Question

The positive muon (?+), an unstable particle, lives on average 2.20×10?6s (measured in its own frame of reference) before decaying. a. If such a particle is moving, with respect to the laboratory, with a speed of 0.910 c , what average lifetime is measured in the laboratory? b. What average distance, measured in the laboratory, does the particle move before decaying?

Answer 1

`4.82383* 10^(-6)\ s`

1316.90559 m

Step-by-step explanation:

`\Delta T'` = Time measured in the laboratory

`\Delta T` = Time measured in its own frame of reference =
`2.2* 10^(-6)\ s`

c = Speed of light =
`3* 10^8\ m/s`

v = 0.91 c

Time dilation is given by

`\Delta T'=\frac{\Delta T}{\sqrt{1-(v^2)/(c^2)}}\\\Rightarrow \Delta T'=\frac{2* 10^(-6)}{\sqrt{1-(0.910^2c^2)/(c^2)}}\\\Rightarrow \Delta T'=4.82383* 10^(-6)\ s`

The average lifetime is measured in the laboratory is
`4.82383* 10^(-6)\ s`

Distance measured would be

`L=v\Delta T'\\\Rightarrow L=0.91* 3* 10^8* 4.82383* 10^(-6)\\\Rightarrow L=1316.90559\ m`

The distance is 1316.90559 m