Fundamentals of Physics Extended (10th Edition)

Published by Wiley
ISBN 10: 1-11823-072-8
ISBN 13: 978-1-11823-072-5

Chapter 44 - Quarks, Leptons, and the Big Bang - Problems - Page 1366: 50b

Answer

The decay scheme is $p \longrightarrow e^+ \hspace{2mm}+ \hspace{2mm} \nu_e$ $p$ = proton $e^+$= positron $\nu_e$ = electron-neutrino This does not violate the energy conservation law.

Work Step by Step

It would be sufficient if we go to the rest frame of the proton ($p$) and see if the decay is possible. Mass of proton = $1.673 \times 10^{-27}$ kg. Mass of positron = Mass of electron = $9.11 \times 10^{-31}$ kg. We can take neutrinos to be almost massless. Thus, the combined mass of the positron and electron-neutrino is less than the mass of the proton. In special relativity, mass is another form of energy. Thus, it is energetically favourable to destroy a proton and create a positron and an electron-neutrino. Thus, the decay scheme does not violate energy conservation.
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