Example 1: Find the hole concentration concentration is 2 ×1012cm3 and intrins 1.25 x10 cm-3.

At what temperature, in terms of Tc, is the critical field of a superconductor one-half its value at T = 0 K?

The measured density of a NaF crystal is 2.558 g/cm3 . What is the equilibrium separate distance of Na+ and Flions?

Why is tbe equilibrium separation distance between K+ and Cl- different for a diatomic molecule than for solid KCl?

To obtain a more clearly defined picture of the FermiDirac distribution, consider a system of 20 FermiDirac particles sharing 94 units of energy. By drawing diagrams like Figure P10.11, show that there are nine different microstates. Using Equation 10.2, calculate and plot the average number of particles in each energy level from 0 to 14E. Locate the Fermi energy at 0 K on your plot from the fact that electrons at 0 K fill all the levels consecutively up to the Fermi energy. (At 0 K the system no longer has 94 units of energy, but has the minimum amount of 90E.) 1 Microstate8 others? One of the nine equally probable microstates for 20 FD particles with a total energy of 94E.

Consider the HCl molecule, which consists of a hydrogen atom of mass 1 u bound to a chlorine atom of mass 35 u. The equilibrium separation between the atoms is 0.128 nm, and it requires 0.15 eV of work to increase or decrease this separation by 0.01 nm. (a) Calculate the four lowest rotational energies (in eV) that are possible, assuming the molecule rotates rigidly. (b) Find the molecules spring constant and its classical frequency of vibration. (Hint: Recall that U=12Kx2.) (c) Find the two lowest vibrational energies and the classical amplitude of oscillation corresponding to each of these energies. (d) Determine the longest wavelength radiation that the molecule can emit in a pure rotational transition and in a pure vibrational transition.

To give a helium atom nonzero angular momentum requires about 21.2 eV of energy (that is, 21.2 eV is the difference between the energies of the lowest-energy or ground state and the lowest-energy state with angular momentum). The electron-volt or eV is defined as 1.601019 J. Find the temperature T where this amount of energy equals kTB/2 . Does this explain why we can ignore the rotational energy of helium for most purposes? (The results for other monatomic gases, and for diatomic gases rotating around the axis connecting the two atoms, have comparable orders of magnitude.)

A tightly wound solenoid at 4.0 K is 50 cm long and is constructed from Nb wire of radius 1.5 mm. What maximum current can the solenoid carry if the wire is to remain superconducting?

The NaCl crystal structure is FCC. The equilibrium spacing is r0=0.282nm. If each ion occupies a cubic 3 volume of r03 , estimate the distance between “nearest neighbor” Na+ ions (center-to-center)?

Determine the Fermi energies for (a) Mg, (b) Na, and (c) Zn.