Question: A positively charged K meson-a K⁺ kaon-with a momentum p = 8.2 GeV/c enters a bubble chamber (a device in which charged particles leave visible tracks) and decays into two pions: K⁺ → π⁺ + π⁰. The rest mass of the kaon is 494 MeV/c2 and that of each pion is 140 MeV/c2.

a. Calculate the total energy of the kaon. Do this exactly.

b. What is the value of γ? Find the speed of the kaon in terms of c. Is the ultra-relativistic approximation valid for this kaon?

c. The K+ has an average lifetime of 12.4 ns in its rest frame. What lifetime would you measure in the rest frame of the bubble chamber?

d. In the rest frame of the bubble chamber how far (on average) would a kaon travel before decaying? What distance would this be in the kaon's frame of reference?

e. Suppose that the two pions have the same kinetic energy. What would that kinetic energy be? What is the value of γ for either pion? What is the magnitude of the momentum of either pion?

f. Assuming that the paths of the pions make equal angles θ, find θ (Fig.).

Fig. - A positively charged kaon travelling through a bubble chamber disintgrates into two pions. This diagram shows their momenta before and after the disintegration.