Question

A radioactive particle has a half life of 1 second. If it moves at 3/5 the speed of light, from my point of view standing still it's new half-life will be

Answer 1

The half-life observed by an observer at rest is 1.25 s

Explanation:

In this problem, the particle is travelling at a significant fraction of the speed of light: therefore, we have to consider the phenomenon of the time dilation. The half-life of the particle as measured by an observer at rest is given by

$T=\frac{T_0}{\sqrt{1-(\frac{v}{c})^2}}$

where

$T_0$ is the proper half-life of the particle

v is the speed of the particle

c is the speed of light

For the particle in this problem,

$T_0 = 1 s$

$v=\frac{3}{5}c=0.6 c$

Substituting into the equation, we find:

$T=\frac{1}{\sqrt{1-(\frac{0.6c}{c})^2}}=1.25 s$

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