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

Answer 1

(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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This concludes the answers. Check the answer and let me know if it's correct. If you need any more clarification, modification or correction, feel free to ask.....