6.2 Problems 325
6.58 A particleAdecays at rest viaA→B+C. Find the total energy ofBin
termsofthemassesofA,BandC.
6.59 Calculate the maximum energy of the positron emitted in kaon decay at rest
K+→e++π^0 +γe.
6.60 Consider a symmetric elastic collision between a particle of massmand
kinetic energyTand a particle of the same mass at rest. Relativistically, show
that the cosine of the angle between the two particles after the collision is
T/(T+4mc^2 )
6.61 An electron has kinetic energy equal to its rest energy. Show that the energy
of a photon which has the same momentum as this electron is given by
Eγ=
√
3 E 0 , whereE 0 =mec^26.62 Consider the decay of muon at rest. If the energy released is divided equally
among the final leptons, then show that the angle between paths of any two
leptons is approximately 120◦(neglect the mass of leptons compared to the
mass of muon mass).
6.63 If a proton of 10^9 eV collides with a stationary electron and knock it off at
3 ◦with respect to the incident direction, what is the energy acquired by the
electron?
[Osmania University 1963]
6.64 Calculate (a) the mass of the pion in terms of the mass of the electron, given
that the kinetic energy of the muon from the pion decay at rest is 4.12 MeV
and (b) the maximum energy of electron (in MeV) from the decay of muon
at rest (mass of muon is 206. 9 me). The mass of the electron is equivalent to
0.511 MeV)
[University of Durham 1961]
6.65 Antiprotons are captured at rest in deuterium giving rise to the reaction.
p−+d→n+π^0
Find the total energy of theπ^0. The rest energies forp−,d,n,π^0 are 938.2,
1875.5, 939.5 and 135.0 MeV respectively.
6.66 As a result of a nuclear interaction aK∗+particle is created which decays to a
Kmeson and aπ−meson with rest masses equal to 966meand 273merespec-
tively. From the curvature of the resulting tracks in a magnetic field, it is con-
cluded that the momentum of the secondaryKandπmesons are 394 MeV/c
and 254 MeV/c respectively, their initial directions of motion being inclined
to one another at 154◦. Calculate the rest mass of theK∗particle
[Bristol 1964, 1966]
6.67 A proton of kinetic energy 940 MeV makes an elastic collision with a station-
ary proton in such a way that after collision, the protons are travelling at equal
angles on either side of the incident proton. Calculate the angle between the
directions of motion of the protons.
[Liverpool 1963]