would reach the target without having decayed.
Find the time it takes, in the rest frame of the particles, for a particle to travel from the machine to the target.
Chapter 2 Solutions
Modern Physics for Scientists and Engineers
Ch. 2 - Michelson used the motion of the Earth around the...Ch. 2 - If you wanted to set out today to find the effects...Ch. 2 - Prob. 3QCh. 2 - Prob. 4QCh. 2 - Prob. 5QCh. 2 - Prob. 6QCh. 2 - Prob. 7QCh. 2 - Prob. 8QCh. 2 - Devise a system for you and three colleagues, at...Ch. 2 - In the experiment to verify time dilation by...
Ch. 2 - Can you think of an experiment to verify length...Ch. 2 - Would it be easier to perform the muon decay...Ch. 2 - On a spacetime diagram, can events above t = 0 but...Ch. 2 - Prob. 14QCh. 2 - What would be a suitable name for events connected...Ch. 2 - Prob. 16QCh. 2 - Prob. 17QCh. 2 - Explain how in the twin paradox, we might arrange...Ch. 2 - In each of the following pairs, which is the more...Ch. 2 - Prob. 20QCh. 2 - Prob. 21QCh. 2 - A salesman driving a very fast car was arrested...Ch. 2 - A salesman driving a very fast car was arrested...Ch. 2 - Show that the form of Newtons second law is...Ch. 2 - Prob. 2PCh. 2 - Prob. 3PCh. 2 - A swimmer wants to swim straight across a river...Ch. 2 - Prob. 5PCh. 2 - Prob. 6PCh. 2 - Prob. 7PCh. 2 - Prob. 8PCh. 2 - Prove that the constancy of the speed of light...Ch. 2 - Prob. 10PCh. 2 - Prob. 11PCh. 2 - Prob. 12PCh. 2 - Two events occur in an inertial system K as...Ch. 2 - Is there a frame K in which the two events...Ch. 2 - Prob. 15PCh. 2 - An event occurs in system K at x = 2 m, y = 3.5 m,...Ch. 2 - Prob. 17PCh. 2 - Prob. 18PCh. 2 - A rocket ship carrying passengers blasts off to go...Ch. 2 - Prob. 20PCh. 2 - Particle physicists use particle track detectors...Ch. 2 - The Apollo astronauts returned from the moon under...Ch. 2 - A clock in a spaceship is observed to run at a...Ch. 2 - A spaceship of length 40 m at rest is observed to...Ch. 2 - Prob. 25PCh. 2 - A mechanism on Earth used to shoot down...Ch. 2 - Prob. 27PCh. 2 - Imagine that in another universe the speed of...Ch. 2 - Prob. 29PCh. 2 - Prob. 30PCh. 2 - Prob. 31PCh. 2 - A proton and an antiproton are moving toward each...Ch. 2 - Imagine the speed of light in another universe to...Ch. 2 - Prob. 34PCh. 2 - Three galaxies are aligned along an axis in the...Ch. 2 - Prob. 36PCh. 2 - Prob. 37PCh. 2 - Consider a reference system placed at the U.S....Ch. 2 - Prob. 39PCh. 2 - Prob. 40PCh. 2 - Use the Lorentz transformation to prove that s2 =...Ch. 2 - Prob. 42PCh. 2 - Prove that for a spacelike interval, two events...Ch. 2 - Given two events, (x1, t1) and (x2, t2), use a...Ch. 2 - Prob. 45PCh. 2 - Consider a fixed and a moving system with their...Ch. 2 - Prob. 47PCh. 2 - An astronaut is said to have tried to get out of a...Ch. 2 - Prob. 49PCh. 2 - Do the complete derivation for Equation (2.33)...Ch. 2 - A spacecraft traveling out of the solar system at...Ch. 2 - Prob. 52PCh. 2 - Prob. 53PCh. 2 - Prob. 54PCh. 2 - Newtons second law is given by F=dp/dt. If the...Ch. 2 - Use the result of the previous problem to show...Ch. 2 - Prob. 57PCh. 2 - Prob. 58PCh. 2 - A particle having a speed of 0.92c has a momentum...Ch. 2 - A particle initially has a speed of 0.5c. At what...Ch. 2 - Prob. 61PCh. 2 - Prob. 62PCh. 2 - Prob. 63PCh. 2 - Prob. 64PCh. 2 - Prob. 65PCh. 2 - Prob. 66PCh. 2 - Prob. 67PCh. 2 - Prob. 68PCh. 2 - Prob. 69PCh. 2 - Prob. 70PCh. 2 - What is the speed of an electron when its kinetic...Ch. 2 - Prob. 72PCh. 2 - Prob. 73PCh. 2 - Prob. 74PCh. 2 - Prob. 75PCh. 2 - Calculate the energy needed to accelerate a...Ch. 2 - Prob. 77PCh. 2 - Prob. 78PCh. 2 - Prob. 79PCh. 2 - Prob. 80PCh. 2 - The Large Hadron Collider at Europes CERN facility...Ch. 2 - What is the kinetic energy of (a) an electron...Ch. 2 - A muon has a mass of 106 MeV/c2. Calculate the...Ch. 2 - Prob. 84PCh. 2 - The reaction 2H + 3H → n + 4He is one of the...Ch. 2 - Instead of one positive charge outside a...Ch. 2 - Prob. 87PCh. 2 - Show that the following form of Newton’s second...Ch. 2 - Prob. 89PCh. 2 - For the twins Frank and Mary described in Section...Ch. 2 - Frank and Mary are twins. Mary jumps on a...Ch. 2 - A police radar gun operates at a frequency of 10.5...Ch. 2 - Prob. 93PCh. 2 - Prob. 94PCh. 2 - A proton moves with a speed of 0.90c. Find the...Ch. 2 - A high-speed K0 meson is traveling at a speed of...Ch. 2 - Prob. 97PCh. 2 - The International Space Federation constructs a...Ch. 2 - Prob. 99PCh. 2 - Prob. 100PCh. 2 - A spaceship is coming directly toward you while...Ch. 2 - Quasars are among the most distant objects in the...Ch. 2 - One possible decay mode of the neutral kaon is K0...Ch. 2 - Prob. 104PCh. 2 - Prob. 105PCh. 2 - Small differences in the wavelengths in the sun’s...
