Consmic ray muons, which decay spontaneously with proper lifetime 2.2 µs, are produced in the atmo sphere, at a height of 5 km above sea level. These move straight downwards at 98%of the speed of light. Find the percent ratio 100 × (N/N) of the number of muons measured at the top of two mountains A and B, which are at heights 4,848 m and 2,682 m respectively above mean sea level. A
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- The fraction of particles that have an x-component velocity between C and Cx + dCx is described by (7)¹/²e-mc3/2kT e-mc/2kT dCx. Derive the average value of the positive values of Cx.A beam of π+meson (pions) at Fermilab are traveling at a speed of 0.92cwithrespect to the laboratory. The proper mean lifetime for these pions is 2.6×10−8s.(a) Is this proper lifetime measured in the laboratory frame or the frame of the pions?Why? (b) What is the mean lifetime as measured in the other frame of reference?An alpha particle has a mass of 6.4E-27kg is propagating at relativistic speeds and has an energy of 6.48GeV (so 6.48E9 eV) What is the speed of the particle, expressed in units of c, c being the speed of light. Keep three significant digits.
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- Suppose a cosmic ray colliding with a nucleus in the Earth's upper atmosphere produces a muon that has speed v = 0.99c. The muon then travels at constant speed and lives 1.5 μs as measured in the muon's frame of reference. (You can imagine this as the muon's internal clock.)Randomized Variablesv = 0.99 ct = 1.5 μs Part (a) How many kilometers does the muon travel according to an Earth-bound observer? Part (b) How many kilometers of the Earth pass by as viewed by an observer moving with the muon? Base your calculation on its speed relative to the Earth and its lifetime (proper time).139, 6 MeV/c², resting in the laboratory, A pion of positive electric charge (n*) and mass m, = decays in a muon with the same electric charge (u*) and a neutrin of muon (v), The mass of the muon is equal to m, = 105,7 MeV/c² and that of the neutrin is practically null. a) Determine the muon speed according to an observer in the laboratory. b) What conservation laws should be considered in the present problem? Why?What is the kinetic energy in MeV of a π -meson that lives 1.40×10−16 s as measured in the laboratory, and 0.840×10−16 s when at rest relative to an observer, given that its rest energy is 135 MeV?
- The neutron has a mass of 1.67 ✕ 10−27 kg. Consider a neutron moving with a speed of 0.960c. (Enter your answer in GeV.) (a) What is its rest energy? GeV (b) What is its total energy? GeV (c) What is its kinetic energy? GeVT9 please help me with the answer and full solutionElectrons are accelerated to an energy of 13.0 GeV in the 3.00 km long Stanford Linear Accelerator. (a) What is the γ factor for the electrons?(b) What is their speed? Answer to 10 decimal places. c(c) How long does the accelerator appear to them? cm