An unstable high-energy particle is created in the laboratory, and it moves at a
ID: 1620753 • Letter: A
Question
An unstable high-energy particle is created in the laboratory, and it moves at a speed of 0.989c. Relative to a stationary reference frame fixed to the laboratory, the particle travels a distance of 1.77 times 10^-3 m before disintegrating. What is (a) the proper distance and (b) the distance measured by a hypothetical person traveling with the particle? Determine the particle's (c) proper lifetime and (d) its dilated lifetime (a) Number ______________ Units (b) Number ____________ Units (c) Number __________________ Units (d) Number _______________ UnitsExplanation / Answer
(a)
The proper distance is L = 1.77X10-3 m
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(b)
The distance measured by a hypothetical person traveling with the particle will be,
L' = L[1-v2/c2] = (1.77X10-3 m)[1-(0.989c)2/c2]
or, L' = 2.62X10-4 m
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(c)
The proper lifetime will the time measured by the hypothetical person for the particle to disintegrate...
t = L'/v = (2.62X10-4 m)/(0.989X3X108 m/s)
or, t = 8.82X10-13s is the proper lifetime.
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(d)
Dilatedl lifetime is,
t' = t/[1-(0.989c)2/c2] = (8.82X10-13s)/[1-(0.989c)2/c2]
or, t' = 5.96X10-12s
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