324
6 Special Theory of Relativity
(c) If the alphas are to further break into neutrons and protons, then show that
the overall energy needed is identical with the results in (a)
6.45 The kinetic energy and the momentum of a particle deduced from measurements on its track in nuclear photographic emulsions are 250 MeV and
368 MeV/c, respectively. Determine the mass of the particle in terms of electron mass and identify it.
[University of Durham]
6.46 What is the rest mass energy of an electron (m e = 9.1 × 10
−31 kg)?
6.47 What potential difference is required to accelerate an electron from rest to
velocity 0.6 c?
6.48 At what velocity does the relativistic kinetic energy differ from the classical
energy by
(a) 1% (b) 10%?
6.49 Prove that if ν/c 1, the kinetic energy of a particle will be much less
than its rest energy. Further show that the relativistic expression reduces to the
classical one for small velocities.
6.50 Find the effective mass of a photon for
(a) λ = 5,000 ˚
A (visible region) (b) λ = 1 ˚
A (X-ray region)
6.51 Show that 1 amu = 931.5 MeV/c
2
6.52 Estimate the energy that is released in the explosion of a fission bomb containing 5.0 kg of fissionable material
6.53 A proton moving with a velocity βc collides with a stationary electron of mass
m and knocks it off at an angle θ with the incident direction. Show that the
energy imparted to the electron is approximately
T = 2mc
2
β
2 cos
2
θ/(1 − β
2 cos
2
θ)
6.54 A positive pion (m π = 273 m e ) decays into a muon (m μ = 207 m e ) and
a neutrino (m ν = 0) at rest. Calculate the energy carried by the muon and
neutrino, given that m e c
2
= 0.511 MeV
6.55 A body of rest mass m travelling initially at a speed of β = 0.6 makes a completely inelastic collision with an identical body initially at rest. Find (a) the
speed of the resulting body (b) its rest mass in terms of m.
6.56 A neutral particle is observed to decay into a kaon and a pion. They are produced in the opposite direction, each of them with momentum 861 MeV/c.
Calculate the mass of the neutral particle and identify it. (Mass of kaon is
494 MeV/c
2 , Mass of pion is 140 MeV/c
2 ).
6.57 A pion at rest decays via π → μ + ν. Find the speed of the muon in terms of
the masses involved.
6 Special Theory of Relativity
(c) If the alphas are to further break into neutrons and protons, then show that
the overall energy needed is identical with the results in (a)
6.45 The kinetic energy and the momentum of a particle deduced from measurements on its track in nuclear photographic emulsions are 250 MeV and
368 MeV/c, respectively. Determine the mass of the particle in terms of electron mass and identify it.
[University of Durham]
6.46 What is the rest mass energy of an electron (m e = 9.1 × 10
−31 kg)?
6.47 What potential difference is required to accelerate an electron from rest to
velocity 0.6 c?
6.48 At what velocity does the relativistic kinetic energy differ from the classical
energy by
(a) 1% (b) 10%?
6.49 Prove that if ν/c 1, the kinetic energy of a particle will be much less
than its rest energy. Further show that the relativistic expression reduces to the
classical one for small velocities.
6.50 Find the effective mass of a photon for
(a) λ = 5,000 ˚
A (visible region) (b) λ = 1 ˚
A (X-ray region)
6.51 Show that 1 amu = 931.5 MeV/c
2
6.52 Estimate the energy that is released in the explosion of a fission bomb containing 5.0 kg of fissionable material
6.53 A proton moving with a velocity βc collides with a stationary electron of mass
m and knocks it off at an angle θ with the incident direction. Show that the
energy imparted to the electron is approximately
T = 2mc
2
β
2 cos
2
θ/(1 − β
2 cos
2
θ)
6.54 A positive pion (m π = 273 m e ) decays into a muon (m μ = 207 m e ) and
a neutrino (m ν = 0) at rest. Calculate the energy carried by the muon and
neutrino, given that m e c
2
= 0.511 MeV
6.55 A body of rest mass m travelling initially at a speed of β = 0.6 makes a completely inelastic collision with an identical body initially at rest. Find (a) the
speed of the resulting body (b) its rest mass in terms of m.
6.56 A neutral particle is observed to decay into a kaon and a pion. They are produced in the opposite direction, each of them with momentum 861 MeV/c.
Calculate the mass of the neutral particle and identify it. (Mass of kaon is
494 MeV/c
2 , Mass of pion is 140 MeV/c
2 ).
6.57 A pion at rest decays via π → μ + ν. Find the speed of the muon in terms of
the masses involved.