A pion lives 26 ns in its rest frame.It travels 15 cm down a beam pipe in a particle accelerator before it decays into other particles.How far is this in the rest frame of the pion?
A)19.026 cm
B)18.465 cm
C)16.123 cm
D)14.997 cm
E)12.886 cm

Question

Quizplus · Accepted Answer

The distance in the rest frame of the pion can be calculated using the formula for length contraction: $L = L_0 / \gamma$, where $L_0$ is the length measured in the laboratory frame (15 cm), and $\gamma$ is the Lorentz factor, which is defined as $1/\sqrt{1 - v^2/c^2}$. Given that the pion lives 26 ns, we can find its velocity using the time dilation formula $t = \gamma t_0$, where $t_0$ is the proper time (26 ns). However, without directly calculating $\gamma$, we can understand that the length in the pion's rest frame must be shorter than in the lab frame due to length contraction, making 14.997 cm the only option that is shorter than 15 cm.

A Pion Lives 26 Ns in Its Rest Frame