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Fundamentals of Physics, Volume 1, Chapter 1-20
10th Edition
ISBN: 9781118233764
Author: David Halliday
Publisher: WILEY
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Chapter 38, Problem 50P
To determine
To find:
a) The value of
b) The ratio of
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(a) A particle with mass m has kinetic energy equal to three times its rest energy. What is the de Broglie wavelength of this particle? (Hint: You must use the relativistic expressions for momen- tum and kinetic energy: E2 = (pc2) + (mc2)2 and K = E - mc2.) (b) Determine the numerical value of the kinetic energy (in MeV) and the wavelength (in meters) if the particle in part (a) is (i) an electron and (ii) a proton.
Electrons accelerated to an energy of 50 GeV have a de Broglie wavelength l small enough for them to probe the structure within a target nucleus by scattering from the structure. Assume that the energy is so large that the extreme relativistic relation p = E/c between momentum magnitude p and energy E applies. (In this extreme situation, the kinetic energy of an electron is much greater than its rest energy.) (a)What is l? (b) If the target nucleus has radius R = 5.0 fm, what is the ratio R/l?
The muon is unstable and has a mean lifetime of about 2.2
microseconds. A muon is an elementary particle similar to the electron.
with an electric charge of -1 e, but with a much greater mass. The mass
of a muon is 0.1135u, where the Atomic mass unit u = 1.66 x 10^-27 kg. It decays into an electron and two neutrinos. What is the energy released in this decay (in MeV)? Recall 1 eV = 1.6 x 10^-19 J).
Chapter 38 Solutions
Fundamentals of Physics, Volume 1, Chapter 1-20
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- If the rest energies of a proton and a neutron (the two constituents of nuclei) are 938.3 and 939.6 MeV, what is the difference in their mass in kilograms?arrow_forward(a) What is the uncertainty in the energy released in the decay of a due to its short lifetime? (b) What traction of the decay energy is this, noting that the decay mode is (so that all the mass is destroyed)?arrow_forwardIn an experiment, a light source of 620 nm is used to eject electrons from a material. Initially, there is emission. The emission takes place when the material is moved towards the material at a velocity of 0.3c. From this data calculate the work function of the material.arrow_forward
- One proton is accelerated through a potential difference of 106 volts and another is accelerated through a potential energy of 1010 volts. For each proton, find the total energy, the momentum (actually find pc in MeV), and the wavelength.arrow_forwardAn ultra high energy electron (ß ≈ 1) emits a photon. (a) Derive an expression to express the emission angle 0 in the lab system in terms of 0*, the angle of emission in the rest frame of the electron. Also, (b) Show that half of the photons are emitted within a cone of half angle 01/y.arrow_forwardA linear particle accelerator using beta particles collides electrons with their anti-matter counterparts, positrons. The accelerated electron hits the stationary positron with a velocity of 19 x 106 m/s, causing the two particles to annihilate.If two gamma photons are created as a result, calculate the energy of each of these two photons, giving your answer in MeV (mega electron volts), accurate to 1 decimal place. Take the mass of the electron to be 5.486 x 10-4 u, or 9.109 x 10-31 kg.Note: Assume that the kinetic energy is also converted into the gamma rays, and is included in the two photons.arrow_forward
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