Answer to Question #322769 in Astronomy | Astrophysics for Jonna

Question

1.   A certain type of elementary particle travels at a speed of 2.70 𝑥 108 𝑚/𝑠. At this speed, the average lifetime is measured to be 4.76 𝑥 10−6 𝑠. What is the particle’s lifetime at rest?

Answer 1

Speed of particle is $v=2.7\times 10^8 m/s$

Measured lifetime of particle is $\Delta t=4.76\times 10^{-6} s$

The average lifetime of particle at rest is

$\Delta t_0=\Delta t \sqrt{1- (\frac{v}{c})^2}$

$=(4.76\times 10^{-6} s)\sqrt{1- (\frac{2.7 \times10^8}{3.0 \times10^8})^2}$

$=2.075 \times 10^{-6} s$