A moving radioactive particle of mass 5m and kinetic energy T disintegrates into two particles. One of the final particles has mass m and is at rest while the other final particle is massless and is in the forward direction as shown in the figure. What is the threshold/minimum kinetic energy T for this process to occur?
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A moving radioactive particle of mass 5m and kinetic energy T disintegrates into two particles. One of the final particles has mass m and is at rest while the other final particle is massless and is in the forward direction as shown in the figure. What is the threshold/minimum kinetic energy T for this process to occur?


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- An unstable particle at rest breaks up into two fragments of unequal mass. The mass of the lighter fragment is equal to 2.60 x 10° -28 kg and that of the heavier fragment is 1.66 × 10° -27 kg. If the lighter fragment has a speed of 0.893c after the breakup, what is the speed of the heavier fragment?An unstable particle at rest spontaneously breaks into two fragments of unequal mass. The mass of the first fragment is m1 = 2.50 x 10-28 kg, and that of the other is m2 = 1.67 x 10-27 kg. If the speed of m1 is equal to 0.893c after the breakup, where c = 3 x 108 m/s. What is the final speed of m2?A kaon with a speed 0.8c in the laboratory decays into two pions, one positively charged and the other negatively charged. The rest mass of the kaon is 498 MeV/c2 and the rest mass of the pion is 140 MeV/c2. (a) What is the total energy of the kaon in the laboratory frame? (b) In the rest frame the two pions must go off in opposite directions to conserve momentum. What is the energy of each of the pions in the kaon rest frame? (c) Assume that the positive pion continues to travel in the same direction as the kaon was traveling. What is the total energy of each of the pions in the laboratory? (d) In what direction, relative to the kaon’s original direction of travel, does the negatively charged pion travel?
- Consider the inelastic collision. Two lumps of matter are moving directly toward each other. Each lump has a mass of 0.500 kgand is moving at a speed of 0.910?. The two lumps collide and stick together. Answer the questions, keeping in mind that relativistic effects cannot be neglected in this case. What is the final speed ?f of the combined lump, expressed as a fraction of ?? ?f= ? What is the final mass ?f of the combined lump immediately after the collision, assuming that there has not yet been significant energy loss due to radiation or fragmentation? ?f=Antimatter: When a particle and its anti-particle collide, energy and momentum are conserved. However, the particles can annihilate each other and produce two gamma rays - high energy photons. An electron and an anti-electron each have a rest mass of 9.11 × 10-31 kg. Suppose the particles are each accelerated to a speed of 0.98c in a particle accelerator with a length of 1543 m for a head on collision. (Each particle is moving at this speed with respect to the lab, and the particles are moving in opposite directions.) They collide head on and annihilate. What is the wavelength of the gamma rays produced in this collision?a) What is the kinetic energy of a 1.0 g particle with a speed of 0.800c? b) What is the rest energy of a 1.0 g particle with a speed of 0.800c? c) What is the total energy of a 1.0 g particle with a speed of 0.800c?
- The star of a distant solar system explodes as a supernova. At the moment of the explosion, an resting exploration spaceship is 15 AU away from the shock wave. The shock wave of the explosion travels with 25000 km/s toward the spaceship. To save the crew, the spacecraft makes use of a special booster that uniformly accelerates at 150 m/s^2 in the opposite direction. Determine if the crew manages to escape from the shock wave. (Neglect relativistic effects.)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?Six identical particles have a speed 2m/s except for the last ( which is the seventh) particle which has a speed of 4m/s. What is the vavg of these particles?
- The muon is an unstable subatomic particle witha mean lifetime of 2.2 μs, and about 10,000 muons reach everysquare meter of the earth's surface a minute. A muon has a linear momentum G, and after some short time it decays into two other elementary particles with masses m1 and m2. The energy Q released during the decay is converted entirely into the kinetic energy of the decay products (i.e., into kinetic energy of m1 and m2). Find linear momenta of decay products. Draw a vector diagram showing a range of momenta decay products can take.A proton and anti-proton with rest energy of, E0 - 931 MEV/C“ was traveling in opposite direction at a speed of, V = 0.9995*C (where C is a speed of light equal to 3.0 * 108 m/s). After travelling in a vacuum chamber, the two particles collide head on to produce a new massive particle in the center of the chamber What is the new kinetic energy the proton and anti-proton in Giga electron Volt, after reaching the new speed? OKAn unstable particle is at rest and suddenly breaks up into two fragments. No external forces act on the particle or its fragments. One of the fragments has a velocity of +0.837c and a mass of 1.77 × 10-27 kg, and the other has a mass of 5.29 × 10-27 kg. What is the velocity of the more massive fragment (as a multiple of c)? (Hint: This problem is similar to Example 6 in Chapter 7.) Unstable particle at rest Number i V2 m2 Units m1 V1 Recoiling fragments