The structure of atoms. What will be covered?

1. The nucleus 2. Atomic weight 3. Electronic structure 4. Electronic configuration of the elements 5. Valence 6. Hybridization 7. Periodic table

Why do we need to know this material? Atomic structure is the foundation of Materials Science. This material will form the basis for understanding the interatomic and intermolecular forces to be covered in the next section. Fundamentals. Atoms consist of nuclei and electrons. Nuclei are composed of protons and neutrons. Protons carry a positive charge of 1.69x10-19 coulombs and have a mass at rest of 1.67x10-24 g. Neutrons have no charge and have the same rest mass as protons. Overall the nucleus is thus positively charged. This charge is balanced by an equal charge due to a number of electrons equal to the number of protons (for neutral atoms). Each electron carries a charge of –1.69x10-19 coulombs. Nucleus. The number of protons in the nucleus is called the atomic number (this defines the elemental identity).

The number of neutrons in a nucleus is larger than or equal to the number of protons, with the larger excess of neutrons occurring for the larger atomic numbers. Many elements have isotopes, i.e. their nuclei contain an equal number of protons but have different numbers of neutrons; some of these isotopes are stable while others decompose via radioactive decay. Atomic weight. The atomic weight is given in terms of atomic mass units (amu) and indicates the mass of the atom in units of 1/12 the mass of the carbon isotope with 6 protons and 6 neutrons. The isotope therefore has an arbitrary atomic weight of 12 amu and is represented as 6C12. Here the subscript is the atomic number and the superscript the mass number, i.e. the sum of the number of protons and neutrons. Atomic weights are not whole numbers except for C12 by definition. The actual masses of the nuclei are not equal to the sum of the masses of all protons and neutrons but differ from that sum by the binding energy expresses as mass according to E=mc2. Atomic weights are normally weighted according to the natural abundance of the isotopes. For elements with large atomic masses, the binding energy is such that if an atom is split, the sum of the binding energies of the two resulting smaller nuclei is smaller than that of the parent nucleus. The difference is liberated as energy (fission). For the case of elements with small atomic masses such as hydrogen, energy is liberated when nuclei are fused (fusion). Electronic structure. From a basic materials science point of view, the arrangement of the electrons is the most important aspect of atomic structure.

The electronic structure determines the type and strength of the chemical bonds that can be established with other atoms and hence determines many important materials properties. For our purpose, we can consider electrons as particles, which surround the nucleus in some particular fashion such that their number is equal to the atomic number of the element (for neutral atoms). Example: the carbon atom: outside the nucleus it has six electrons. Using the Bohr theory of atomic structure, these were believed to be arranged in orbits of increasing distance from the nucleus. These orbits corresponded to gradually increasing levels of energy, that of the lowest energy, the 1s, accommodating two electrons, the next 2s, also accommodating two electrons and the remaining two electrons of the carbon atom going into the 2p level, which is actually capable of accommodating a total of six electrons. The Heisenberg uncertainty principle and the wave mechanical view of the electron have made it necessary to do away with anything so precisely defined as actual orbits. Instead, the wave-like electrons are now symbolized by wave functions such that the precise classical orbitals of Bohr are superceded by three-dimensional atomic orbitals of differing energy level. Thus, from quantum theory it can be established that electrons have different energies; discrete electron energy levels can be described in terms of quantum numbers.

Schrödinger Wave Equation (SWE):

where h is Plank’s constant, m is the particle mass, V(x,y,z) is the potential energy, and Ψ(x,y,z,t) is the wave function. Solutions to the SWE generate four quantum numbers. There is a principal quantum number (n), which can assume only integer values (n = 1,2,3,4…). Each of these numbers designates a shell around the atom in which certain electrons exist. Generally, the larger the value of n, the larger the energy of the electron in that shell. Within each shell the electrons carry a further quantum number (I). This azimuthal quantum number is associated with the total orbital angular momentum and can assume values from 0 to n-1. As a rule, energy increases with increasing I (although there are exceptions). The shells are further subdivided by the magnetic quantum number mI are ±1. Finally, a fourth quantum number (s) which takes into account the electron spin direction is assigned values of ±1/2. In order to develop a simple model of electron distribution in the elements we must take into account the Pauli exclusion principle: only one electron can be in a particular quantum state at a particular time, i.e. no two electrons can have identical values of the four quantum numbers. The maximum number of electrons that can exist in each shell is given by 2n2.

