320
6 Special Theory of Relativity
6.11 A π -meson with a kinetic energy of 140 MeV decays in flight into μ-meson
and a neutrino. Calculate the maximum energy which (a) the μ-meson (b) the
neutrino may have in the Laboratory system (Mass of π -meson = 140 MeV/c
2 ,
mass of μ-meson = 106 MeV/c, mass of neutrino = 0)
[University of Bristol 1968]
6.12 A positron of energy E + , and momentum p + and an electron, energy E − ,
momentum p − are produced in a pair creation process
(a) What is the velocity of their CMS?
(b) What is the energy of either particle in the CMS?
6.13 A particle of mass m collides elastically with another identical particle at rest.
Show that for a relativistic collision
tan θ tan ϕ = 2/(γ + 1)
where θ, ϕ are the angles of the out-going particles with respect to the direction of the incident particle and γ is the Lorentz factor before the collision.
Also, show that θ + ϕ ≤ π/2 where the equal sign is valid in the classical
limit
6.14 A K
+ meson at rest decays into a π
+ meson and π
0 meson. The π
+ meson
decays into a μ meson and a neutrino. What is the maximum energy of the
final μ meson? What is its minimum energy?
(m K = 493.5 MeV/c
2
, m π + = 139.5 MeV/c
2
, m π 0 = 135 MeV/c
2
,
m μ = 106 MeV/c
2
, m ν = 0)
6.15 An unstable particle decays in its flight into three charged pions (mass
140 MeV/c
2 ). The tracks recorded are shown in Fig. 6.2, the event being
coplanar. The kinetic energies and the emission angles are
T 1 = 190 MeV, T 2 = 321 MeV, T 3 = 58 MeV
θ 1 = 22.4
◦
, θ 2 = 12.25
◦
Estimate the mass of the primary particle and identify it. In what direction was
it moving?
Fig. 6.2 Decay of a kaon into
three poins
6.2.2 Length, Time, Velocity
6.16 If a rod travels with a speed ν = 0.8 c along its length, how much does it
shrink?
6 Special Theory of Relativity
6.11 A π -meson with a kinetic energy of 140 MeV decays in flight into μ-meson
and a neutrino. Calculate the maximum energy which (a) the μ-meson (b) the
neutrino may have in the Laboratory system (Mass of π -meson = 140 MeV/c
2 ,
mass of μ-meson = 106 MeV/c, mass of neutrino = 0)
[University of Bristol 1968]
6.12 A positron of energy E + , and momentum p + and an electron, energy E − ,
momentum p − are produced in a pair creation process
(a) What is the velocity of their CMS?
(b) What is the energy of either particle in the CMS?
6.13 A particle of mass m collides elastically with another identical particle at rest.
Show that for a relativistic collision
tan θ tan ϕ = 2/(γ + 1)
where θ, ϕ are the angles of the out-going particles with respect to the direction of the incident particle and γ is the Lorentz factor before the collision.
Also, show that θ + ϕ ≤ π/2 where the equal sign is valid in the classical
limit
6.14 A K
+ meson at rest decays into a π
+ meson and π
0 meson. The π
+ meson
decays into a μ meson and a neutrino. What is the maximum energy of the
final μ meson? What is its minimum energy?
(m K = 493.5 MeV/c
2
, m π + = 139.5 MeV/c
2
, m π 0 = 135 MeV/c
2
,
m μ = 106 MeV/c
2
, m ν = 0)
6.15 An unstable particle decays in its flight into three charged pions (mass
140 MeV/c
2 ). The tracks recorded are shown in Fig. 6.2, the event being
coplanar. The kinetic energies and the emission angles are
T 1 = 190 MeV, T 2 = 321 MeV, T 3 = 58 MeV
θ 1 = 22.4
◦
, θ 2 = 12.25
◦
Estimate the mass of the primary particle and identify it. In what direction was
it moving?
Fig. 6.2 Decay of a kaon into
three poins
6.2.2 Length, Time, Velocity
6.16 If a rod travels with a speed ν = 0.8 c along its length, how much does it
shrink?