. (a) Comment on the achievements and failures of the Free Electron model. (b) Defin e Fermi Dirac distribution and density of energy states.
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5. (a) Comment on the achievements and failures of the Free Electron model. (b) Defin
e Fermi Dirac distribution and density of energy states.
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- 1) Derive an expression for the density of states in a l-dimensional square well, expressed as a function of energy. Calculate the Fermi Energy for lead. [eV]5. (a) What is the physical significance of the Fermi-Dirac function? Explain how the Fermi level changes in the intrinsic semiconductor as a function of effective mass of electrons and holes for T > 0K. (CO-3) (b) Find the conductivity of intrinsic silicon at room temperature. It is given that ni at room temperature for silicon is 1.5 x 1016 /m³ and the mobilities of electrons and holes in silicon are 0.13 m²/V sec and 0.05 m²/V sec, respectively. (CO-3)1. (a) Compute the concentration of holes and electrons in an intrinsic sample of Si at room temperature. You may take me = 0.7m and mh = m. (b) Determine the position of the Fermi level under these conditions.
- Example (3-4): Calculate the concentration of the electrons and the holes in intrinsic silicon at (300°k). The energy gap equals (1.12 eV) and (N=N,=2.5 x 10 25 m-3). Find the value of Fermi energy level. Sol.)4) Consider the paramagnetic two- and one-dimensional free electron gas, respectively the 2DEG and 1DEG, systems. Calculate their a) density of states, b) Fermi wavevector, c) dimensionless interaction parameter r,. d) Express their Fermi energy in terms of the free electron density n, kp, and r,.Pls help ASAP. Pls show all work and do all parts of the question.
- Can you please solve the question and make explanation step by step?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…(a) Describe the free electron gas model of metals. How does it help to explain the lattice heat capacity and electrical conductivity of metals?