Basic concept:s atom
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.
A neutron and a proton have approximately the same mass and, relative to these, an electron has negligible mass (Table 1.1). The charge on a proton is positive and of equal magnitude, but opposite sign, to that on a negatively charged electron. A neutron has no charge. In an atom of any element, there are equal numbers of protons and electrons and so an atom is neutral. The nucleus of an atom consists of protons and (with the exception of protium, see Section 10.3) 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, but the volume of the nucleus is only a tiny fraction of that of the atom; the radius of the nucleus is
about 1015 m while the atom itself is about 105 times larger than this. It follows that the density of the nucleus is enormous, more than 1012 times that of the metal Pb. Although chemists tend to consider the electron,
proton and neutron as the fundamental (or elementary) particles of an atom, particle physicists deal with yet smaller particles.
Atomic number, mass number and isotopes
Nuclides, atomic number and mass number
A nuclide is a particular type of atom and possesses a characteristic atomic number, Z, which is equal to the number of protons in the nucleus. Because the atom is electrically neutral, Z also equals the number of electrons. The mass number, A, of a nuclide is the number of protons and neutrons in the nucleus. A shorthand method of showing the atomic number and mass number of a nuclide along with its symbol, E, is:
Relative atomic mass
Since the electrons are of minute mass, the mass of an atom essentially depends upon the number of protons and neutrons in the nucleus. As Table 1.1 shows, the mass of a single atom is a very small, non-integral number, and for convenience a system of relative atomic masses is adopted. The atomic mass unit is defined as 1/12th of the mass of a 12/ 6C atom so that it has the value 1:660 x 10-27 kg. Relative atomic masses (Ar) are therefore all stated relative to 12 6C ¼ 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 10-27 kg).
Nuclides of the same element possess the same number of protons and electrons but may have different mass numbers. The number of protons and electrons defines the element but the number of neutrons may vary. Nuclides of a particular element that differ in the number of neutrons and, therefore, their mass number, are called isotopes (see Appendix 5). Isotopes of some elements occur naturally while others may be produced artificially.
Elements that occur naturally with only one nuclide are monotopic and include phosphorus, 31/15P, and fluorine, 19/9F. Elements that exist as mixtures of isotopes include C (12/6C and 13/6C) and O (16/8O, 17/8O and 18/8O). 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.
Worked example 1.1 Relative atomic mass
Calculate the value of Ar for naturally occurring chlorine if the distribution of isotopes is 75.77% 35/17Cl and 24.23% 37/17Cl. Accurate masses for 35Cl and 37Cl are 34.97 and 36.97.
The relative atomic mass of chlorine is the weighted mean of the mass numbers of the two isotopes:
Isotopes can be separated by mass spectrometry and Fig. 1.1a shows the isotopic distribution in naturally occurring Ru. Compare this plot (in which the most abundant isotope is set to 100) with the values listed in Appendix 5. Figure 1.1b shows a mass spectrometric trace for molecular S8, the structure of which is shown in Fig. 1.1c; five peaks are observed due to combinations of the isotopes of sulfur. (See end-of-chapter problem 1.5.)
Isotopes of an element have the same atomic number, Z, but different atomic masses.
Successes in early quantum theory
We saw in Section 1.2 that electrons in an atom occupy a region of space around the nucleus. The importance of electrons in determining the properties of atoms, ions and molecules, including the bonding between or within them, means that we must have an understanding of the electronic structures of each species. No adequate discussion of electronic structure is possible without reference to quantum theory and wave mechanics. In this and the next few sections, we review some crucial concepts. The treatment is mainly qualitative, and for greater detail and more rigorous derivations of mathematical relationships, the references at the end of Chapter 1 should be consulted.
The development of quantum theory took place in two stages. In 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 (exact only for species involving light atoms).
Since all the results obtained by using the older quantum theory may also be obtained from wave mechanics, it may seem unnecessary to refer to the former; indeed, sophisticated treatments of theoretical chemistry seldom do. However, most chemists often find it easier and more convenient to consider the electron as a particle rather than a wave.
Some important successes of classical quantum theory
Historical discussions of the developments of quantum theory are dealt with adequately elsewhere, and so we focus only on some key points of classical quantum theory (in which the electron is considered to be a particle).
