In a laboratory bubble chamber experiment [H.Whiteside et al. American Journal of Physics 34,1005 (1966)], a K^- meson was observed to interact with a stationary particle according to this scheme:
 

The bubble chamber is subjected to a strong magnetic field perpendicular to the plane of the picture.

(b) Why do the tracks that ORIGINATE at O indicate that the K meson was at rest at the time of the interaction ?
What can be inferred about the momenta of X and p⁺ from this ?
 

(c) Why are the tracks of all the particles curved ?
 

(d) What can you infer about the polarity of the magnetic field and the sign of the charge on particle X ? Explain your answer.

(e) Show that the (relativistic) momentum of a particle of charge q moving in a magnetic field B with speed v is given by
 

where R is the radius of curvature of the particle's path.

(f) (Difficult) By using conservation of momentum and the relativistic energy invariant
 

calculate the rest mass of particle X and hence its rest energy in MeV.

(g) Thus identify particle X from the selection :

(h) What other conservation law could have been used to help this identification ?

(i) What conservation law appears to be violated in this interaction ?

(j) If momentum p(v) = m(v)v where m(v) = m_o / (1-v²/c²)^1/2 write down a formula for the momentum of a particle in terms of m₀ ,v and c alone .
 

Hence derive a formula for the speed of the particles p⁺ and X and evaluate their speeds after the interaction described above.