Question

An unstable particle produced in an accelerator experiment travels at constant velocity, covering 1.00 m in 3.44 ns in the lab frame before changing ("decaying") into other particles.In the rest frame of the particle determine how long it lived before decaying?

Answer 1

Answer:

$1.3922\times 10^{-8}\ s$

Explanation:

$\Delta x$ = Distance covered = 1 m

$\Delta t_l$ = Time taken = 3.44 ns

c = Speed of light = $3\times 10^8\ m/s$

Velocity would be

$v=\frac{\Delta x}{\Delta t_l}\\\Rightarrow v=\frac{1}{3.44\times 10^{-9}}\\\Rightarrow v=290697674.4186\ m/s$

Time in rest frame is given by

$\Delta t'=\frac{\Delta t_l}{\sqrt{1-\frac{v^2}{c^2}}}\\\Rightarrow \Delta t'=\frac{3.44\times 10^{-9}}{\sqrt{1-\frac{290697674.4186^2}{(3\times 10^8)^2}}}\\\Rightarrow \Delta t'=1.3922\times 10^{-8}\ s$

It lived $1.3922\times 10^{-8}\ s$ before decaying