7) The number of allowed electron state per unit energy range is defined by: g(s) = (2m) ¹/24/2 V 2x²h³ where Vis the volume of the lattice and m the mass of an electron. The lowest energy state of N electron is obtained by filling the N states of lowest energy. 1. Using the density of state find an expression of the number of states N with energy less than the Fermi energy &
7) The number of allowed electron state per unit energy range is defined by: g(s) = (2m) ¹/24/2 V 2x²h³ where Vis the volume of the lattice and m the mass of an electron. The lowest energy state of N electron is obtained by filling the N states of lowest energy. 1. Using the density of state find an expression of the number of states N with energy less than the Fermi energy &
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Transcribed Image Text:7) The number of allowed electron state per unit energy range is defined by:
g(s)=
(2m) ³/2/2
2z²h³
where Vis the volume of the lattice and m the mass of an electron. The lowest energy state of N electron
is obtained by filling the N states of lowest energy.
1. Using the density of state find an expression of the number of states N with energy less than
the Fermi energy & <&F.
2.
Show that the kinetic energy of a free electron gas at absolute zero is E=
E=N&y.
ĆE
av
the Fermi energy, EF and the electron concentration n - N/V.
4. The atomic number of potassium (K) is Z = 19, the mass density, pm = 856 kg/m³ and the
atomic mass is 39.098 g.
i) Write the electronic configuration of K atom and determine the valence.
ii) Calculate the electron concentration n-N/V and the Fermi energy, &F.
3. Derive an expression of the pressure p=
and the bulk modulus B=-V-
av
in terms of
iii) Estimate the contribution of the conduction electrons to the bulk modulus, B for potassium
and compare your answer to the experimental measured bulk modulus 0.37x10¹0 N/m².
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