An unstable high-energy particle is created in the laboratory, and it moves at 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 _______________ Units

Explanation / 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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