B/ answer with the word true or false and correct the error, 1- The total energy of the electron is usually greater than zero. If 2)the electron moves from one orbit to another higher than it, the velocity of the electron in the higher orbit increases 3- The hydrogen bond is mostly ionic
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- : A uniform piece of n-type of silicon that is lum long senses a voltage of 1 v. Determine the velocity of the electrons. Use p1350 cm/V.sesA 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.B- When 4Volt applied on 100 meters wire, electron drift with 10* m/sec velocity and current density = 0.48A/mm2 find : 1- Number of collisions in one second. 2- Resistivity of this wire. 3- Energy of Fermi level. 4- Maximum velocity of free electron. %3D
- 1 (a) The width of an infinite potential well for a free electron of an 1-D material is 10.5 A°. Determine the first four allowed energy levels in eV for this free electron. Also find E2-E1, E3-E2 and E4-E3 in eV. Comment on the separation between successive levels. n²n²h? En %3D 2mа? (b) Suppose for Fermi-Dirac probability distribution function, E-EF = 0.15 eV. Find the temperature at which (i) the ff(E) = 0.05 and (ii) the ff(E) = 0.095. Why at higher temperature, the probability of occupancy of a state E > EF is higher? %3D 1 fr (E) = E-EF 1+e kT1)A Si crystal in the form of a cube of side 1.0 nm is at equilibrium at 300 K.The edge of the conduction band is Ec = -1.0 eVa) What is the energy of a conduction electron in the ground state (in eV) ?b) What is the energy of the conduction electron in the first excited state (in eV)?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…
- 1.Compare probabilities of electron occupying a level situated kBT and 3kBT above the Fermi level. Estimate when (in kBT units) Boltzmann approximation gives the same results as F-D function within 1 % accuracy?Suppose we have an ideal fermion gas of identical particles in a "box" at T = 0 K. Which of the following statements are true? a. The multiplicity of the gas is =1 b. The multiplicity of the gas is =N! C. If the gas consists of electrons with densities that correspond to the typical densities of conduction electrons in metals, only a part of the electrons can contribute to the heat capacity of the system as the temperature rises. d. If the gas consists of electrons with densities corresponding the typical densities of conduction electrons in metals, all electrons can easily contribute to the heat capacity of the system as the temperature rises.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).
- 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.6. In a regular FCC, determine number of atoms per unit area in (1 1 0) plane 7. In a BCC unit cell, determine number of atoms per unit area in (1 1 1) plane 8. Assuming that each Au atom donates one conduction electron, calculate the drift mobility and drift velocity of the conduction electrons in gold at 20° C if the applied electric field is 200 V/cm. What is the mean free path of the conduction electrons if their mean speed is 1.4 x 10°m s ? Resistivity of pure gold at 0°C (273 K) is po= 22.8 n2 m. a, for Au from Table 2.1 is 1/251 K'. Given that Au is FCC with lattice parameter of 0.407nm. 9. Na is a monovalent metal (BCC) with a lattice parameter of 0.43nm. The drift mobility of clectrons in Na is 53 cm V's'. Calculate the electrical conductivity of Na and the mean scattering time of conduction electrons. 10. Determ ine Miller Indices for the following: A 1/2Q#04. Calculate the number of atoms per unit area in (100), (110) and (111) planes of in bcc crystal with the lattice parameter of 2.5 angstrom.