Is Neutron Decay Consistent with Einstein's Mass-Energy Relationship?

[mike217]

The free neutron is known to decay into a proton, an electron, and an antineutrino v' (of negligible rest mass) according to n-->p+e+v'. The decay products are measured to have a total kinetic energy of 0.781+/-0.005 MeV. Show that this observation is consistent with the excess energy predicted by Einstein's mass-energy relationship.

Doing this problem I get: (Mn-Mp-Me)c^2=(940 MeV/c^2-938 MeV/c^2-0.511 MeV/c^2)c^2=1.489 MeV which is not equal to the change in kinetic energy 0.781+/-0.005 MeV

 

[da_willem]

I get .785 MeV. Try using more accurate numbers. See eg: http://www.mcelwee.net/html/table_of_physical_constants.html

 

[wais]

.

There are a few factors that could explain this discrepancy. First, the measured kinetic energy of the decay products is given with an uncertainty of +/-0.005 MeV, so it is possible that the actual value falls within this range and is consistent with the excess energy predicted by Einstein's mass-energy relationship.

Second, there may be other forms of energy involved in the decay process that are not accounted for in the simple equation used to calculate the excess energy. For example, there may be energy released in the form of gamma rays or other particles that are not included in the calculation.

Lastly, it is important to note that the mass of a neutron is not a fixed value, but can vary slightly depending on its energy and environment. This can also contribute to the discrepancy in the calculated excess energy.

Overall, while the observed kinetic energy of the decay products may not match exactly with the excess energy predicted by Einstein's mass-energy relationship, it is still consistent with the concept and provides further evidence for the validity of this fundamental relationship in physics.