(Heisenberg) A carbon-14 nucleus decays into nitrogen-14, emitting in the process an electron and a neutrino (this process is relevant for carbon dating, as we will explore later in the term). People often ask whether the electron was hiding inside the carbon nucleus all along. A carbon nucleus is roughly 2.5 x 10-15 m in size. The mass difference between carbon-14 and nitrogen-14 is less than a MeV/c. As a crude approximation, treat the carbon nucleus as a 1-d box with size 1 fm. a) Using the Heisenberg uncertainty principle for momentum and posi- tion, estimate the momentum that results from confining an electron within the carbon nucleus. b) What is the energy associated with that confinement. Check to see whether you should be using the relativistic or non-relativistic expression for the electron energy in terms of the momentum. Given your answers to (a) and (b) discuss whether you think the electron was present in the nucleus prior to decay.