Silver has exactly one conduction electron per atom. (a) Use the density of silver (1.05 x10^4 kg/m^3) and the mass of 107.87 g/mol to find the density of conduction electrons insilver. (b) At what temperature is A = 1 for silver (where A is the normalization constantin the Maxwell-Boltzmann distribution)? (c) At what temperature is A = 10^-3?

Copper, a monovalent metal, has molar mass 63.54 g/mol and density 8.96 g/cm3. What is the number density n of conduction electrons in copper?

Aluminum has a density of 2.70 x 103 kg/m3 at a temperature of 293 K, and its molar mass is 26.98 g. (a) Compute the number of aluminum atoms per unit volume at that temperature. (b) Use the fact that EF 11.63 eV for aluminum at 293 K to fi nd the number density of free electrons. (c) Combine your results from (a) and (b) to estimate the number of conduction electrons per atom—the valence number for aluminum

At a certain temperature, the electron and hole mobilities in intrinsic germanium are given as 0.43 and 0.21 m2/V s, respectively. If the electron and hole concentrations are both 2.3 x 10'® m, find the conductivity at this temperature.

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)?

For the simple cubic crystal described above, i.e. a = 0.7\: nma=0.7nm, calculate the surface density of atoms (i.e. number of atoms per unit area) on the (100) plane in unit of cm^{-2}cm−2. Values within 5% error will be considered correct.

One description of the potential energy of a diatomic molecule is given by the Lennard–Jones potential,                          U = (A)/(r12) - (B)/(r6)where A and B are constants and r is the separation distance between the atoms. For the H2 molecule, take A = 0.124 x 10-120 eV ⋅ m12 and B = 1.488 x 10-60 eV ⋅ m6. Find (a) the separation distance r0 at which the energy of the molecule is a minimum and (b) the energy E required to break up theH2 molecule.

Stars similar to our sun eventually become white dwarfs, in which the hydrogen and helium have fused to form carbon and oxygen. The star has collapsed to a much smaller radius, which is why it is described as a “dwarf.” The electrons are not bound to the nuclei and form a degenerate Fermi gas within the white dwarf. Consider a white dwarf with a mass equal to the sun’s mass (1.99 x 1030 kg) but a radius of only 6.96 x 106 m, which is just 1% of the sun’s present radius. (a) If the white dwarf consists of equal parts carbon and oxygen, how many electrons are present? (b) What is the number density of electrons? (c) Find the Fermi energy of the electrons (in units of eV) and comment on the result.

Silver contains 5.8 * 1028 free electrons per cubic meter. At absolute zero, what is the Fermi energy (in J and eV) of silver?

The Fermi energy of sodium is 3.23 eV. (a) Find the average energy Eav of the electrons at absolute zero. (b) What is the speed of an electron that has energy Eav ? (c) At what Kelvin temperature T is kT equal to EF ? (This is called the Fermi temperature for the metal. It is approximately the temperature at which molecules in a classical ideal gas would have the same kinetic energy as the fastest-moving electron in the metal.)