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The Electronic Structure of Atoms

 

The Electronic Structure of Atoms



1. Atomic structure

At the beginning of any study of chemistry, we learn that compounds are built up from atoms, that a single atom consists of a nucleus and surrounding electrons, and that the nucleus consists of protons and neutrons.
An element is uniquely identified by its
atomic number (Z), which is the number of protons in the nucleus (the magnitude of its positive charge) and equal to the number of electrons around the nucleus of a (neutral) atom of the element. If it is needed, Z is given as a lower prefix to the chemical symbol of an element; see Figure 1.1. As indicated above, the nucleus of an atom of a specified element has neutrons in addition to protons, and the sum of the number of protons and neutrons in the nucleus is the mass number (A); this is indicated as an upper prefix to the chemical symbol of the element if it is needed.

Figure 1.1 Symbolic representation of an element.

Figure 1.1 Symbolic representation of an element.


The forms of an element with different numbers of neutrons in the nucleus are called isotopes, and they are chemically equivalent; they have the same value for Z but different values for A. Isotopes exist in proportions (natural abundances) which vary only slightly according to the distribution of the element in nature.
Masses of atoms are exceedingly small and commonly expressed in atomic mass units (1 amu
1.66 × 10-27 kg). More conveniently, however, an atomic mass is usually expressed as its relative atomic mass (Ar), the standard being the mass of one atom of a specific isotope of a specific element; the modern standard is the 12C isotope of carbon whose mass is defined as 12.0000 amu. Normally, however, we are not dealing with isotopically pure elements, but with the mixtures which occur in nature. Consequently, the relative atomic mass of an element (as opposed to that of just one of its isotopes) is the weighted mean of the values of Ar of the naturally occurring isotopes. For 13C, the less common stable isotope of carbon whose natural abundance is about 1.11%, Ar = 13.0034, and the value for the element carbon is 12.011.


2. Electrons and atomic orbitals

According to quantum theory, the energy of an electron outside the nucleus of an atom cannot be continuously variable—it is quantized—and only certain energy levels, which are called atomic orbitals (AOs), are available to the electron. In addition to being an energy level, an AO has spatial character which is identified by letters of the Roman alphabet, s, p, d, and f (an s orbital, for example, is spherical). In other words, an AO restricts the space available to an electron in an atom in addition to limiting its energy.
An electron is characterized by
spin as well as by its energy and spatial properties.
This is a property which originates in quantum theory and can have only one of two possible values. It does not matter whether we call these values plus and minus, left and right, or up and down (we cannot attach a simple physical significance to
spin). Any AO can accommodate a single electron of either spin, or two electrons if they are of opposite spin (when they are said to be spin-paired).
Atomic orbitals available to the electrons around the nucleus of an atom are grouped into
shells of increasing energy according to their principal quantum numbern (1, 2, 3, …); n also determines the types and number of orbitals within the shell. The shell of lowest energy with n = 1 has only a single s orbital, labelled 1s, so it can contain only two electrons. The next shell (n = 2) also contains an s orbital (labelled 2s) and, in addition, three p orbitals (2px, 2py, and 2pz); these three are degenerate—they are of the 
same energy. 

Atomic orbitals involved in shells of n = 1–4: 

Shell 1: 1s
         2: 2s, 2p
         3: 3s, 3p, 3d
         4: 4s, 4p, 4d, 4f


The four AOs of this second shell (n = 2) can accommodate a total of up to eight electrons. The third shell (n = 3) contains one 3s and three 3p orbitals (3px, 3py,and 3pz) plus a set of five degenerate 3d orbitals—a total of 9 AOs which (together) can hold up to 18 electrons.

The relative energies of some of the atomic orbitals mentioned above for an unspecified atom are shown in Figure 1.2. The s orbitals of increasing energy with principal quantum numbers 1–5 are shown in the column on the left; in the centre column, the p orbitals are seen to increase in energy starting from n = 2; the five degenerate d orbitals only start with n = 3 (and no higher ones are shown). None of the seven-fold degenerate f orbitals are shown as they are higher in energy and do not start until n = 4; they are of minimal importance in organic chemistry.

Figure 1.2 Energy levels of atomic orbitals.

Figure 1.2 Energy levels of atomic orbitals.


Figure 1.3 The shapes of s and p atomic orbitals.

Figure 1.3 The shapes of s and p atomic orbitals.

