Suppose one observes cosmic rays creating a new particle high in the atmosphere and the particle moves at 99.7% the speed of light. It is observed to decay in an average 37.0 $\mu$s. What is the proper lifetime of the particle?
A) 2.86 $\mu$s
B) 18.1 $\mu$s
C) 5.33 ms
D) 12.4$\mu$s
E) 4.33 $\mu$s

Question

Quizplus · Accepted Answer

The proper lifetime of the particle is calculated using the time dilation formula in special relativity, $\tau = \frac{\tau_0}{\sqrt{1 - v^2/c^2}}$, where $\tau$ is the dilated lifetime (37.0 $\mu$s), $v$ is the velocity of the particle (99.7% the speed of light, or 0.997c), $c$ is the speed of light, and $\tau_0$ is the proper lifetime we need to find. Rearranging the formula to solve for $\tau_0$, we get $\tau_0 = \tau \sqrt{1 - v^2/c^2}$. Substituting the given values, we find that the proper lifetime is significantly shorter than the observed lifetime due to time dilation, leading to the correct answer of 2.86 $\mu$s.

Suppose One Observes Cosmic Rays Creating a New Particle High μ\muμ

Suppose One Observes Cosmic Rays Creating a New Particle High $\mu$