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 500 km from the surface of the Earth). The particles are found to be moving at speed 0.999 c when detected on the surface of the Earth. These particles are known to be produced at the top of the atmosphere. Despite (half life=223.93microseconds) times the speed of particles being less than the thickness of the atmosphere, scientists find that less than half of the exotic particles have decayed after traveling through the atmosphere. Explain this?

Answer 1

TA The life time of the particle To = 223.93 us = 223.93x106 see. Velocity of the particle u =o.ggge = 0.999 x 3x108 mys. :. According to classical theory, the distance cover by the particle in time to Log = いて。 = 0.999x3x108 x 223.93 x166 m 671x103 m 6701 km But the thickness of the atomsphere is too Lo=500 km. Hence they can't reach ground. Now from the special theory of relativity, the length of the atmosphene will decrease from the high speed particle point of view, so the length of the aton atmosphere to the particle L = 500 |- (812 = 500 x1-0.999)2 2 22.35 km

so the thickness of the portitle atmosphere, de is less them of that what they treaved before decaying. The length contraction is the explanation for this.