The maximum number of electrons that can occupy the 1 subshell is 2(2I+1). An alternate scheme is often used to indicate the electron quantum values in terms of capital letter for the principal quantum numbers (K,L,M,…) and lower case letters for the azimuthal quantum numbers (s, p, d and f).

Electronic configuration of the elements. The electrons of an atom are generally assigned spaces in shells and subshells according to increasing energy. As a rule, this is in order of increasing n, and within n in order of increasing I. There are important exceptions to this scheme. The energy of the typical 4s shell is lower than the energy of the 3d shell; similarly, the energy of the typical 5s shell is lower than the energy of the 4d shell. Therefore, the s shells are filled before the d shells with the lower main quantum number. This has important consequences regarding the magnetic properties of the affected elements.

Valence. This is related to the ability of the atom to enter into the chemical combination with other elements, i.e. atomic bonding. Valence is often determined by the number of electrons in the outermost combined sp level. These sp electrons may be added to, lost or shared with other atoms thus determining the nature of the atomic bonds. The ground state of the carbon atom will be: 1s2 2s2 2px1 2py1 with the 2pz orbital unoccupied. The two unpaired electrons are available for the formation of bonds with other atoms and at first sight appears divalent whereas the majority of stable compounds appear as quadrivalency. The 2s2 is therefore uncoupled to give 1s2 2s1 2px1 2py12pz1. Hybridization. A carbon atom combining with four other atoms clearly does not use the one 2s and the thre 2p atomic orbitals that would now be available for this would lead to the formation of three directed bonds, mutually at right angles to one another (with the three 2p orbitals), and one different, non-directed bond (with the spherical 2s orbital). Whereas in fact, the four C-H bonds in, for example, methane (CH4) are known to be identical and symmetrically (tetrahedrally) disposed at an angle of 109o 28’ to each other. This may be accounted for on the basis of re-deploying the 2s and the three 2p atomic obitals so as to yield four new (identical) orbitals, which are capable of forming stronger bonds. These new orbitals are known as sp3 hybrid atomic orbitals, and the process by which they are formed is known as hybridization. When a carbon combines with three other atoms (e.g. ethylene, C2H4) we have three sp2 hybrid atomic orbitals disposed at 120o to each other in the same plane (plane trigonal hybridization). When a carbon atom combines with two other atoms (e.g. acetylene, C2H2), two sp1 hybrid atomic orbitals disposed 180o to each other (digonal hybridization) are formed. In each case the s orbital is always involved as it is the one of lowest energy. Hybridization takes place so that the atom concerned can form as strong a bond as possible, and so that the atoms thus bonded (and the electron pairs constituting the bonds) are as far apart from each other as possible

to ensure that the total intrinsic energy of the resultant compound is at a minimum. Periodic table of the elements. Based upon their electronic configurations, the elements can be sensibly ordered in an arrangement known as the periodic table. The chemical character of an element is controlled by its atomic number and by the configuration of the outermost electrons. The electronic arrangement determines the group (vertical columns) into which the element will fall whereas the atomic number determines the position within this group. Columns refer to the number of electrons present in the outermost sp energy level and correspond to the most common valence. Horizontal rows are called periods and correspond to the value of the principal quantum numbers. Arranged in this way, there is a certain similarity of the chemical properties of the elements in a group as well as a systematic variation across a period. Some groups of elements are given certain names to emphasize their chemical similarity: Group IA: alkali metals Group IIA: alkaline earth metals Group VIIA: halogens Group O: noble gases Electronegativity of the elements increases progressively from left to right and bottom to top. Metals are electropositive whereas non-metals are electronegative. Classification according to 16 non-metals, 6 intermediates and the balance as metals.