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):

where \Delta t_{0} 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:

Answer: 4) 7 times.

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