A proton or a neutron can sometimes “violate” conservation of energy by emitting

Question

A proton or a neutron can sometimes “violate” conservation of energy by emitting and then reabsorbing a -meson, which has a mass of 135 MeV/c2. This is possible as long as the -meson is reabsorbed within a short enough time t consistent with the uncertainty principle: E.t <=h/4
a) Consider p--> p+. By what amount E is energy conservation violated ? (Ignore any kinetic energies)
b) For how long a time t can the -meson exist ?
c) Assuming the -meson to travel at very nearly the speed of light, how far from the proton can it go ?

Explanation / Answer

1) Since we ignoring kinetic energy the change in energy is just the rest mass of the meson. so E=135 MeV/c2

2) Uncertainty principle is Ethbar/4*pi so t=hbar/E=(6.59E-16eV s)/(135E6 eV)/(4*Pi)=3.89E-25 s

3) d=v*t=3E8*3.89E-25=1.17E-16 m

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