Question

A kaon with a speed 0.8c in the laboratory decays into two pions, one positively charged and the other negatively charged. The rest mass of the kaon is 498 MeV/c2 and the rest mass of the pion is 140 MeV/c2.

(a) What is the total energy of the kaon in the laboratory frame?

(b) In the rest frame the two pions must go off in opposite directions to conserve momentum. What is the energy of each of the pions in the kaon rest frame?

(c) Assume that the positive pion continues to travel in the same direction as the kaon was traveling. What is the total energy of each of the pions in the laboratory?

(d) In what direction, relative to the kaon’s original direction of travel, does the negatively charged pion travel?

Answer 1

(a) Total energy of the kaon in the laboratory frame

(b) Energy of pion in the kaon’s frame

Conservation of energy in the rest frame of the kaon

Velocity of pion in Kaon’s frame

Velocities of pions in the lab frame of reference

Relative velocity of the kaon with the laboratory frame is 0.8c

(c) Energy of the pion in the laboratory frame

(d) Direction of the negative pion

The negative pion travels opposite to the direction of the kaon, since the positive pion travels in the positive direction. Refer the velocity of the second pion in laboratory frame calculated above.