Answer to Question #88109 in Mechanics | Relativity for Sridhar

Question #88109
how many times will the half life of an unstable particle increases as observed by an observer on the Earth if the particle moves with a velocity of 0.99C with respect to the observer 1)4 times 2)5 times 3)6 times 4)7 times
1
Expert's answer
2019-04-24T10:09:47-0400

Lorentz transformations predict the following relation between the time intervals in the moving (with the object) and laboratory (that is "at rest") frames (i.e., the time dilation phenomenon):


@$\Delta t = \frac{\Delta t_0}{\sqrt{1-\frac{v^2}{c^2}}},@$

where \Delta t0 is the time interval in the frame of the moving unstable particle and \Delta t is the time interval in the laboratory frame. Hence, the increase in the half-life period of the unstable particle in respect to the laboratory frame can be obtained as follows:


@$\frac{\Delta t}{\Delta t_0} = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}} = \frac{1}{\sqrt{1-0.99^2}} \approx 7@$

Answer: 4) 7 times.



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