Chapter 1

Basic concepts: atomsTOPICS Fundamental particles. Atomic number, mass number and isotopes. An overview of quantum theory. Orbitals of the hydrogen atom and quantum numbers. The multi-electron atom, the aufbau principle and electronic configurations. The periodic table. Ionization energies and electron affinities.

1.1 Introduction

Inorganic chemistry is the chemistry of all elements except carbon. Inorganic chemistry is not simply the study of elements and compounds; it is also the study of physical principles.Examples1- In order to understand solubility, we apply laws of thermodynamics.2- To propose details of a reaction mechanism, then a knowledge of reaction kinetics is needed.3- Overlap between physical and inorganic chemistry is also significant in the study of molecular structure.

Inorganic chemistry: it is not an isolated branch of chemistry

1.2 Fundamental particles of an atom

An atom is the smallest unit quantity of an element that is capable of existence, either alone or in chemical combination with other atoms of the same or another element. The fundamental particles of which atoms are composed are the proton , electron and neutron.

The nucleus of an atom consists of protons and (with the exception of protium) neutrons, and is positively charged; the nucleus of protium consists of a single proton. The electrons occupy a region of space around the nucleus. Nearly all the mass of an atom is concentrated in the nucleus.The volume of the nucleus is only a tiny fraction of that of the atom.

The radius of the nucleus is about 10-15 m while the atom itself is about 105 times larger than this.

1.3 Atomic number, mass number and isotopes

Relative atomic massAtomic mass unit (amu) is 1/12 the mass of 12C (1.660 × 10-27 kg)

Relative atomic masses ( Ar) are thus all stated relative to 12C = 12.0000. The masses of the proton and neutron can be considered to be 1 u where u is the atomic mass unit (1 u 1.660 x10-27 kg).Isotopes Nuclides of a particular element that differ in the number of neutrons and, therefore, their mass number, are called isotopes .Isotopes of some elements occur naturally while others may be produced artificially.

Elements that occur naturally with only one nuclide are monotopic

Elements that exist as mixtures of isotopes

Since the atomic number is constant for a given element, isotopes are often distinguished only by stating the atomic masses, e.g.12C and 13C.

Isotopes and allotropesDo not confuse isotope and allotrope ! Sulfur exhibits bothisotopes and allotropes.

Allotropes of an element are different structural modifications of that element. Allotropes of sulfur include cyclic structures, e.g. S6 and S8, and Sx-chains of various lengths (poly catenasulfur).

Allotropes: element's atoms are bonded together in a different manner

Isotopes can be separated by mass spectrometry

Figure 1.1b shows a mass spectrometric trace for molecular S8, the structure of which is shown in Figure 1.1c; five peaks are observed due to combinations of the isotopes of sulfur.

1.4 Successes in early quantum theory

The development of quantum theory took place in two stages. In the older theories (1900–1925), the electron was treated as a particle, and the achievements of greatest significance to inorganic chemistry were the interpretation of atomic spectra and assignment of electronic configurations.

In more recent models, the electron is treated as a wave (hence the name wave mechanics) and the main successes in chemistry are the elucidation of the basis of stereochemistry and methods for calculating the properties of molecules

Some important successes of classical quantum theory

Planck suggested that energy could be absorbed or emitted only in quanta of Magnitude E related to the frequency of the radiation, ,

The Planck constant (h = 6.626 x10-34 J s)

The hertz, Hz, is the SI unit of frequency.

c is the speed of light in a vacuum (c = 2.998 x108ms-1)

is the wavelength

Rutherford–Bohr model of the atom. When an electric discharge is passed through a sample of dihydrogen, the H2 molecules dissociate into atoms, and the electron in a particular excited H atom may be promoted to one of many high energy levels.These states are transient and the electron falls back to a lower energy state, emitting energy as it does so. The consequence is the observation of spectral lines in theemission spectrum of hydrogen

Balmer pointed out that the wavelengths of the spectral lines observed in the visible region of the atomic spectrum of hydrogen obeyed the following equation.

n is an integer 3, 4, 5 .

Other series of spectral lines occur in the ultraviolet (Lymanseries) and infrared (Paschen, Brackett and Pfund series)

All lines in all the series obey the general expression given in the following equation:

For the Lyman series, n =1, For the Balmer series, n = 2, and For the Paschen, Brackett and Pfund series, n = 3, 4 and 5 respectively

Energy is absorbed or emitted only w he n an electron moves from one stationary state to another and the energy change is given by the following equation:

If we apply the Bohr model to the H atom, the radius of each allowed circular orbit can be determined

An increase in the principal quantum number from n = 1 to n = has a special significance.

Ionization energy, IE, can be determined

Although the SI unit of energy is the joule, ionization energies are often expressed in electron volts (eV) (1 eV = 96:4853 = 96:5 kJ mol-1). Therefore, the ionization energy of hydrogen can also be given as 13.60 eV.

