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Chapter 37: Q5P (page 1145)

An unstable high-energy particle enters a detector and leaves a track of length 1.05 mm before it decays. Its speed relative to the detector was 0.992c. What is its proper lifetime? That is, how long would the particle have lasted before decay had it been at rest with respect to the detector?

Short Answer

Expert verified

The proper life time for particle is 0.446ps.

Step by step solution

01

Identification of given data

The speed of particle relative to detector is v=0.992c

The length of track is L=1.05mm

The time dilation is used to find the duration for particle before decay from detector.

02

Determination of proper life time before decay of particle

The proper life time for particle is given as:

t0=LV1-vc2

Here, is the speed of light and its value is 3脳108m/s.

Substitute all the values in equation.

t0=1.05mm1m103mm0.992c3脳108m/sc1-0.992cc2t0=0.0446脳10-11st0=0.0446脳10-11s1ps10-12st0=0.446ps

Therefore, the proper life time for particle is 0.446ps .

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