particle of rest mass m decays from rest into a particle of rest mass m0 and a massless photon moving to the right. Find the energy of the two particles in the final state in terms of m and m0 , as observed from a reference frame moving at velocity v to the right
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- There is a free neutron that is at rest. It decays into a proton (mass energy is 938.30 MeV), an electron (mass energy is 0.50 MeV, and an antineutrino (mass energy is negligible on the scale of MeV). What is the total kinetic energy of the decay products?An object is moving with ordinary speed 0.5c in S reference frame along a direction making an angle (tan 9 = 2) with respect to the positive x - axis. Find the zeroth component of the proper velocity.(a) A spaceship moves along the x' axis of frame S' with velocity 0.40c. Frame S' moves with velocity 0.60c with respect to frame S. Find the velocity of the spaceship with respect to frame S in unit of e. (b) After the spaceship in (a) travels 1 year in his own frame, how long of the journey with respect to frame S? (c) Given that the mass of 235 U is 235.0429 u, 231Th is 231.0363 u, and *He is 4.0026 u. Where 1 u = 1.66054 × 10-27 kg. Calculate the energy released in the nuclear reaction in unit of Joule, 235 U → 231Th + *He (d) Given elementary charge e = 1.60 × 10-19C. Convert the answer in (c) into unit of eV.
- Consider a particle that, once it comes to existence, decays on average after a short time t, where t is a time measured in the particle's frame of reference. If such a particle travels with speed v in an observer’s frame, what is the distance the particle has travelled as observed by the observer?An elementary particle produced in a laboratory experiment travels 0.230 mm through the lab at a relative speed of 0.960c before it decays (becomes another particle). (a) What is the proper lifetime of the particle? (b) What is the distance the particle travels as measured from its rest frame?When pions are brought to rest their lifetime is 1.77´10-8 s. A beam of pions is produced in an accelerator and moves at a speed of 0.99c relative to the laboratory. After moving 39 m as measured in the la, half the pions have decayed. a) from the viewpoint of an observer in the lab frame and b) from an observer at rest in the frame of the moving pions that the two numerical results given in the problem for the half-life of the pions are consistent.
- Consider a cosmic ray colliding with a nucleus in the Earth's upper atmosphere that produces a muon which has a velocity v = 0.916c. The muon then travels at constant velocity and lives 1.52 µs as measured in the muon's frame of reference. (You can imagine this as the muon's internal clock.) (a) How far (in km) does the muon in travel according to an Earth-bound observer? (b) How far (in km) does it travel as viewed by an observer moving with it? Base your calculation on its velocity relative to the Earth and the time it lives (proper time).A particle of some unknown rest mass mx, moving at +0.8c Ây relative to a stationary laboratory, collides head-on with another particle of rest mass m,, moving at – 0.6c âx relative to the same stationary lab frame. After the collision, the two particles stick together and stay stationary. (a) What is m, in terms of m,? (b) What is the mass of the final stationary object in terms of m,? (c) What is the change in kinetic energy in this collision, in terms of m,c²? 0bc 0,8CAn unstable high-energy particle is created in the laboratory, and it moves at a speed of 0.992c. Relative to a stationary reference frame fixed to the laboratory, the particle travels a distance of 1.05 × 10-3 m before disintegrating. What is (a) the proper distance and (b) the distance measured by a hypothetical person traveling with the particle? Determine the particle's (c) proper lifetime and (d) its dilated lifetime. (a) Number Units (b) Number Units (c) Number Units (d) Number Units