3.3 Electronic configurations and the Periodic Table
Figure 21 has been designed for use in a particular thought experiment. The purpose of the thought experiment is to see how the electronic configuration of the atoms changes as one moves through the Periodic Table from beginning to end. We start with the hydrogen atom, which has one proton and one electron. Then we
1.2 Chemical elements Atoms of the same atomic number behave virtually identically in chemical reactions. They are therefore given the same chemical name and chemical symbol. For example, the atom of atomic number 6, which is shown in Figure 1, is a carbon atom, whose symbol is C. All materials are made of atoms, but there is a special class of substan
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). 4.1 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 3.6 Scattering in three dimensions Sophisticated methods have been developed to analyse scattering in three-dimensions. The complexity of these methods makes them unsuitable for inclusion in this unit but it is appropriate to say something about the basic quantities involved. In three dimensions, we are obliged to think in terms of scattering at a given angle, rather than in terms of one-dimensional reflection or transmission. We distinguish between the incident particles (some of which may be unaffected by the target) a 3.5 Scattering from finite square wells and barriers The procedure used to analyse scattering from a finite square step can also be applied to scattering from finite square wells or barriers, or indeed to any combination of finite square steps, wells and barriers. The general procedure is as follows: Divide the x-axis into the minimum possible number of regions of constant potential energy. Write down the general solution of the relevant time-independent Schrödinger equation in 3.4 Probability currents The expressions we have derived for reflection and transmission coefficients were based on the assumption that the intensity of a beam is the product of the speed of its particles and their linear number density. This assumption seems very natural from the viewpoint of classical physics, but we should always be wary about carrying over classical ideas into quantum physics. In this section we shall establish a general quantum-mechanical formula for the beam intensity. The formula will be consi 3.3 Scattering from a finite square step The kind of one-dimensional scattering target we shall be concerned with in this section is called a finite square step. It can be represented by the potential energy function 2.1 Overview Session 2 discusses the scattering of a particle using wave packets. We shall restrict attention to one dimension and suppose that the incident particle is initially free, described by a wave packet of the form This is a superposition of de Broglie waves, with the function Acknowledgements The content acknowledged below is Proprietary (see terms and conditions). This content is made available under a Creative Commons Attribution-NonCommercial-ShareAlike 2.0 Licence The author of this unit is Peter Sheldon. Grateful acknowledgement is made to the following sources for permission to reproduce material 4.4 Other Wenlock Limestone fossils Among the other fossils common in the Wenlock Limestone are brachiopods (Figure 12a and b), gastropods (Figure 12c) and bryozoans (Figure 12d). You may need to reread Section 1.3 to remind yourself about various aspects of these groups. Figure 13 (the unit image) is a reconstruction of a typical scene from a Wenlock Limestone environment. See
