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physics
modern physics

Physics 10th edition David Young, Shane Stadler - Solutions

For the decay Λ0 → n + π –, calculate (a) The Q-value (energy released), and (b) The kinetic energy of the p and π –, assuming the Λ0 decays from rest. (Use relativistic formulas).
(a) Show, by conserving momentum and energy, that it is impossible for an isolated electron to radiate only a single photon.(b) With this result in mind, how can you defend the photon exchange diagram in Fig. 32-7?
What would be the wavelengths of the two photons produced when an electron and a positron, each with 420keV of kinetic energy, annihilate head on?
In the rare decay π+ →e+ + ve, what is the kinetic energy of the positron? Assume the π+ decays from rest.
Which of the following reactions and decays are possible? For those forbidden, explain what laws are violated. (a) π – + p → n + η0 (b) π + + p → n + π0 (c) π + + p → p + e0 (d) p →e+ + vp (e) μ + →e+ + vp (f) p → n + e + + vc
Calculate the kinetic energy of each of the two products in the decay Ξ →Λ0 + π –. Assume the decays from rest.
Could a π + meson be produced if a 100-MeV proton struck a proton at rest? What minimum kinetic energy must the incoming proton have?
Calculate the maximum kinetic energy of the electron in the decay μ– → e– + vc + vμ.
Use Fig. 32-11 to estimate the energy width and then the lifetime of the ∆ resonance using the uncertainty principle.
The measured width of the J/ψ meson is 88keV. Estimate its lifetime.
The measured width of the ψ (3685) meson is 277 keV. Estimate its lifetime.
What is the energy width (or uncertainty) of? (a) η0, and (b) ∑0? See Table 32-2.
The B – meson is a bu quark combination.(a) Show that this is consistent for all quantum numbers.(b) What are the quark combinations for B+, B0, B0?
What are the quark combinations that can form? (a) A neutron, (b) An anti neutron, (c) A Λ0, (d) A ∑0
What particles do the following quark combinations produce?(a) uud, (b) us,(d) du,(e) cs?
What is the quark combinations needed to produce a D0 meson (Q = B = S = 0, c = + 1)?
The Ds meson has S = c = + 1, B = 0, what quark combination would produce it?
Draw a possible Feynman diagram using quarks (as in Fig 32-13c) for the reaction π – + p → π0 + n.
Draw a Feynman diagram for the reaction n + vμ → p + μ–.
What is the total energy of a proton whose kinetic energy is 25GeV? What is its wavelength?
Assume there are 5.0 X 1013 protons at 1.0TeV stored in the 1.0-km-radius ring of the Tevatron.(a) How much current (ampere as) is carried by this beam?(b) How fast would a 1500-kg car have to move to carry the same kinetic energy as this beam?
Protons are injected into the 1.0-km-radius Fermilab Tevatron with an energy od 150GeV. If they are accelerated by 2.5MV each revolution, how far do they travel and approximately how long does it take for them to reach 1.0TeV?
(a) How much energy is released when an electron and a positron annihilate each other? (b) How much energy is released when proton and an anti proton annihilate each other? (All particles KE ≈ 0)
Which of the following reaction are possible, and by what interaction could they occur? For those forbidden explain why. (a) π – + p → K+ + ∑– (b) π + + p → K+ + ∑+ (c) π – + p → Λ0 + K0 + π 0 (d) π + + p →∑0 +
Which of the following reactions are possible, and by what interaction could they occur? For those forbiddevn explain why. (a) π – + p → K0 + p + π 0 (b) K– + p → Λ0 + π 0 (c) K+ + n → ∑+ + π0 + y (d) K + → π0 + π 0 +
One decay mode for a π+ is π+ →vμ. What would be the equivalent decay for a π –? Check conservation rules.
Symmetry breaking occurs in the electroweak theory at about 10–18m. Show that this corresponds to an energy that is on the order of the mass of the W±.
The mass of π0 can be measured by observing the reaction π– + p → π0 + n at very low incident π– kinetic energy (assume it is zero). The neutron is observed to be emitted with a kinetic energy of 0.60MeV. Use conservation of energy and momentum to determine the π0
Calculate the Q-value for each of the reactions, Eq. 32-4, for producing a pion.
Calculation the Q-value for the reaction π– + p → Λ0 + K0 +, when negative pions strike stationary protons. Estimate the minimum pion kinetic energy needed to produce this reaction.
How many fundamental fermions are there in a water molecule?
A proton and an anti proton annihilate each other at rest and produce two pions, π – and π+. What is the kinetic energy of each pion?
(a) Show that the so-called unification distance of 10–32 m in grand unified theory is equivalent to an energy of about 10 16GeV. Use the uncertainty principle, and also de Broglie’s wave length formula, and explain how they apply.(b) Calculate the temperature corresponding to 10 16GeV.
