Half-Life of He-6 Nucleus: 40 GeV

[sawhai]

Homework Statement

The question asks: "What is the half-life of a He-6 nucleus with total(kinetic+rest) energy E=40 GeV?"

How can we approach this problem?

Homework Equations

E=mc2 ;

The Attempt at a Solution

I thought of getting the mass of the He-6 using M=E/c2 =>40GeV/931.5MeV = 4.25 amu = 7.05*10^-26 kg. I am not sure if this helps and what to do next.

Thanks

 

[tiny-tim]

hi sawhai!

(try using the X₂ button just above the Reply box )

my guess is that you're supposed to find the speed, and then use time dilation to find the half-life (looking up the stationary half-life in a table)

 

[sawhai]

Ok, I think I now understand. Here is what I did:

Gamma = E/mc^2 = 40GeV/6*931.5MeV = 7.15

t1/2 = t1/2 (Stationary)*gamma = 7.15*807ms

Does this sound ok?

 

[tiny-tim]

looks ok!

 

[sawhai]

Thanks. Now another question

An electron accelerated to 106 keV colides with another free electron and recoils. Its energy after the collision is 26 keV.
(a) What is the energy of the other electron that was initially at rest? I said E=106-26=80keV
(b)Assume the target electron is from the innermost shell of a Tungsten atom. Is the bound electron ionized in this collision? (the potential energy of the Tungsten ground state is 70keV). I said yes because 106keV is more than 70keV

Do you see any thing wrong with these answers?

Thanks

 

[Borek]

For b it is not because 106 is larger than 70, but because 80 is larger than 70.