2. Consider an ideal fermionic gas in one-dimension with N electrons in a volume V. Calculate the wavevector at the Fermi level (kF) also the total energy of the system (Etotal) in terms of the number density (n).
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- I need the answer as soon as possibled) A primitive cell is a unit cell that contains exactly one lattice point. (i) Illustrate primitive bcc cell using Weigner-Seitz method. (ii) Discuss the procedures to draw the Weigner-Seitz cell step by step on two-dimensional space lattice.A 2-D square lattice has side, a=2.5 A with the fermi surface touching the first Brillouin zone. Given Planck's constant, h=6.63 x 10-34 J.s and mass of electron, m.-9.1 x 10-31 kg. Using the information given i. Calculate the energy of the electron at the fermi surface. Calculate the electron concentration at the fermi surface. Draw the fermi sphere in first Brillouin zone.
- 1. A model for the potential energy interaction between the two nitrogen atoms in the N2 molecule is proposed that has the form: v(4) = 4E, (4)* - ()'] 12 a. Find the position of the potential minimum and its value there, in terms of o and Eo, respectively. What do these parameters represent physically about the molecule? b. Draw a hand sketch of V(r) showing rmin, V(rmin) and where V crosses the r axis. c. If the atom is disturbed from its equilibrium by a small amount, show that the 7.56. frequency of oscillation is w = d. For molecular nitrogen, the bond length is 1.1 x 10-1°m, the bond (binding) energy is 9.79 eV (15.66 x 10-19 J), the mass is 14 amu = 23.38 x 10-27 kg. In the spectroscopy laboratory, this vibration is measured to be 8.8 x 1013 Hz. Is this a good model for the interatomic potential? (Recall o = 2n times frequency in Hz) where m is the mass of a nitrogen atom.Calculate the total interfacial surface energy (in J) for 9 x 1018 spheres of copper, each with the critical radius r*. (Assume that the critical radius of copper is 1.251 x 10-7 cm.) J Need Help? Submit Answer Read It Watch It NATAMAM4. Diatomic chain. Consider the normal modes of a linear chain in which the force constants between the nearest-neighbor atoms are C and 10C. Let the masses be equal and let the nearest-neighbor separation be a/2. Find w(K) at K = 0 and K = π/a. Sketch in the dispersion relation by eye. The problem simulates a crystal of diatomic molecules such as H₂.
- Plz find the solution of advance physics asap1. (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.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,.
- 21. 14-4 Lattice specific heat of a 1D crystal of inert gas atoms. Consider a one-dimensional crystal of inert gas atoms. Let L be the length of the crystal and N the number of atoms. Let a be the lattice constant. . Evaluate the phonon density of states for this crystal. i. Derive an integral expression for the lattice specific heat of the crystal. iii. Evaluate the lattice specific heat in the high- and low- temperature limits.3-a Draw a cubic system lattice, which has the base: .... 3-b Draw a Tetragonal system lattice, which has the base: OO...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…