Assuming that there are 1.5 free electrons per gold atom. The electrical conductivity and density for Au are 4.3 x 10' (N-m) and 19.32 g/cm?, respectively. (a) Calculate the number of free electrons per cubic meter for gold (b) Compute the electron mobility for gold.
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- Given the fermi energy and electron concentration 7.00 eV and 8.0×10²6 e¯/m³ respectively of a Copper of resistivity 1.7×108 2-m, calculate the mean free path. (a) 3780 nm (b) 5000 nm (c) 4100 nm (d) 7000 nmSince the Fermi energy level of zinc is EF = 9.47 eV, what is the number of electrons per unit energy per unit volume at this energy level? Since the resistivity of zinc is 5.90 x 10^-8 ohm.m, calculate the average time interval between collisions of electrons.Assume that the total volume of a metal sample is the sumof the volume occupied by the metal ions making up the lattice andthe (separate) volume occupied by the conduction electrons. Thedensity and molar mass of sodium (a metal) are 971 kg/m3 and 23.0g/mol, respectively; assume the radius of the Na+ ion is 98.0 pm. (a)What percent of the volume of a sample of metallic sodium is occupiedby its conduction electrons? (b) Carry out the same calculationfor copper, which has density, molar mass, and ionic radius of8960 kg/m3, 63.5 g/mol, and 135 pm, respectively. (c) For which ofthese metals do you think the conduction electrons behave morelike a free-electron gas?
- The number density of conduction electrons in a metal can be found from the density ρ of the metal, the mass per mole M of the metal, the number of conduction electrons per metal atom, and Avogadro’s number NA. If we assume one conduction electron per atom, which of the following gives the number density of conduction electrons for a given metal? a. NA ρM b.NA ρ/M c. NA M/ρ d. NA /ρMGold has an atomic mass of 197 u, a density of 19.3 x 10^3 kg/m^3, a Fermi energy of 5.54 eV, and a resistivity of 2.04 x 10^-8 ohms. Estimate the mean free path in atom spacings between collisions of the free electrons in gold under the assumption that each gold atom contributes one electron to the electron gas.What is the magnitude of the electrostatic force between a singly charged sodium ion (Na+, of charge +e) and an adjacent singly charged chlorine ion (Cl-, of charge -e) in a salt crystal if their separation is 2.82 * 10-10 m?
- What is the number density of conduction electrons in gold, which is a monovalent metal? Use the molar mass and density provided in Appendix FWhat mass of phosphorus is needed to dope 1.0 g of silicon so that the number density of conduction electrons in the silicon is increased by a multiply factor of 106 from the 10^16 m-3 in pure silicon.Calculate the number density (number per unit volume) for (a) molecules of oxygen gas at 0.0°C and 1.0 atm pressure and (b) conduction electrons in copper. (c) What is the ratio of the latter to the former? What is the average distance between (d) the oxygen molecules and (e) the conduction electrons, assuming this distance is the edge length of a cube with a volume equal to the available volume per particle (molecule or electron)?
- What is the probability that, at a temperature of T = 300 K, an electron will jump across the energy gap Eg (= 5.5 eV) in a diamond that has a mass equal to the mass of Earth? Use the molar mass of carbon in Appendix F; assume that in diamond there is one valence electron per carbon atom.When a photon enters the depletion zone of a p-n junction, the photon can scatter from the valence electrons there, transferring part of its energy to each electron, which then jumps to the conduction band. Thus, the photon creates electron–hole pairs. For this reason, the junctions are often used as light detectors, especially in the x-ray and gamma-ray regions of the electromagnetic spectrum. Suppose a single 662 keV gamma-ray photon transfers its energy to electrons in multiple scattering events inside a semiconductor with an energy gap of 1.1 eV, until all the energy is transferred. Assuming that each electron jumps the gap from the top of the valence band to the bottom of the conduction band, find the number of electron – hole pairs created by the process.Is it feasible to describe the distinction between a conductor and an insulator using a semiconductor as an example? Why not use a graph to explain your points?