What is the relationship between energy and half life in special relativity?

[QuantumJG]

Homework Statement

A particle has a rest mass of m₀ and a half life of t₀. An observer measures the half life of the particle, which has a total energy of E and a momentum of p.

Find an algebraic expression for the half life the observer measures for the particles, using only the symbols defined above.

I really don't know how to start this problem!

 

[tiny-tim]

Hi QuantumJG! :smile

With questions like this, be logical …

start by writing out all the relevant equations you know (in this case, including the decay-rate equation) …

what do you have? ​

 

[QuantumJG]

Really all that I have is:

E^2 = (pc)^2 + (mc^2)^2

t = γt_0

 

[eXorikos]

And the equations for the decay?

 

[diffusion]

Hi Joel. :)

This problem becomes very simple when you recognize that

$\gamma = \frac{E_{total}}{E_{rest}}$