For the reaction p + p → 3p + p, where one of the initial protons is at rest, use relativistic formulas the show that the threshold energy is 6mpc2, equal to three times the magnitude of the Q-value of the reaction, where mp is the proton mass.
The lifetimes listed in Table 32-2 are in terms of proper time, measured in reference frame where the particle is at rest. If a Tau lepton is created with a kinetic energy of 450MeV, how long would its track be as measured in the lab, on average, ignoring any collisions?
Identify the missing particle in the following reactions. (a) p + p → p + n + π+ +? (b) p + ? → n + μ+
Use the quark model to describe the reaction p + n → π– + π0.
What fraction of the speed of light c is the speed of a 7.0-TeV proton?
Calculate the kinetic energies of protons whose moment a are 0.10, 1.0, and 10GeV/c, where c is the velocity of light.
Find the mean path travelled by pions whose kinetic energy exceeds their rest energy η = 1.2 times. The mean lifetime of very slow pions is τ0 = 25.5 ns.
Negative pions with kinetic energy T = 100 MeV travel an average distance l = 11 m from their origin to decay. Find the proper lifetime of these pions.
There is a narrow beam of negative pions with kinetic energy T equal to the rest energy of these particles. Find the ratio of fluxes at the sections of the beam separated by a distance l = 20 m. The proper mean lifetime of these pions is τ0 = 25.5 ns.
A stationary positive pion disintegrated into a muon and a neutrino. Find the kinetic energy of the muon and the energy of the neutrino.
Find the kinetic energy of a neutron emerging as a result of the decay of a stationary Σ- hyperons (Σ- →n +π-).
A stationary positive muon disintegrated into a positron and two neutrinos. Find the greatest possible kinetic energy of the positron.
A stationary neutral particle disintegrated into a proton with kinetic energy T = 5.3 MeV and a negative pion. Find the mass of that particle. What is its name?
A negative pion with kinetic energy T = 50 MeV disintegrated during its flight into a muon and a neutrino. Find the energy of the neutrino outgoing at right angles to the pion's motion direction.
A Σ+ hyperons with kinetic energy TΣ = 320 MeV disintegrated during its flight into a neutral particle and a positive pion outgoing with kinetic energy Tπ = 42 MeV at right angles to the hyperon's motion direction. Find the rest mass of the neutral particle (in MeV units).
A neutral pion disintegrated during its flight into two gamma quanta with equal energies. The angle of divergence of gamma quanta is Θ = 60°. Find the kinetic energy of the pion and of each gamma quantum.
A relativistic particle with rest mass m collides with a stationary particle of mass M and activates a reaction leading to formation of new particles: m + M → m1 + m2 + . . ., where the rest masses of newly formed particles are written on the right-hand side. Making use of the invariance of
A positron with kinetic energy T = 750 keV strikes a stationary free electron. As a result of annihilation, two gamma quanta with equal energies appear. Find the angle of divergence between them.
Find the threshold energy of gamma quantum required to form (a) An electron-positron pair in the field of a stationary electron; (b) A pair of pions of opposite signs in the field of a stationary proton.
Protons with kinetic energy T strike a stationary hydrogen target. Find the threshold values of T for the following reactions: (a) p + p → p + p + p + p ; (b) p + p → p + p + π0.
A hydrogen target is bombarded by pions. Calculate the threshold values of kinetic energies of these pions making possible the following reactions: (a) π- + p → K+ + Σ-; (b) π0 + p → K+ + Λ0.
Find the strangeness S and the hypercharge Y of a neutral elementary particle whose isotopic spin projection is Tz = + ½ and baryon charge B = +1. What particle is this?
Suppose the two lightning bolts shown in Fig. 37.5a are simultaneous to an observer on the train. Show that they are not simultaneous to an observer on the ground. Which lightning strike does the ground observer measure to come first?
The positive muon (µ+), an unstable particle, lives on average 2.20 x 10-6 s (measured in its own frame of reference) before decaying. (a) If such a particle is moving, with respect to the laboratory, with a speed of 0.900c, what average lifetime is measured in the laboratory? (b) What average
How fast must a rocket travel relative to the earth so that time in the rocket "slows down'" to half its rate as measured by earth-based observers? Do present-day jet planes approach such speeds?
