# Determining dilated lifetime of muons.

The question provides momentum that the muons move with (3094 MeV/c) and proper lifetime (2.198 micro seconds) and asks to find the dilated lifetime.

2. t= to/((1-u^2/c^2)^1/2) and p=(mv)/((1-v^2/c^2)^1/2)

3. I think that I am supposed to use the momentum given to back order velocity then use that with the time dilation equation but I'm not sure what units I should use for the mass of the muon. I saw one with kg and one with MeV/c and I feel like I should use MeV/c but I'm not getting the units to work out and I'm just going no where right now. Any help would be nice. Thanks.

## Answers and Replies

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kuruman
Homework Helper
Gold Member
If you know γ, can you find the dilated lifetime? What equation relates relativistic momentum to γ? Since you are given the momentum, you can use that equation to find γ and then the dilated lifetime. Forget kilograms. If you use MeV/c units for the momentum and MeV/c2 units for the rest mass, the equation will work out fine.

OK thank you very much I'll work that out and see what I come out with.