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The expression for the Fermi energy of electrons in a stellar interior is Z 12/3 Amp EF ħ² 2me 3π² Derive the condition on the temperature and density for the electrons in the stellar interior to be degenerate. Briefly explain the reason for this limit. Demonstrate that the condition for degeneracy you have found corresponds to a straight line in a plot of log T versus log p. Use the condition you have found to calculate whether the centre of the white dwarf Sirius B is degenerate. Use values of pc = 3.0 x 10⁹ kg m-³, T = 7.6 x 107 K, and Z/A = 0.5.

The expression for the Fermi energy of electrons in a stellar interior is Z 12/3 Amp EF ħ² 2me 3π² Derive the condition on the temperature and density for the electrons in the stellar interior to be degenerate. Briefly explain the reason for this limit. Demonstrate that the condition for degeneracy you have found corresponds to a straight line in a plot of log T versus log p. Use the condition you have found to calculate whether the centre of the white dwarf Sirius B is degenerate. Use values of pc = 3.0 x 10⁹ kg m-³, T = 7.6 x 107 K, and Z/A = 0.5.

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The 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 be
degenerate. Briefly explain the reason for this limit.


Demonstrate that the condition for degeneracy you have found corresponds to a straight line in
a plot of log T versus log ρ.


Use the condition you have found to calculate whether the centre of the white dwarf Sirius B is
degenerate. Use values of ρc = 3.0 × 109 kg m−3,  Tc = 7.6 × 107 K,  and Z/A = 0.5.

The expression for the Fermi energy of electrons in a stellar interior is ħ² 3,22—²7³. 2Z P 2me Amp. EF Derive the condition on the temperature and density for the electrons in the stellar interior to be degenerate. Briefly explain the reason for this limit. Demonstrate that the condition for degeneracy you have found corresponds to a straight line in a plot of log T versus log p. Use the condition you have found to calculate whether the centre of the white dwarf Sirius B is degenerate. Use values of pc = 3.0 x 10⁹ kg m-³, T = 7.6 x 107 K, and Z/A=0.5.
Transcribed Image Text:The expression for the Fermi energy of electrons in a stellar interior is ħ² 3,22—²7³. 2Z P 2me Amp. EF Derive the condition on the temperature and density for the electrons in the stellar interior to be degenerate. Briefly explain the reason for this limit. Demonstrate that the condition for degeneracy you have found corresponds to a straight line in a plot of log T versus log p. Use the condition you have found to calculate whether the centre of the white dwarf Sirius B is degenerate. Use values of pc = 3.0 x 10⁹ kg m-³, T = 7.6 x 107 K, and Z/A=0.5.
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