1.5 An introduction to wave mechanicsThe wave-nature of electronsIn 1924, Louis de Broglie argued that if light were composed of particles and yetshowed wave-like properties, the same should be true of electrons and other particles. This phenomenon is referred to as wave–particle duality.

momentum mv ( m = mass and v = velocity of the particle)

The uncertainty principle

Heisenberg’s uncertainty principle:it is impossible to know exactly both the momentum and position of the electron at the same instant in time

In order to get around this problem, rather than trying to define its exact position and momentum, we use the probability of finding the electron in a given volume of space.

1.6 Atomic orbitals

Degenerate orbitals possess the same energy.

Fig. 1.5 Plots of the radial parts of the wavefunction, R ( r ), against distance, r , from the nucleus for (a) the 1s and (b) the 2 s atomic orbitals of the hydrogen atom; the nucleus is at r = 0. The vertical scales for the two plots are different but the horizontal scales are the same.

The radial part of the wavefunction,R (r )

Fig. 1.6 Plots of radial parts of the wavefunction R (r ) against r for the 2 p,3p,4p and 3d atomic orbitals; the nucleus is at r =0.

The radial distribution function, 4 r2R(r )2

A useful way of depicting the probability density is to plot aradial distribution function and this allows us to envisage the region in space in which the electron is found.

The probability of finding the electron somewhere in space is taken to be 1.

Each function is zero at the nucleus, following from the r2 term and the fact that at the nucleus r = 0.Each plot of 4r2R(r)2 shows at least one maximum value for the function, corresponding to a distance from the nucleus at which the electron has the highest probability of being found.Points at which 4r2R(r)2 = 0 (ignoring r = 0) correspond to radial nodes where R(r) = 0.

The angular part of the wavefunction, A (, )

The amplitude of a wavefunction may be positive or negative; this is shown using + and - signs, or by shading the lobes in different colours.chemists often indicate the amplitude by a sign or by shading because of the importance of the signs of the wavefunctions with respect to their overlap during bond formation

Orbital energies in a hydrogen-like species

For the hydrogen atom, Z = 1, but for the hydrogen-like He+ ion, Z = 2. The dependence of E on Z2 therefore leads to a significant lowering of the orbitals on going from H to He+

.

The spin quantum number and the magnetic spin quantum number

Angular momentum, the inner quantum number, j , and spin--orbit coupling

1.7 Many-electron atoms

Ground state electronic configurations: experimental dataThe following sequence is approximately true for the relative energies (lowest energy first) of orbitals in neutral atoms :

Some irregularities: see Table 1.3 in textbook

Penetration and shielding

Effective nuclear charge and Slater’s rules

Thus, an electron in the 4s (rather than the 3d) atomic orbital is under the influence of a greater effective nuclear charge and in the ground state of potassium, it is the 4s atomic orbital that is occupied.

Collective names for some of the groups of elements in the periodic table are given in Table 1.4.

The periodic table in Figure 1.13 shows elements up to Z =112. Three additional elements with Z = 114, 116 and 118 have been reported, but still await IUPAC authentication.

1.9 The aufbau principle

Ground state electronic configurations

. Orbitals are filled in order of energy, the lowest energy orbitals being filled first.

. Hund’s first rule (often referred to simply as Hund’s rule): in a set of degenerate orbitals, electrons may not be spin-paired in an orbital until each orbital in the set contains one electron; electrons singly occupying orbitals in a degenerate set have parallel spins, i.e. they have the same values of ms.

. Pauli exclusion principle: no two electrons in the same atom may have the same set of n, l, ml and ms quantum numbers; it follows that each orbital can accommodate a maximum of two electrons with different ms values (different spins = spin-paired).

(aufbau means ‘building up’ in German)

Valence and core electronsThe configuration of the outer or valence electrons is of particular significance. These electrons determine the chemical properties of an element

Electrons that occupy lower energy quantum levels are called core electrons Diagrammatic representations of electronic configurations

In this case, the electrons are represented by arrows

with the direction of the arrow corresponding to

1.10 Ionization energies and electron affinitiesThe first ionization energy, IE1, of an atom is the internal energy change at 0 K, U(0 K), associated with the removal of the first valence electron (equation 1.17); the energy change is defined for a gas-phase process. The units are kJ mol-1 or electron volts (eV)

IE2

IE3

Several repeating patterns are apparent and some features to note are:. the high values of IE1 associated with the noble gases;. the very low values of IE1 associated with the group 1 elements;. the general increase in values of IE1 as a given period is crossed;. the discontinuity in values of IE1 on going from an element in group 15 to its neighbour in group 16;. the decrease in values of IE1 on going from an element in group 2 or 12 to its neighbour in group 13;. the rather similar values of IE1 for a given row of d-block elements.

Electron affinitiesThe first electron affinity (EA1) is minus the internal energy change for the gain of an electron by a gaseous atom. The second electron affinity of atom Y is defined for process. Each reaction occurs in the gas phase.