PHYS 3310 Module 2 Self Assessment Practice Problems

Module 2 Self Assessment Practice Problems

2.1
Electromagnetic radiation from a star is observed with an earth-based telescope. The star is moving away from the earth with a speed of 0.555c. If the radiation has a frequency of 8.64 x 1014 Hz in the rest frame of the star, what is the frequency measured by an observer on earth?
Answer: 4.62 x 1014 Hz
2.2

A red dwarf star at 3000 K has a peak in its emittance at 1000 nm but observing from Earth, the red dwarf appears red (650 nm). Estimate its speed with respect to Earth.
Answer: 0.403c
2.3
A muon is traveling at 0.984c.
(a) What is its momentum? (The mass of such a muon at rest in the laboratory is 207 times the electron mass.)
(b) What is its kinetic energy?
Answer: (a) 584 MeV/c (b) 488 MeV
2.4
Electrons are accelerated through a potential difference of 750 kV, so that their kinetic energy is 7.5 x 105 eV.
(a) What is the ratio of the speed of an electron having this energy to the speed of light, c?
(b) What would the speed be if it were computed from the principles of classical mechanics?
Answer: (a) 0.914 (b) 1.71c
2.5
Find the momentum, kinetic energy, and total energy of a proton moving at a speed of 0.835c.
Answer: 1423 MeV/c, 767 MeV, 1705 MeV
2.6
(a) According to observer O, a certain particle has a momentum of 1256 MeV/c and a total relativistic energy of 1351 MeV. What is the rest energy of this particle?
(b) An observer O′ in a different frame of reference measures the momentum of this particle to be 857 MeV/c. What does O′ measure for the total relativistic energy of the particle?
Answer: (a) 498 MeV (b) 991 MeV
2.7
An electron and a proton are each accelerated starting from rest through a potential difference of 12.0 million volts. Find the momentum (in MeV/c) and the kinetic energy (in MeV) of each, and compare with the results of using the classical formulas.
Answer: electron: 12.5 MeV/c and 12.0 MeV; proton: 150.5 MeV/c and 12.0 MeV
2.8
A muon has a rest mass energy of 105.7 MeV, and it decays into an electron and a massless particle.
(a) If all the lost mass is converted into the electron’s kinetic energy, find 𝛾 for the electron.
(b) What is the electron’s velocity?
Answer: (a) 208 (b) 0.999988c
2.9
(a) Find the energy released as gamma rays when 2H captures a neutron to form 3H. Assume all kinetic energies are negligibly small. Atomic masses can be found in the table at the end of this module.
(b) Repeat for capture of a neutron by 3He to form 4He.
Answer: (a) 6.26 MeV (b) 20.8 MeV
2.10
In a nuclear reactor, each atom of uranium (of atomic mass 235 u) releases about 210 MeV when it fissions. What is the change in mass when 1.50 kg of uranium-235 is fissioned?
Answer: 1.4 grams