Write the formula for Fermi-Dirac distribution function.
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Write the formula for Fermi-Dirac distribution function.
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- Let f (e) be the Fermi Dirac distribution function and U be the chemical potential. Obtain the expression for derivative of f (e) with respect to e at e=uThe 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.For a system of particles at room temperature, how large must € - μ be before the Fermi-Dirac, Bose-Einstein, and Boltzmann distributions agree within 1% ? Is this condition ever violated for the gases in our atmosphere? Explain.