4.2 Ionic and covalent bonding We begin by applying simple bonding theories to molecular chlorine gas (Cl2) and non-molecular sodium chloride (NaCl), whose structures were discussed in Section 1. Figure 28 shows the result. 4.1 Introduction Simple theories of chemical bonding are based on the idea of the electron-pair bond, and the extent to which the electron pair is shared between the bound atoms. There is also an assumption that the electronic structures of noble gas atoms are especially stable, and that many elements try to attain these structures when they react to form chemical compounds. These ideas were the brainchild of the American chemist, G. N. Lewis (Box 3). In developing them, we shall simplify the electronic confi 3.6 Summary of Section 3 The electronic configuration of an atom can be obtained by allocating its electrons to s, p, d and f sub-shells in the order given by Figure 21. This procedure generates a periodicity in electronic configuration which matches that of the Periodic Table. The typical elements have 3.5 Electron states and box diagrams So far, we have represented the electronic state of an atom as a collection of sub-shells. Now we turn to the states of the electrons within those sub-shells. Just as shells can be broken down into sub-shells, so sub-shells can be broken down into atomic orbitals. Each atomic orbital describes an allowed spatial distribution about the nucleus for an electron in the sub-shell. Here we shall only be concerned with their number. Consider the formula for the sub-shell electron capaci 3.1 Introduction Section 2 used some simple examples to illustrate chemical periodicity. But how can we explain such periodicity? The answer lies in the way that the electrons in atoms are arranged about the positively charged nucleus. In chemical reactions, atoms change partners. We know that the outsides of atoms consist of electrons, so contact and connection between atoms is likely to take place through their electrons, and in particular, through the electrons in their outer shells. So similarities in 2.4 Summary of Section 2 The typical elements can be displayed in a mini-Periodic Table of eight Groups and seven Periods (Figure 18). The Periods are numbered from 1 to 7 and the Groups are labelled I-VIII. Metals appear on the left of this table, non-metals on the right and semi-metals in between. 2.1 Chemical periodicity The chemistry of the elements is immensely varied. But amidst that variety there are patterns, and the best known and most useful is chemical periodicity: if the elements are laid out in order of atomic number, similar elements occur at regular intervals. The discovery of chemical periodicity is particularly associated with the nineteenth-century Russian chemist Dmitri Ivanovich Mendeléev (Figure 16). The periodicity is represented graphically by Periodic Tables. Author(s): 1.1 Introduction The idea that everything that we can see is an assembly of tiny particles called atoms is chemistry's greatest contribution to science. There are about 120 known kinds of atom, and each one is distinguished by a name, by a chemical symbol, and by a number called the atomic number. The meaning of atomic number is best understood from the Rutherford model of the atom (Author(s): Learning outcomes After studying this unit you should be able to: explain what is meant by isotopes, atomic numbers and mass numbers of the atoms of chemical elements by referring to the Rutherford model of the atom; give an example of how differences in the molecular structures of chemical compounds give rise to differences in macroscopic properties; given a Periodic Table, point to some sets of elements with similar chemistry and to others in which there are progre Introduction This unit is an adapted extract from the course The molecular world
(S205) This unit will provide you with a detailed understanding of some of the important problems and topics that are being studied by the chemists of today, and of the ways in which associated problems might be solved by chemical methods. But to acquire this understanding you must have a good grasp of fundamental chemic Acknowledgements The material acknowledged below is Proprietary (see terms and conditions) and used under licence (not subject to Creative Commons licence). The content is from SM358_1 Book 1 Wave Mechanics – Chapter 7 Scattering and Tunnelling, pages 178–209. Grateful acknowledgement is made to the following sources 6 Summary Scattering is a process in which incident particles interact with a target and are changed in nature, number, speed or direction of motion as a result. Tunnelling is a quantum phenomenon in which particles that are incident on a classically impenetrable barrier are able to pass through the barrier and e 5.4 The scanning tunnelling microscope The scanning tunnelling microscope (STM) is a device of such extraordinary sensitivity that it can reveal the distribution of individual atoms on the surface of a sample. It can also be used to manipulate atoms and even to promote chemical reactions between specific atoms. The first STM was developed in 1981 at the IBM Laboratories in Zurich by Gerd Binnig and Heinrich Rohrer. Their achievement was recognised by the award of the 1986 Nobel prize for physics. In an STM the sample 5.3 Stellar astrophysics If tunnelling out of nuclei is possible then so is tunnelling in! As a consequence it is possible to trigger nuclear reactions with protons of much lower energy than would be needed to climb over the full height of the Coulomb barrier. This was the principle used by J.D. Cockcroft and E.T.S. Walton in 1932 when they caused lithium-7 nuclei to split into pairs of alpha particles by bombarding them with high-energy protons. Their achievement won them the 1951 Nobel prize for physics. The same p 5.2 Alpha decay You have probably met the law of radioactive decay, which says that, given a sample of N0 similar nuclei at time t = 0, the number remaining at time t is N(t) = N0e−λt, where λ, the decay constant for a particular kind of nucleus, determines the rate at which the nuclei decay. The half-life is the time needed for half of any sufficiently large sample to decay. It is related to the de 5.1 Overview The discovery that quantum mechanics permits the tunnelling of particles was of great significance. It has deep implications for our understanding of the physical world and many practical applications, particularly in electronics and the developing field of nanotechnology. This section introduces some of these implications and applications. Applications naturally involve the three dimensions of the real world, and realistic potential energy functions are never perfectly square. Despite these 4.4 Stationary states and tunnelling in one dimension We will now use the stationary-state approach to analyse the tunnelling of particles of energy E0 through a finite square barrier of width L and height V0 when E0 < V0 (see Figure 21). 4.3 Stationary states and barrier penetration The example of tunnelling we have just been examining can be regarded as a special case of scattering; it just happens to have E0 < V0. As long as we keep this energy range in mind, we can apply the same stationary-state methods to the study of tunnelling that we used earlier when studying scattering. As before, we shall start by considering the finite square step, whose potential energy function was defined in Equations 4.2 Wave packets and tunnelling in one dimension
Figure 18 shows a sequence of images captured from a wave packet simulation program. The sequence involves a Gaussian wave packet, with energy expectation value 〈E〉 = E0, incident from the left on a finite square barrier of height V0. The sequence is broadly simil 4.1 Overview One of the most surprising aspects of quantum physics is the ability of particles to pass through regions that they are classically forbidden from entering. This is the phenomenon of quantum-mechanical tunnelling that was mentioned in Session 1. In Session 4 we first demonstrate the phenomenon of tunnelling with the ai
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