Consider a degenerate electron gas in which essentially all of theelectrons are highly relativistic (€ » mc2 ), so that their energies are € pc (where p is the magnitude of the momentum vector).(a) Modify the derivation given above to show that for a relativistic electron gas at zero temperature, the chemical potential (or Fermi energy) is given by μ = hc(3N/87πV)1/3.(b) Find a formula for the total energy of this system in terms of Nand μ

Consider a degenerate electron gas in which essentially all of theelectrons are highly relativistic (€ » mc2 ), so that their energies are € pc (where p is the magnitude of the momentum vector).(a) Modify the derivation given above to show that for a relativistic electron gas at zero temperature, the chemical potential (or Fermi energy) is given by μ = hc(3N/87πV)1/3.(b) Find a formula for the total energy of this system in terms of Nand μ

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A physical field present around an electrically charged particle that exerts a force on all other charged particles is called an electric field. The charged particles present in the field either repel or attract. From electric charges or time-varying magnetic fields, the electric field originates. One of the manifestations of electromagnetic force which is one of the four fundamental forces present in nature are the electric fields and magnetic fields.

Question

Consider a degenerate electron gas in which essentially all of the
electrons are highly relativistic (€ » mc² ), so that their energies are € pc (where p is the magnitude of the momentum vector).
(a) Modify the derivation given above to show that for a relativistic electron gas at zero temperature, the chemical potential (or Fermi energy) is given by μ = hc(3N/87πV)^1/3.
(b) Find a formula for the total energy of this system in terms of Nand μ

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