(a) Calculate the distance it travels before decaying. (b) If the two photons em

Question

(a) Calculate the distance it travels before decaying.

(b) If the two photons emitted travel along the x axis, what are their speeds?

One of the decay modes of the no produces two photons. M pi o = 135.0 MeV/c^2 mean lifetime = 8.4x10^-15 s The pion is moving at 0.8c in the +x direction relative to the detector in the lab. (e) If the photons travel along the y axis, determine the 4-momenta for each one. (f) Using your answer to (e), write the 4-momenta for the photons if they travel along the x axis. (g) Transform your answer to (f) to a frame where the pion is moving at 0.8c in the +x direction. n degree = gamma + gamma

Explanation / Answer

The life time of pion with respect to earth is

t = t / sqrt ( 1 - ( v /c )^2 )

t = (8.4*10^ -15 s ) / sqrt ( 1 - ( 0.8c/c)^2 )

= 1.4*10^ -14 s

distance travelled by the pion is

d = v t

= ( 0.8) ( 3*10^ 8 m/s ) ( 1.4*10^ -14 s )

= 3.36*10^ -6 m

b)

since the photons are mass less particle, the speed of phtotons iis equal to the speed of light. c.

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