Physics 8510, Fall 2005

 

Problem Set 3

 

 

1) Problem 3 from Chapter 2 of Ashcroft & Mermin.

 

2) NaCl crystallizes as a cubic structure. If the molecular weight of NaCl is 58.46 and the density at room temperature is 2.167g/cm³ find the distance between adjacent atoms. (Ans: half of lattice constant 5.64A)

 

3) Fermi gases in astrophysics. 

(a) Given M₀ = 2 x 10³³ g for the mass of the Sun, estimate the number of electrons in the Sun. In a white dwarf star this number of electrons may be ionized and contained in a sphere of radius 2 x 10⁹ cm; find the Fermi energy of the electrons in electron volts. 

(b) The energy of an electron in the relativistic limit is related to the wave vector as  .  Show that the Fermi energy, in this limit, is  . 

(c) If the above number of electrons were contained within a pulsar of radius 10 km, show that the Fermi energy would be ~10⁸ eV.  

This value explains why pulsars are believed to be composed largely of neutrons rather than of protons and electrons, for the energy re­lease in the reaction n  p + e- is only 0.8 X 10⁶ eV, which is not large enough to enable many electrons to form a Fermi sea. The neutron decay proceeds only until the electron concentration builds up enough to create a Fermi level of 0.8 X 10⁶ eV, at which point the neutron, proton, and electron concentrations are in equilibrium.

 

 

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