How much voltage must be used to accelerate a proton (radius 1.2 ×10−15m) so that it has sufficient energy to just penetrate a silicon nucleus? A silicon nucleus has a charge of +14e, and its radius is about 3.6 ×10−15m. Assume the potential is that for point charges.

The nuclear potential that binds protons and neutrons in the nucleus of an atom is often approximated by a square well. imagine a proton conned in an innite square well of length 105 nm, a typical nuclear diameter. calculate the wavelength and energy associated with the photon that is emitted when the proton undergoes a transition from the rst excited state (n 2) to the ground state (n 1). in what region of the electromagnetic spectrum does this wavelength belong?