Question

An elementary particle has a half-life of 1.5 x 10^-6 s when at rest. Find the half-life of the particle if it travels at 0.97c.

Answer 1

The half life of the particle is increases when it is moving with high speed (nearly equals to the speed of the light).

If T is the half life of the particle when it rest then the half life of the particle when it is moving with speed v is

T^| = T / [ 1- (v/c)² ]

here T = 1.5 x 10^-6 s , v = 0.97 c.

T^| = (1.5 x 10^-6 s ) / [ 1- (0.97 c /c)² ]

T^| =25.38 x 10^-6 s

T^| =2.54 x10^-5 s.

Therefore the halflife of the particle when it is moving with speed 0.97c is 2.54 x10^-5 s.