As mentioned above, the atomic orbital occupied by an electron indicates the space available to it as well as its energy. An s orbital is spherical, while each p orbital is elongated and circularly symmetrical about one of the three mutually perpendicular Cartesian axes (so they are labelled px, py, and pz), as illustrated in Figure 1.3 (see also Sub-section 2.2.1)



3. Electronic configuration of an atom

The number of electrons around the nucleus of an isolated neutral atom is determined by its atomic number (Z, equal to the number of protons in its nucleus). In principle, these electrons can be distributed amongst the atomic orbitals in many ways, and any one distribution is referred to as an electronic configuration (or electronic structure). 

The different configurations correspond to different total electronic energies, and the most important is the one of lowest energy; this is called the ground-state electronic configuration. We can imagine a nucleus of an atom and a number of electrons equal to its atomic number being fed into the available orbitals; this is done according to the following three rules (sometimes known collectively as the Aufbau Principle from the German word meaning ‘building up’):

  1. Electrons are added to orbitals in the order of their increasing energy (see Figure 1.2).
  2. Any orbital can hold one electron of either spin or two electrons of opposite spin.
  3. When the next available orbitals are degenerate, electrons with the same spin (i.e. unpaired) are added to them one at a time until they are all singly occupied (Hund's rule); a second electron of opposite (or paired) spin may then be added to each of them in turn.


To give a specific example, the result of following these rules for carbon (
Z=6, so there are 6 electrons to be fed in) leads to the ground-state electronic configuration 1s22s22px12p1shown in Figure 1.4.

Figure 1.4 Ground-state electronic confi guration of a carbon atom (1s22s22p2). Electrons of opposite spin are represented by arrows pointing up and down.
Figure 1.4 Ground-state electronic confi guration of a carbon atom (1s22s22p2). Electrons of opposite spin are represented by arrows pointing up and down.

Table 1.1 shows the ground-state electronic configurations of elements of the first three periods of the periodic table. Orbital occupancy is shown by a suffix (1 or 2) to the orbital designation. The first column corresponds to the first period with the addition of electrons to the 1s orbital to give hydrogen first then the noble gas element, helium.

This completes the first shell (1s2) which then becomes the inner shell, abbreviated by [He], for elements of the second period listed in the second column of Table 1.1 where electrons are added to the second shell (n = 2). Amongst these, for example, the electronic configuration of 6C is given as [He]2s22p1x2p1y (see Figure 1.4); this shows that the ground state of a C atom contains the filled inner shell of He ([He]), 2 electrons in the 2s orbital, and 1 electron in each of 2px and 2py orbitals.

The second shell is complete (two electrons in each of the four orbitals available) with the electronic configuration of neon. The third column of Table 1.1 corresponds to elements of the third period where electrons are being added to the third shell (n = 3), the inner first and second shells being complete; this period ends with the third noble gas element, argon.

We have already seen that an element is uniquely identified by its atomic number (Zwhich, in the neutral atom, is equal to the total number of electrons around the nucleus.

However, it is the electrons in the outermost shell (the valence shell) which characterize the nature of the element, and these are called the valence electrons of the atom. The electrons of the full inner shells are called core electrons; they have only a minor influence on the chemical properties of the element and are not involved in the formation of  chemical bonds. 

For example, lithium has one valence electron (2s1), fluorine has seven (2s22p5), and carbon has four (2s22p2) in the n = 2 valence shell. Atoms of these three elements have 1s2 inner core electrons and, as for all elements, their chemical properties are determined principally by their valence electrons.

a . The symbol of each element is given with its atomic number. The fi lled inner shells of the second and third period elements are indicated by the bracketed symbol of the last noble gas before the element, [He] or [Ne]; these are called the core electrons (see above).

a . The symbol of each element is given with its atomic number. The fi lled inner shells of the second and third period elements are indicated by the bracketed symbol of the last noble gas before the element, [He] or [Ne]; these are called the core electrons (see above).


4. Lewis representation of atoms

In 1902, the American G.N. Lewis proposed a method of representing atoms which gave prominence to their valence electrons and facilitated comparisons between different elements. The Lewis representation of an atom is the normal chemical symbol of the element with valence electrons shown by dots, i.e. the chemical symbol corresponds to the nucleus and the core electrons (those in the filled inner shells). 

Table 1.2 shows part of the periodic table with Lewis representations of atoms. By comparing the Lewis representations with the ground-state electronic configurations in Table 1.1, we see that the four dots around the C for carbon correspond to two electrons in the 2s orbital and one electron in each of two 2p orbitals. For the oxygen atom, two electrons in the 2s orbital and four electrons in 2p orbitals are represented by six dots around the O. The maximum number of dots for the valence electrons of the main group elements shown here (periods 1–3) is eight—an octet.

Table 1.2 shows part of the periodic table with Lewis representations of atoms.

Table 1.2 shows part of the periodic table with Lewis representations of atoms.



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