Question

An exotic particle with a half life of 223.93microseconds, according to clocks with no relative motion, is observed to travel through the atmosphere (with a thickness of about 500km to reach the surface of the Earth). The particles are found to be moving at speed 0.999c when detected on the surface of the Earth. These particles are known to be produced at the top of the atmosphere. Calculate the fraction of particles that make through the surface of the Earth before decaying. (Answer with three sig figs)

My Answer: 0.00572

Answer 1

at rest frame - 223.93 x half life time lo byer Δί half life time observed by earth Observer 223.93*10-6 VI-Y? st= - 2 C2 0.9990) - 5008.48 x10-6 sec In2 Now decay constant d ot 138.39 > Sv Now time required to reach at earch earth's surface (observed from earth) 500 km = 1.668 X10-3 sec t = 0.999c st Now It No e No NO N = e-(138-39x1.668x10-3) (0.2 308 3452) No 0.794