320 6 Special Theory of Relativity
6.11 Aπ-meson with a kinetic energy of 140 MeV decays in flight intoμ-meson
and a neutrino. Calculate the maximum energy which(a)theμ-meson(b)the
neutrino may have in the Laboratory system (Mass ofπ-meson=140 MeV/c^2 ,
mass ofμ-meson=106 MeV/c, mass of neutrino=0)
[University of Bristol 1968]
6.12 A positron of energyE+, and momentump+and an electron, energyE−,
momentump−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 massmcollides elastically with another identical particle at rest.
Show that for a relativistic collision
tanθtanφ= 2 /(γ+1)
whereθ,φare the angles of the out-going particles with respect to the direc-
tion of the incident particle andγis the Lorentz factor before the collision.
Also, show thatθ+φ≤π/2 where the equal sign is valid in the classical
limit
6.14 AK+meson at rest decays into aπ+meson andπ^0 meson. Theπ+meson
decays into aμmeson and a neutrino. What is the maximum energy of the
finalμmeson? What is its minimum energy?
(mK= 493 .5MeV/c^2 ,mπ+= 139 .5MeV/c^2 ,mπ 0 =135 MeV/c^2 ,
mμ=106 MeV/c^2 ,mν=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. 6.2Decay of a kaon into
three poins
6.2.2 Length, Time, Velocity .........................
6.16 If a rod travels with a speedν= 0. 8 calong its length, how much does it
shrink?