A spaceship flies past Mars with a speed of 0.985c relative to the surface of the planet. When the spaceship is directly overhead, a signal light on the Martian surface blinks on and then off. An observer on Mars measures that the signal light was on for 75.0µ.s.(a) Does the observer on Mars or
The negative pion (π-) is an unstable particle with an average lifetime of 2.60 x 10-8 s (measured in the rest frame of the pion). (a) If the pion is made to travel at very high speed relative to a laboratory, its average lifetime is measured in the laboratory to be 4.20 x 10-7s. Calculate
As you pilot your space utility vehicle at a constant speed toward the moon a race pilot flies past you in her space racer at a constant speed of 0.800c relative to you. At the instant the space racer passes you, both of you start timers at zero. (a) At the instant when you measure that the space
A spacecraft flies away from the earth with a speed of 4.80 x 106 m/s relative to the earth and then returns at the same speed. The spacecraft carries an atomic clock that has been carefully synchronized with an identical clock that remains at rest on earth. The spacecraft returns to its starting
An alien spacecraft is flying overhead at a great distance as you stand in your backyard. You see its searchlight blink on for 0.190 s. The first officer on the spacecraft measures that the searchlight is on for 12.0 ms. (a) Which of these two measured times is the proper time? (b) What is the
A spacecraft of the Trade Federation flies past the planet Corus cant at a speed of 0.600c. A scientist on Com scant measures the length of the moving spacecraft to be 74.0 m. The spacecraft later lands on Corus cant and the same scientist measures the length of the now stationary spacecraft. What
A meter stick moves past you at great speed. Its motion relative to you is parallel to its long axis. If you measure the length of the moving meter stick to be 1.00 ft (1 ft = 0.3048 m)-for example, by comparing it to a I-foot ruler that is at rest relative to you--at what speed is the meter stick
Why Are We Bombarded by Muons? Muons are unstable subatomic particles that decay to electrons with a mean lifetime of 22p.s. They are produced when cosmic rays bombard the upper atmosphere about 10km above the earth's surface, and they travel very close to the speed of light. The problem we want to
An unstable particle is created in the upper atmosphere from a cosmic ray and travels straight down toward the surface of the earth with a speed of 0.99540c relative to the earth. A scientist at rest on the earth's surface measures that the particle is created at an altitude of 45.0km. (a) As
As measured by an observer on the earth, a spacecraft runway on earth has a length of 3600 m. (a) What is the length of the runway as measured by a pilot of a spacecraft flying past at a speed of 4.00 x 107 m/s relative to the earth? (b) An observer on earth measures the time interval from when the
Solve Eqs (37.21) to obtain x and f in terms of x' and t', and show that the resulting transformation has the same form as the original one except for a change of sign for u.
An observer in frame S' is moving to the right (+ x-direction) at speed u = 0.600c away from a stationary observer in frame S. The observer in S' measures the speed v' of a particle moving to the right away from her. What speed v does the observer in S measure for the particle if (a) v' = 0.400c;
Space pilot Mavis zips past Stanley at a constant speed relative to him of O.800e. Mavis and Stanley start timers at zero when the front of Mavis's ship is directly above Stanley. When Mavis reads 5.00 s on her timer, she turns on a bright light under the front of her spaceship. (a) Use the Lorentz
A pursuit spacecraft from the planet Tatooine is attempting to catch up with a Trade Federation cruiser. As measured by an observer on Tatooine, the cruiser is traveling away from the planet with a speed of 0.600c. The pursuit ship is traveling at a speed of 0.800e relative to Tatooine, in the same
Equation 37.23 gives the transformation for only the x-component of an object's velocity. Suppose the object considered in the derivation also moved in the y/y'-direction. Find an expression for u, in terms of the components of u', v, and c, which represents the transformation for the y-component
Two particles are created in a high-energy accelerator and move off in opposite directions. The speed of one particle, as measured in the laboratory, is 0.650c, and the speed of each particle relative to the other is 0.950c. What is the speed of the second particle, as measured in the laboratory?
Two particles in a high-energy accelerator experiment are approaching each other head-on, each with a speed of 0.9520e as measured in the laboratory. What is the magnitude of the velocity of one particle relative to the other?
Two particles in a high-energy accelerator experiment approach each other head-on with a relative speed of 0.890c. Both particles travel at the same speed as measured in the laboratory. What is the speed of each particle, as measured in the laboratory?
An enemy spaceship is moving toward your star fighter with a speed, as measured in your frame, of 0.400c. The enemy ship fires a missile toward you at a speed of 0.700c relative to the enemy ship (Fig. 37.28).(a) What is the speed of the missile relative to you? Express your answer in terms of the
An. imperial spaceship, moving at high speed relative to the planet Arrakis fires a rocket toward the planet with a speed of 0.920c relative to the spaceship. An. observer on Arrakis measures that the rocket is approaching with a speed of 0.360c. What is the speed of the spaceship relative to
Rewrite Eq. 37.25 to find the relative velocity u between the electromagnetic source and an observer in terms of the ratio of the observed frequency and the source frequency of light. What relative velocity u will produce? (a) A 5.0% decrease in frequency and (b) An increase by a factor of 5 of the
Tell It to the Judge. (a) How fast must you be approaching a red traffic light (λ = 615 nm) for it to appear yellow (λ = 575 nm)? Express your answer in terms of the speed of light (b) If you used this as a reason not to get a ticket for running a red light, how much of a fine would
Show that when the source of electromagnetic waves moves away from us at 0.600c, the frequency we measure is half the value measured in the rest frame of the source.
