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- 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.1. Given the following properties for Germanium – Diamond cubic structure (a = 0.5658 nm; Intrinsic carrier density at 300K (n; = 2.4 x 1013 cm-3) Electron mobility (He = 3900 cm²/v-s) Hole mobility (uh = 1900 cm?/v-s) %3D %3D Calculate the following - a. The ratio of the intrinsic carrier density to the atomic density b. The conductivity of intrinsic Ge at 300K4. Calculate the potential energy of the system of Na* and CI ions when they are at a distance of 4Å.
- A cubic crystal has lattice constant 4.3 A and its density 963 kg/m. If its atomic mass is 23, then what type of cubic unit cell does it form? (Avogadro's number, Na = 6.02x10"). Select one: a. FCC b. SC c. NON OF THE ABOVE d. BCCa. Label the below energy diagram and draw the density of states (DoS). To do so, assign a, b, c, and d to an atom, solid, small molecule, and large molecule. Then draw the density of states expected based on the diagram in the box on the right (including axis labels for both the x and y axes). Label the conduction and valence bands of the metal. You may redraw the whole or any parts of the diagram on a separate piece of paper. b. C. d. Draw DoS in box!Q8. Estimate the mean free path of electrons in copper. Assume the Fermi energy of copper is 7.03eV. The number of electrons per unit volume is 8.49 x1028 m³. The effective mass of an electron in copper is 1.47 times the rest mass of the electron. The conductivity of copper is 5.9x107 S/m.
- GaAs is utilized to manufacture infrared light-emitting diodes (LEDs). The band gap is 1.42 eV, and the effective masses of electrons and holes are 0.067 and 0.45 of the free-electron mass, respectively.a. Calculate the intrinsic electron and hole concentration of pure GaAs at room temperature.b. What is the carrier concentration intrinsic?c. Where is the Fermi energy level located?A silicon p-n junction consists of a p-type region containing 3x1016 cm-3 acceptors and an n- type region containing also 1017 cm-3 donors. a. Calculate the density of electrons and holes in both p-type and n-type regions under thermal equilibrium at room temperature. b. Calculate the built-in potential of the p-n junction? c. Calculate the width of the depletion layer under a reverse bias of 1.0 V. d. Based on c, calculate the junction capacitance. Note that the junction cross-session area is 1.2 mm2.Q2. Transistors are manufactured by doping semiconductors. The diffusion coefficient of phosphorus in Si is D = 6.5 x 10-11 mm2/s at a temperature of 950°C. Assume the source provides a surface concentration of 1020 atoms/cm3 and the diffusion time is one hour. Assume that the silicon wafer initially contains no phosphorus. Calculate the depth at which the concentration of phosphorus will be 1018 atoms/cm3.
- D. Copper has the atomic radius of 0.128 nm, an FCC crystal structure and an atomic weight of 63.5 g/mol. Calculate the following: Cell edge length Vc - Unit cell volume i. ii. Vs – Sphere volume Density. ii. - iv. V. APF - Atomic Pack FactorQuestion 1 a) Ina closed circuit, an electric current of intensity i goes through a resistor of resistance R. The electric potential at the edges of R is measured to be V. If now we write R would this generally bethe definition ofthe resistance quantity R, or the expression of Ohm's Law? Explain. b) We define the resistivity (via the familiar notation) as E p= Thus show that the resistance R can be written as, R =p- here Lis the length ofthe resistor, and A is the cross-sectional area ofit. c) Let J the curent density (i/A). Express J in tems of the electron density n (electrons/m), the electron drift velocity va, and the electron charge e. d) Show that the resistivity can be expressed (via the familiar notation) as, m p= ne't here m is the electronmass; t is the period of time that elapses between two subsequent collisions, the electron undergoes with copper nuclei throughout its chaotic motion in the body of copper (supposing that the current carrying cable is made of copper). Hint:…Question 1 (a) Semiconductors are materials which have a conductivity between conductors. Based on your knowledge, describe at least three particles that make up the atom and briefly describe the difference between n-type and p-type semiconductor materials. Classify the three particles that make up the atom and briefly describe the difference between n-type and p-type semiconductor materials. (b) Figure 1 shows a basic diode with p-type and n-type semiconductors with complete Voltage Bias. Identify the depletion region when the diode is conducted in reverse bias. With the aid of suitable diagram, briefly explain the region occur when the 5 V supply voltage is аpplied. p region n region VBIAS Figure 1 (c) Figure 2 shows the class of materials based on relative comparisons. Based on Figure 2 description, identify the materials that affected the conduction and valence band. As an engineer, explain the consequences if the atomic number of a neutral atom is 8, and the maximum number of…