Recall That a π⁺ Meson Produced at Rest Has a Lifetime

question 75

Essay

Recall that a π⁺ meson produced at rest has a lifetime of 18 billionths of a second.Thus,in its own reference frame,a π⁺ meson will always "think" it is at rest and therefore decay after 18 billionths of a second
(1.8 × 10⁻⁸ s).Suppose a π⁺ meson is produced in a particle accelerator traveling at 0.998c.
a.According to scientists in the lab,how long will the π⁺ meson last compared to its normal lifetime of 18 billionths of a second (e.g. ,shorter,the same,or longer)?
b.Recall that the time dilation formula is:
$t^{\prime}=\sqrt[t]{1-\left(\frac{v}{c}\right)^{2}}$ 0
where t is the time in the laboratory and is the time for the moving particle.Use the time dilation formula to calculate how long scientists will see the π⁺ meson last before it decays.