# Physics Assignments

## DENSITY OF STATES

DENSITY OF STATES Later we’ll need to know the number dn of quantum states that have energies in a given range dE. The number of states per unit energy range dnIdE is called the density of states, denoted by g(E). We’ll begin by working out an expression for g(E). Think of a three-dimensional space with coordinates (nx’ n” …

## FREE-ELECTRON MODEL OF METALS

FREE-ELECTRON MODEL OF METALS Studying the energy states of electrons in metals can give us a lot of insight into their electrical and magnetic properties, the electron contributions to heat capacities, and other behavior. As we discussed in Section 44-4, one of the distinguishing features of a metal is that one or more valence electrons are detached …

## INSULATORS AND SEMICONDUCTORS

INSULATORS AND SEMICONDUCTORS The nature of the energy bands determines whether the material is an electrical conductor or an insulator. In insulators and semiconductors at absolute zero temperature the valence electrons completely fill the highest occupied band, called the valence band. Tile energy gap separating the valence band and the conduction band may be of the r ofl …

## ENERGY BANDS

ENERGY BANDS The energy band concept is a great help in understanding several properties of solids. To introduce the idea, suppose we have a large number N of identical atoms, far enough apart that their interactions are negligible. Every atom has the same energy-level diagram. We can draw an energy-level diagram for the entire system. It looks just …

## BONDING IN SOLIDS

BONDING IN SOLIDS The forces that are responsible for the regular arrangement of atoms in a crystal are the same as those involved in molecular bonds, plus one additional type. Not surprisingly, ionic and covalent molecular bonds are found in ionic and covalent crystals, respectively. The most familiar ionic crystals are the alkali halides, such as ·ordinary salt (NaCl). …

## CRYSTAL LATIICES

CRYSTAL LATIICES A crystal lattice is a repeating pattern of mathematical points that extends throughout space. There are 14 general types of such patterns; Fig. 44-11 shows small portions of a few common examples. The simple cubic lattice (sc) has a lattice point at each corner of a cubic array (Fig. 44-11a). The face-centered cubic lattice (fee) is …

## STRUCTURE OF SOLIDS

STRUCTURE OF SOLIDS The term condensed matter includes both solids and liquids. In both states, the interactions between atoms or molecules are strong enough to give the material a definite volume that changes relatively little with applied stress. In condensed matter, adjacent atoms attract one another until their outer electron charge clouds begin to overlap significantly. Thus the distances …

## VIBRATIONAL ENERGY LEVELS

VIBRATIONAL ENERGY LEVELS Molecules are never completely rigid. In a more realistic model of a diatomic molecule we represent the connection between atoms not as a rigid rod but as a spring (Fig. 44–6). Then in addition to rotating, the atoms of the molecule can also vibrate about their equilibrium positions along the line joining them. For small …

## ROTATIONAL ENERGY LEVELS

ROTATIONAL ENERGY LEVELS In this discussion we’ll concentrate mostly on diatomic molecules, to keep things as simple as possible. In Fig. 44-4 we picture a diatomic molecule as a rigid dumbbell (two point masses m, and mz separated by a constant distance r~ that can rotate about axes through its center of mass, perpendicular to the line …

## MOLECULAR SPECTRA

MOLECULAR SPECTRA Molecules have energy levels that are associated with rotational motion of a molecule as a whole and with vibration motion of the atoms relative to each other. Just as transitions between energy levels in atoms lead to atomic spectra, transitions between rotational and vibration levels in molecules lead to molecular spectra.