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
Expert's answer

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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