Speed of a Relativistic Particle?

In summary, particle track detectors are used to measure the speed of particles with known lifetimes. A particle, X, with a lifetime of 256.2 ps is created by a given reaction inside the detector. On average, these particles leave tracks 21.8 cm long before decaying into other unobservable particles. In order to calculate the average speed of these particles in terms of the speed of light, relevant equations for relativistic speed and muons should be researched.
  • #1
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Homework Statement



Particle track detectors are used to measure the speed of particles if the lifetime of the particle is known. Particle X has a lifetime of 256.2 ps. These particles are created in an experiment inside the detector by a given reaction. The particles leave 21.8 cm long tracks on average before they decay into other particles not observable by the detector.
What is the average speed of the particles in terms of the speed of light?


Homework Equations



Not sure?



The Attempt at a Solution


While this is a question of relativistic speed of the particle... I'm not sure what the average track length relates to the lifetime of the particle? Can anyone point me in the direction of the relevant equations? Thanks
 
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  • #2
The particles come into existence inside the detector. They travel some distance in some time, then decay and disappear. If this were non-relativistic, you could just do d=vt, sub in the lifetime as t and the track length as d. But it's relativistic - what do you do?

PS: You might want to look up muons in relation to tests of special relativity.
 

1. What is the speed of a relativistic particle?

The speed of a relativistic particle is defined by the theory of special relativity and can approach the speed of light, which is approximately 299,792,458 meters per second.

2. How is the speed of a relativistic particle calculated?

The speed of a relativistic particle can be calculated using the equation v = c * (1 - (v^2/c^2))^(-1/2), where v is the velocity of the particle and c is the speed of light.

3. What is the significance of the speed of a relativistic particle?

The speed of a relativistic particle is significant because it helps explain the behavior of objects at high speeds and has important implications for understanding the nature of time and space.

4. Can anything travel faster than the speed of light?

According to the theory of special relativity, nothing can travel faster than the speed of light. This is considered a fundamental law of the universe.

5. How does the speed of a relativistic particle affect its energy and mass?

As an object approaches the speed of light, its energy and mass increase infinitely. This is known as relativistic mass and is a key concept in the theory of special relativity.

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