(a) Count the number of electron states N(E) with energy equal to or less than E in Equation 35.8 by finding the volume available to such states in the space with Cartesian coordinate axes nx, ny, nz. (Hint: Consider each set of positive integers, at the corner of a unit cube, and that lies inside a radius
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Essential University Physics: Volume 2 (3rd Edition)
- a) Explain how the alpha parameter in the general E(p) relation, and the channel dimension could be used to determine the density of states as function of the energy E. b) Provide and define the two main parameters (terms) that determine the electron density when temperature is non zero.arrow_forwardThe expression for the Fermi energy of electrons in a stellar interior is εF =ℏ2 /2me [3pi 2 Z/A ρ/mp ] 2/3 (See image) Derive the condition on the temperature and density for the electrons in the stellar interior to bedegenerate. Briefly explain the reason for this limit. Demonstrate that the condition for degeneracy you have found corresponds to a straight line ina plot of log T versus log ρ. Use the condition you have found to calculate whether the centre of the white dwarf Sirius B isdegenerate. Use values of ρc = 3.0 × 109 kg m−3, Tc = 7.6 × 107 K, and Z/A = 0.5.arrow_forwardHep structure. Show that the cla ratio for an ideal hexagonal close-paeked struc- ture is G) = 1.633. If cla is signifieantly larger than this value, the crystal structure may be thought of as composed of planes of closely packed atoms, the planes being loosely stacked. 1/2arrow_forward
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