College Physics (4th Edition)

Published by McGraw-Hill Education
ISBN 10: 0073512141
ISBN 13: 978-0-07351-214-3

Chapter 26 - Problems - Page 1011: 40

Answer

As measured in the lab, the lifetime is 910 seconds.

Work Step by Step

We can find the Lorentz factor $\gamma$: $K = (\gamma-1)~m~c^2$ $\gamma = 1+\frac{K}{m~c^2}$ $\gamma = 1+\frac{ 25~MeV}{939.57~MeV}$ $\gamma = 1.0266$ We can find the decay time $\Delta t$ in the lab frame: $\Delta t = \gamma~\Delta t_0$ $\Delta t = (1.0266)(886~s)$ $\Delta t = 910~s$ As measured in the lab, the lifetime is 910 seconds.
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