Question

The life time of muon in the rest frame is 2 × 10^-6 sec. A beam of muons emerges from a cyclotron with velocity where c is the velocity of light The mean life of muons observed in the laboratory frame will be ______.

Options

• 0.25 × 10^-6 sec

• 0.3 × 10^-6 sec

• 3.3 × 10^-6 sec

• 4.2 × 10^-6 sec

Answer 1

The life time of muon in the rest frame is 2 x 10^-6 sec. A beam of muons emerges from a cyclotron with velocity where c is the velocity of light The mean life of muons observed in the laboratory frame will be 3.3 × 10^-6 sec.

Explanation:

By concept of this dilation

`Delta "t" = (Delta "t"_"o")/sqrt(1 - "V"^2/"C"^2)`

`= (2 xx 10^-6)/sqrt(1 - (0.8)^2)`

`= (2 xx 10^-6)/sqrt(0.36)`

`= 10/3 xx 10^-6`

`= 3.33 xx 10^-6` sec