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A particle that has a lifetime of 3 us is created in a lab. Once created the particle should live for at least 1 s, so that it can be studied. Estimate the speed required to achieve a lifetime of 1 s.

A particle that has a lifetime of 3 us is created in a lab. Once created the particle should live for at least 1 s, so that it can be studied. Estimate the speed required to achieve a lifetime of 1 s.

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**Problem Statement: Estimating Particle Speed for Extended Lifetime** A particle with an intrinsic lifetime of 3 microseconds (μs) is created in a laboratory. For effective study and observation, it is desirable for this particle to have an extended observable lifetime of at least 1 second (s). Calculate the speed that the particle must achieve to attain this prolonged lifetime of 1 second.
Transcribed Image Text:**Problem Statement: Estimating Particle Speed for Extended Lifetime** A particle with an intrinsic lifetime of 3 microseconds (μs) is created in a laboratory. For effective study and observation, it is desirable for this particle to have an extended observable lifetime of at least 1 second (s). Calculate the speed that the particle must achieve to attain this prolonged lifetime of 1 second.
Expert Solution
Concept and Principle:
  • As per the special theory of relativity, the time measured by someone in a moving frame with rest to a clock will be slower than someone in the rest frame of the clock.

 

  • The time that is measured in the clock's rest frame is called the proper time.

 

  • Time dilation can be calculated using the following formula.

Δt=Δt01−v2c2

Here ∆t is the dilated time, ∆t0 is the proper time, v is the velocity, and c is the speed of light.

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