7) The number of allowed electron state per unit energy range is defined by:g(s)=(2m) ³/2/22z²h³where Vis the volume of the lattice and m the mass of an electron. The lowest energy state of N electronis 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 thanthe Fermi energy & <&F.2.Show that the kinetic energy of a free electron gas at absolute zero is E=E=N&y.ĆEavthe 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 theatomic 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-avin terms ofiii) Estimate the contribution of the conduction electrons to the bulk modulus, B for potassiumand compare your answer to the experimental measured bulk modulus 0.37x10¹0 N/m².

Answered: Image /qna-images/answer/96aab621-5818-41e0-826a-499701440940.jpg

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 &