It is possible for some fundamental particles to violateconservation of energy b

Question

It is possible for some fundamental particles to violateconservation of energy by creating and quickly reabsorbing anotherparticle. For example, a proton can emit a + accordingto = n + + where the n represents a neutron. The+ has a mass of 140 MeV/c2. The reabsorptionmust occur with a time t consistent with the uncertaintyprinciple.
a) Considering the example shown, by how much E isenergy conservation violated? (Ignore kinetic energy)
b) For how long t can the + exist?
c) Assuming that the + is moving at nearly the speed of lighthow far from the nucleus could it get in the time t? (this isthe approximate range of the short nuclear force.)

Explanation / Answer

Mass of neutron = 939.550 Mev / c2 Mass of proton   = 939.256    " difference         =       .294 So the total violation of conservation of energy is 140.294Mev / c2 in mass units And in units of energy E =   140.294 Mev* 1.60 * 10E-13 J / Mev = 2.24 * 10E-11 J And in units of energy E =   140.294 Mev* 1.60 * 10E-13 J / Mev = 2.24 * 10E-11 J By the uncertainty principle   E t>= h    and t = 6.625 * 10E-34J sec / 2.24 *10E-11 J = 2.96 * 10E-23 sec Distance s = c t = 2.96 * 10E-23 sec * 3 * 10E8m/sec = 8.9 * 10E-15 m Or about 10E-14 m   or about 10 fermi which is onlya few nuclear radii for smaller nuclei

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