When we applied the Pauli Exclusion Principle to a white dwarf we considered first the one-dimensional case
Question:
When we applied the Pauli Exclusion Principle to a white dwarf we considered first the one-dimensional case and indicated the allowed momenta of the electrons as points on a one-dimensional px axis, which allowed us to determine max. We then extended this argument to the three-dimensional case by considering a three-dimensional “lattice” of allowed momenta in px, py, pz space. Draw a similar “lattice diagram” to indicate the allowed values of neutron momentum in px, py, pz space. According to the Pauli exclusion principle, by what factor is the maximum momentum of the neutrons greater than the minimum momentum? Briefly explain the origin of this factor, using your diagram to support your explanation.
What is the maximum velocity of the neutrons? Express your answer in terms of h, M, R, and mp.
Using your result from the previous part, show a derivation for the minimum neutron star mass required for the neutrons to be gravitationally bound. Express your answer in terms of mp, ρnucl, h, and G.
What is the fundamental difference between the strong nuclear force and the gravitational force that allows a neutron star (a “giant atomic nucleus,” many orders of magnitude larger than a Uranium nucleus) to exist? Based on your result in the previous part, if G were larger, how would this affect the minimum neutron star mass? In one sentence, give a concise intuitive reason why.
Chemistry The Central Science
ISBN: 978-0321696724
12th edition
Authors: Theodore Brown, Eugene LeMay, Bruce Bursten, Catherine Murphy, Patrick Woodward