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 0.990c. Relative to astationary reference frame fixed to the laboratory, the particletravels a distance of 3.00 x 10-3 m beforedisintegrating. What is (a) the proper distanceand (b) the distance measured by a hypotheticalperson traveling with the particle? Determine the particle's(c) proper lifetime and (d) itsdilated lifetime.
I solved (a) and (b) and got answers of 3E-3m and 4.23E-4m.Please Help on (C) and (D). An unstable high-energy particle is created in the laboratory,and it moves at a speed of 0.990c. Relative to astationary reference frame fixed to the laboratory, the particletravels a distance of 3.00 x 10-3 m beforedisintegrating. What is (a) the proper distanceand (b) the distance measured by a hypotheticalperson traveling with the particle? Determine the particle's(c) proper lifetime and (d) itsdilated lifetime.
I solved (a) and (b) and got answers of 3E-3m and 4.23E-4m.Please Help on (C) and (D).

Explanation / Answer

Given :
speed of particle v = 0.990c distance travelled by the particle relative thestationaryframe L0 = 3.0*10-3m a) the proper distance is L0 =3.0*10-3m b) distance measured by a hypothetical person traveling withthe particle is given by length contraction as L = L0* 1-v2/c2 calculate for L c) proper life time    t0 = L0 /v = 3.0x 10-3 m / 0.990*3*108m/s = -------s d) the dilated life time is gievn by t = t0 / 1-v2/c2 calculate for t

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