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- 3.4. Cosmic ray muons are produced high in the atmosphere (at 8000 m, say) and travel toward the earth at very nearly the speed of light (0.998 c, say). (a) Given the lifetime of the muon (2.2 x 10-6 sec), how far would it go before disintegrating, according to prerelativistic physics? Would the muons make it to ground level? (b) Now answer the same question using relativistic physics. (Because of time di- lation, the muons last longer, so they travel farther.) (c) Now analyze the same process from the perspective of the muon. (In its reference frame it only lasts 2.2 x 10-6 sec; how, then, does it make it to ground?) + (d) Pions are also produced in the upper atmosphere. [In fact, the sequence is proton (from outer space) hits proton (in atmosphere) → p + p + pions. The pions then decay into muons: ¯ → μ¯ + D µ; πt → μ† + vµ.] But the lifetime of the pion is much shorter, a hundredth that of the muon. Should the pions reach ground level? (Assume that the pions also have a speed of…arrow_forwardOne of the many fundamental particles in nature is the muon μ. This particle acts very much like a "heavy electron." It has a mass of 106 MeV/c².compared to the electron's mass of just 0.511 MeV/c². (We are using E=mc² to obtain the mass in units of energy and the speed of light c). Unlike the electron, though, the muon has a finite lifetime, after which it decays into an electron and two very light particles called neutrinos (V). We'll ignore the neutrinos throughout this problem. If the muon is at rest, the characteristic time that it takes it to decay is about 2.2 μs (Tμ = 2.2 × 10 s). Most of the time, though, particles such as muons are not at rest and, if they are moving relativistically, their lifetimes are increased by time dilation. In this problem we will explore some of these relativistic effects. Figure Earth μ 27 Proton A stream of particles, often called cosmic rays, is constantly raining down on the earth from outer space. (Figure 1) Most cosmic-ray particles are…arrow_forwardA tau lepton is a particle that decays into a muon and two particles of negligible mass. The tau lepton has a rest mass energy of 1777 MeV, and the muon has a rest mass energy of 105.7 MeV. Suppose the tau lepton is at rest and all of the missing mass goes into the muon's kinetic energy. How fast will the muon move? (Enter your answer in terms of c to at least four significant figures.)arrow_forward
- One of the many fundamental particles in nature is the muon μ. This particle acts very much like a "heavy electron." It has a mass of 106 MeV/c2, compared to the electron's mass of just 0.511 MeV/c2. (We are using E=mc2 to obtain the mass in units of energy and the speed of light c). Unlike the electron, though, the muon has a finite lifetime, after which it decays into an electron and two very light particles called neutrinos (ν). We'll ignore the neutrinos throughout this problem. If the muon is at rest, the characteristic time that it takes it to decay is about 2.2μs (τμ=2.2×10−6s). Most of the time, though, particles such as muons are not at rest and, if they are moving relativistically, their lifetimes are increased by time dilation. In this problem we will explore some of these relativistic effects. Part A: If a muon is traveling at 70% of the speed of light, how long does it take to decay in the observer's rest frame (i.e., what is the observed lifetime τμ of the muon)? Express…arrow_forwardmeasured by this observer to be 10 times longer than its lifetime when at rest relative to the observer? 3. The lifetime of a free neutron is 886 s. If a neutron moves with a speed of 2.9 x 108m/s relative to an observer in the lab, what does the observer measure the neutron's lifetime to be? 4. A computer in a laboratory requires 2.50 us to make a certain calcu- lation, as measured by a scientist in the lab. To someone moving past the lab at a relative speed of 0.995c, how long will the same cal- culation take? 5. The formula for length contraction gives the length of an interval on a ruler moving with velocity v relative to an observer as V1-v²/c² times the length of the same interval on a ruler at rest with respect to the observer. By what fraction is the length of a meter stick reduced if its velocity relative to you is measured to be 95 percent the speed of light? 6. If an electron is speeding down the two-mile-long Stanford Linear Accelerator at 99.98 percent the speed of light,…arrow_forwardA particle has γ=18,399. a) Calculate c-v in m/s. (I would have asked for 1 - v/c, making the answer dimensionless, but the system doesn't seem to take numbers that small. Gamma is chosen to make the particle extremely close to the speed of light.) If your calculator gives problems, you might want to solve the appropriate equation for c-v or c(1 - v/c) and use an approximation. b) In a race to the moon, by 3/4ths the distance, light is one or ten meters ahead of the particle. We routinely approximate mass as zero, gamma as infinite, and speed as the speed of light. ("Massless particles" -- gamma and m have to be eliminated from the expressions. Light is a true massless particle.) If a massless particle has momentum 1,739 MeV/c, calculate its energy in MeV. Thank you so much!!arrow_forward
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