DO PHYSIS ONLINE FROM IDEAS TO IMPLEMENTATION 9.4.3 ATOMS TO TRANSISTORS STRUTURE OF ATOMS AND SOLIDS STRUTURE OF THE ATOM In was not until the early 1930 s that scientists had fully developed a model of the atom based upon quantum physics and that was supported by experimental evidence based upon the existence of the electron, proton and neutron. Atoms consist of a positive nucleus containing protons (positive) and neutrons (neutral). The radius of a nucleus is about 10-15 m. Most of the mass of the atom is due to the nucleus. Electrons being negatively charged are bound to the positively charged nucleus. Typical radii for atoms are about 10-10 m. The number of protons within a nucleus determines the element. For example, carbon: 12 protons and uranium: 92 protons. The electrons are not like planets orbiting the Sun. In quantum physics terms, the bound electrons behave as waves and it is only possible to determine the probability of finding the electron within a small volume. The notion of a trajectory for these electrons is meaningless. The best way to visualize an atom is to think of a small nuclear core embedded in a an electron cloud where at certain locations there is zero probability of finding the electron while at other locations there is a high probability. Probability cloud for a hydrogen atom (2s electron) 10x10-10 m high probability of finding electron zero probability of finding an electron Probability cloud for a hydrogen atom (4d electron) high probability of finding electron zero probability of finding an electron 50x10-10 m Fig. 1. Electron probability clouds for a hydrogen atom. 1
All the information about electrons in an atom is given by a set of four quantum numbers. This set of four numbers determines the state of the atom and this tells us all we can know about the electrons. Principle quantum number (shell) n = 1, 2, 3, Orbital quantum number (subshell) l = 0 (s), 1 (p), 2 (d),, n-1 Magnetic quantum number m l = 0, 1,, l Spin quantum number m s = 1/2 Each electron in an atom has a unique set of these four quantum numbers (Pauli Exclusion Principle). Electrons in an atom have their total energy (kinetic + potential) quantized. For a given atom, there is a set of discrete energy values that the electrons bound to the nucleus can possess. These discrete energy levels are classified by shells (labelled n = 1, 2, 3, ) and subshells (labelled s, p, d, ). These energy levels determine the electronic configuration for an atom. The lowest energy levels are filled first by the electrons. The lowest energy state of an atom is called its ground state. When an atom absorbs energy, electrons can jump only to vacant and available energy levels (excited atoms). The sodium atom (atomic number Z = 11) has 11 electrons. Its electronic configuration can be written as Na Z = 11 1s 2 2s 2 2p 6 3s 1 total energy 3d 4s 3p 3s 2p ground state total energy 3d 4s 3p 3s 2p excited state atom can only absorb an amount of energy equal to the difference between two energy levels number of electrons 2s 1s not to scale 2s 1s not to scale 1s 2 2s 2 2p 6 3s 1 Fig. 2. Energy levels for a sodium atom. The shells shown are n = 1, 2, 3, 4. The subshells are s, p and d. The up arrow is for m s = +1/2 and the down arrow for m s = - ½. Two electrons fill an s-subshell; six electrons fill a p-subshell and 10 electrons fill a d-subshell. shell subshell 2
STRUTURE OF SOLIDS Molecules and solids both exist by virtue of the strong interactions that occur between their atoms. We shall see how quantum theory of the atom can be extended to account for the electrical properties of solids and how this has led to the computer, mobile phones and the internet revolution now happening. The basic building blocks (computer chips, microchips, microprocessors, etc) perform the necessary operations and calculations for devices such as computers and mobile phones. These basic building blocks are constructed from semiconductor materials in which resistors, capacitors, pn junctions and transistors are the fundamental components. Most solids are crystalline in nature, with their constituent atoms arranged in regular, repeated units. The ionic and covalent bonds between atoms that are responsible for the formation of molecules also act to hold many crystalline solids together. In ionic bonding, each ion (charged atom) attracts itself to as many ions of opposite sign that can fit around it. The attraction between opposite charged ions balances the repulsion between similar charged ions to given an equilibrium configuration. Figure 3 shows the ionic structure for a Na + l - crystal. _ large chloride negative ion (l - ) _ + + small positive sodium ion (Na + ) Fig. 3. Ionic structure for Na + l - crystal. 3
In covalent bonding crystals, the attractive interatomic forces holding the crystal together arise from the sharing of electrons between atoms. For example, in diamond, the carbon atoms share electron pairs with the four other carbon atoms adjacent to it. All the electrons in the outer shells of the carbon atoms participate in the binding (electron configuration of carbon 1s 2 2s 2 2p 2 ). This structure is the reason why diamond is extremely hard and it must be heated to a temperature greater than ~3000 o before its crystal structure is disrupted. All the electrons are tightly bound to carbon atoms, so very few electrons are mobile, hence, diamond is a very good electrical insulator. carbon diamond structure: each carbon atoms shares a pair of electrons with four neighbouring carbon atoms Fig. 4. ovalent structure of diamond. Each carbon atom shares electron pairs with four adjacent carbon atoms. 4
Metallic bonding is another very important way in which solids can be held together by strong cohesive forces. A characteristic property of all metal atoms is the presence of only a few electrons in their outer shells, and these electrons can be detached relatively easily to leave behind a positive ion. A useful model of a metal in a solid state is to consider the solid to be an assembly of atoms that have given up their outer most electrons to form an electron gas of freely moving electrons that pervades the entire metal. The electrostatic interaction between the positive cores (nuclei + bound electrons) and the free negative electrons holds the metal together. positive core (nucleus + bound electrons) The repulsion between the positive cores is balanced by the attractive forces with the negative electron cloud negative electron cloud consisting of free electrons that can easily move through crystal structure Fig. 5. The metallic bond The high electrical and thermal conductivities of metals follows from the ability of these free electrons to freely move throughout their crystal structure. This is not the case in covalent or ionic bonding where electrons are tightly bound to single or groups of atoms. Unlike other crystals, metals may be deformed without breaking, because the electron gas allows atoms to slide pass each other whilst maintaining their strength. It is easy to make alloys (mixture of different metals) because of the non-specific nature of the metallic bond. When electromagnetic radiation is incident upon a metal surface, the free electrons start to vibrate because they absorb energy from the oscillating electric and magnetic fields of the incident electromagnetic wave. These oscillating electrons themselves act as sources of electromagnetic radiation, emitting the radiation in all direction at the same frequency as the incident wave. Some of these waves produced from the oscillating electrons will be emitted from the surface of the metal giving rise to the metal surface having a lustrous appearance and also makes the metal a good reflector. (N.B. in reflection from the metal surface, the incident radiation is absorbed, and the emitted radiation is due to the oscillations of the free electrons. 5