At low temperatures, the radiation emitted by a hot body is mainly of low energy and occurs in the infrared, but as the temperature increases, the radiation becomes successively dull red, bright red and white. Attempts to account for this observation failed until, in 1901, Planck suggested that energy could be absorbed or emitted only in quanta of magnitude E related to the frequency of the radiation, , by eq. 1.1. The proportionality constant is h, the Planck constant (h ¼ 6:626 10-34 J s).
The hertz, Hz, is the SI unit of frequency.
The frequency of radiation is related to the wavelength, , by eq. 1.2, in which c is the speed of light in a vacuum (c ¼ 2:998 108 m s1). Therefore, eq. 1.1 can be rewritten in the form of eq. 1.3. This relates the energy of radiation to its wavelength.
On the basis of this relationship, Planck derived a relative intensity/wavelength/temperature relationship which was in good agreement with experimental data. This derivation is not straightforward and we shall not reproduce it here.
When energy is provided (e.g. as heat or light) to an atom or other species, one or more electrons may be promoted from a ground state level to a higher energy state. This excited state is transient and the electron falls back to the ground state. This produces an emission spectrum.
One of the most important applications of early quantum theory was the interpretation of the atomic spectrum of hydrogen on the basis of the 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 the emission spectrum of hydrogen. The spectrum (a part of which is shown in Fig. 1.2) consists of groups of discrete lines corresponding to electronic transitions, each of discrete energy. In 1885, Balmer pointed out that the wavelengths of the spectral lines observed in the visible region of the atomic spectrum of hydrogen obeyed eq. 1.4, in which R is the Rydberg constant for hydrogen, is the wavenumber in cm1 , and n is an integer 3, 4, 5 . . . This series of spectral lines is known as the Balmer series.
Wavenumber is the reciprocal of wavelength; convenient (nonSI) units are ‘reciprocal centimetres’, cm-1
Other series of spectral lines occur in the ultraviolet (Lyman series) and infrared (Paschen, Brackett and Pfund series). All lines in all the series obey the general expression given in eq. 1.5 where n’ > n. For the Lyman series, n ¼ 1, for the Balmer series, n ¼ 2, and for the Paschen, Brackett and Pfund series, n ¼ 3, 4 and 5 respectively. Figure 1.3 shows some of the allowed transitions of the Lyman and Balmer series in the emission spectrum of atomic H. Note the use of the word allowed; the transitions must obey selection rules, to which we return in Section 20.7.
Bohr’s theory of the atomic spectrum of hydrogen
In 1913, Niels Bohr combined elements of quantum theory and classical physics in a treatment of the hydrogen atom. He stated two postulates for an electron in an atom: .
Stationary states exist in which the energy of the electron is constant; such states are characterized by circular orbits about the nucleus in which the electron has an angular momentum mvr given by eq. 1.6. The integer, n, is the principal quantum number.
where m ¼ mass of electron; v ¼ velocity of electron; r ¼ radius of the orbit; h ¼ the Planck constant; h=2 may be written as h.
. Energy is absorbed or emitted only when an electron moves from one stationary state to another and the energy change is given by eq. 1.7 where n1 and n2 are the principal quantum numbers referring to the energy levels En1 and En2 respectively.
If we apply the Bohr model to the H atom, the radius of each allowed circular orbit can be determined from eq. 1.8. The origin of this expression lies in the centrifugal force acting on the electron as it moves in its circular orbit. For the orbit to be maintained, the centrifugal force must equal the force of attraction between the negatively charged electron and the positively charged nucleus.
From eq. 1.8, substitution of n ¼ 1 gives a radius for the first orbit of the H atom of 5:293 1011 m, or 52.93 pm. This value is called the Bohr radius of the H atom and is given the symbol a0. An increase in the principal quantum number from n ¼ 1 to n ¼ 1 has a special significance. It corresponds to the ionization of the atom (eq. 1.9) and the ionization energy, IE, can be determined by combining eqs. 1.5 and 1.7, as shown in eq. 1.10. Values of IEs are quoted per mole of atoms.
One mole of a substance contains the Avogadro number, L, of particles: L ¼ 6:022 1023 mol-1
Although the SI unit of energy is the joule, ionization energies are often expressed in electron volts (eV) (1 eV¼ 96:4853 96:5 kJ mol1). Therefore, the ionization energy of hydrogen can also be given as 13.60 eV.
Impressive as the success of the Bohr model was when applied to the H atom, extensive modifications were required to cope with species containing more than one electron. We shall not pursue this topic further here.