(a) A particle with mass m moves along a straight line under the action of a force F directed along the same line. Evaluate the derivative in Eq. (37.29) to show that the acceleration a = dv/dt of the particle is given by a = (F/m) (l- v2/c2)3/2. (b)Evaluate the derivative in Eq. (37.29) to find
When should you Use Relativity? As you have seen, relativistic calculations usually involve the quantity 'Y. When 'Y is appreciably greater than 1, we must use relativistic formulas instead of Newtonian ones, for what speed v (in terms of c) is the value of' γ (a) 1.0% greater than 1; (b)
(b) A force is applied to a particle along its direction of motion. At what speed is the magnitude of force required to produce a given acceleration twice as great as the force required to produce the same acceleration when the particle is at rest? Express your answer in terms of the speed of light
Relativistic Baseball Calculate the magnitude of the force required to give a 0.145-kg baseball an acceleration a = 1.00 m/S' in the direction of the baseball's initial velocity when this velocity has a magnitude of (a) 10.0 m/s; (b) 0.900c;(c) 0.990c. (d) Repeat parts (a), (b), and (c) If the
What is the speed of a particle whose kinetic energy is equal to (a) its rest energy and (b) five times its rest energy?
A proton (rest mass 1.61 x l0x27 kg) has total energy that is 4.00 times its rest energy. What are (a) The kinetic energy of the proton; (b) The magnitude of the momentum of the proton; (c) The speed of the proton?
(a) How much work must be done on a particle with mass m to accelerate it (a) from rest to a speed of 0.090c and (b) From a speed of 0.900c to a speed of 0.990c? (Express the answers in terms of me2.) (c) How do your answers in parts (a) and (b) compare?
(a) By what percentage does your rest mass increase when you climb 30 m to the top of a ten-story building? Are you aware of this increase? Explain. (b) By how many grams does the mass of a 120-g spring with force constant 200N/cm change when you compress it by 6.0 cm? Does the mass increase or
A 60.0-kg person is standing at rest on level ground. How fast would she have to run to (a) Double her total energy and (b) Increase her total energy by a factor of 10?
An Antimatter Reactor when a particle meets its antiparticle, they annihilate each other and their mass is converted to light energy. The United States uses approximately 1.0 x 1019 J of energy per year.(a) If all this energy came from a futuristic antimatter reactor, how much mass of matter and
A particle has rest mass 6.64 x 10-27 kg and momentum 2.10 x 10-18 kg ∙ m. (a) What is the total energy (kinetic plus rest energy) of the particle? (b) What is the kinetic energy of the particle? (c) What is the ratio of the kinetic energy to the rest energy of the particle?
Starting from Eq. (37.39), show that in the classical limit (pc « mc2) the energy approaches the classical kinetic energy ½ mv2 plus the rest mass energy mc2.
Compute the kinetic energy of a proton (mass 1.61 x 10-27 kg using both the non-relativistic and relativistic expressions, and compute the ratio of the two results (relativistic divided by non-relativistic) for speeds of (a) 8.00 x 107m/s and(b) 285 x 108m/s
What is the kinetic energy of a proton moving at? (a) 0.100c;(b) 0.500c; (c) 0.900c? How much work must he done to (d) Increase the proton's speed from 0.l00c to 0.500c and (e) Increase the proton's speed from 0.500c to 0.900c? (f) How do the last two results compare to results obtained in the
(a) Through what potential difference does an electron have to be accelerated, starting from rest, to achieve a speed of 0.980c?(b) What is the kinetic energy of the electron at this speed? Express your answer in joules and in electron volts.
Creating a Particle two protons (each with rest mass M = 1.67 x 10-7 kg) are initially moving with equal speeds in opposite directions. The protons continue to exist after a collision that also produces a 71° particle (see Chapter 44). The rest mass of the 71° is m = 9.75 x 10-28 kg. (a) If the
Find the speed of a particle whose relativistic kinetic energy is 50% greater than the Newtonian value for the same speed.
Energy of Fusion In a hypothetical nuclear fusion reactor, two deuterium nuclei combine or ''fuse'' to form one helium nucleus. The mass of a deuterium nucleus, expressed in atomic mass units (u), is 20136 u; the mass of a helium nucleus is 4.00l5u (1 u = 1.6605402 x 10-27 kg). (a) How much energy
The sun produces energy by nuclear fusion reactions, in which matter is converted into energy. By measuring the amount of energy we receive from the sun, we know that it is producing energy at a rate of 3.8 x 1026 w. (a) How many kilograms of matter does the sun lose each second? Approximately how

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