Question

Neutrons have an average lifetime of 15 minutes when at rest in the laboratory. Find the lifetime of the neutron, in minutes, with a speed 0.2c.

Answer 1

15.31 minutes

Explanation:

Given:

Time (t) = 15 min

Speed (v) = 0.2 c

where c is the speed of light

We can determine the lifetime using the following formula:

`\begin{gathered} \Delta t^(\prime)=\frac{\Delta t}{\sqrt{1-(v^2)/(c^2)}} \\ \\ \text{ We replacing:} \\ \\ \:\Delta t^(\prime)==\frac{15}{\sqrt{1-(\left(0.2c\right)^2)/(c^2)}} \\ \\ \Delta t^(\prime)=(15)/(√(1-0.4)) \\ \\ \Delta t^(\prime)=(15)/(√(0.96)) \\ \\ \Delta t^(\prime)=15.31\text{ min} \end{gathered}`

Therefore, the lifetime of the neutron is 15.31 minutes.