Answer to Question #322769 in Astronomy | Astrophysics for Jonna

Question #322769

1.   A certain type of elementary particle travels at a speed of 2.70 π‘₯ 108 π‘š/𝑠. At this speed, the average lifetime is measured to be 4.76 π‘₯ 10βˆ’6 𝑠. What is the particle’s lifetime at rest?



1
Expert's answer
2022-04-04T09:06:48-0400

Speed of particle is v=2.7Γ—108m/sv=2.7\times 10^8 m/s

Measured lifetime of particle is Ξ”t=4.76Γ—10βˆ’6s\Delta t=4.76\times 10^{-6} s

The average lifetime of particle at rest is

Ξ”t0=Ξ”t1βˆ’(vc)2\Delta t_0=\Delta t \sqrt{1- (\frac{v}{c})^2}

=(4.76Γ—10βˆ’6s)1βˆ’(2.7Γ—1083.0Γ—108)2=(4.76\times 10^{-6} s)\sqrt{1- (\frac{2.7 \times10^8}{3.0 \times10^8})^2}

=2.075Γ—10βˆ’6s=2.075 \times 10^{-6} s


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