4.2 Intermediate forms In essence, the argument about intermediate forms runs as follows. If whales evolved from a terrestrial ancestor through the accumulation of small differences over time, we should expect to find the fossils of a number of ‘missing links’, i.e. creatures with a mixture of terrestrial and aquatic characteristics. In fact, we might expect to find a succession of such animals, each a little bit more whale-like and a little bit less well adapted to life on land than its predecessor. To m
2.3 Moving about Water is more viscous than air, so it can take more effort to move through water (try running in a swimming pool). Friction between the body and the water causes turbulence, which holds a swimmer back, and the faster the swimmer tries to move, the greater the turbulence. One way of avoiding the problem is to leave the water for short periods and travel through air, and some of the smaller pinnipeds and cetaceans resort to ‘porpoising’, leaping from the water for short periods when they ne
8 Reviewing and reflecting
Figure 55 is a conceptual diagram that summarises this unit. Molecules are made of atoms, so it was with atoms, to the left of Figure 55, that we began. Early in Section 1 they acquired a structure with a positively charged nucleus surrounded by negatively charged electrons. To a chemist, the most important property of an atom is the
5.2 Summary of Section 5 The structural formulae of organic molecules can be divided into the carbon-hydrogen framework or skeleton, and the functional group(s). In the first approximation, the functional groups are the sites where reaction occurs, the framework remaining unreactive. This approximation works best when the framework consists of saturated carbon atoms. 4.5 More about covalent bonding So far, the valencies in Table 1 have just been numbers that we use to predict the formulae of compounds. But in the case of covalent substances they can tell us more. In particular, they can tell us how the atoms are linked together in the molecule. This information is obtained from a two-dimensional drawing of the structural form 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 6.2 Specific difficulties Some students contend with physical difficulties in reading. Here is one:
And here is another being offered advice by a friend:
3.1 Overview Scattering calculations using wave packets are so laborious that they are generally done numerically, using a computer. However, in many cases, scattering phenomena can be adequately treated using a procedure based on stationary states. This approach can give valuable insight into the scattering process without the need for computer simulations. Session 3 introduces the stationary-state approach to scattering. The discussion is mainly confined to one dimension, so a stationary-state sol 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 4.1 Trilobites As we've seen, the Cambrian explosion left the seas teeming with a huge variety of animals. In the following activity you will study some of the marine life at one particular time in the Palaeozoic Era – the middle part of the Silurian Period, 430 Ma ago. You'll look in detail at some fossils which come from a deposit in the UK called the Wenlock Limestone, famous for its many beautiful fossils. The Wenlock Limestone crops out mainly around Birmingham and the borders of Wales. Figure 4.4 Obesity and cardiovascular diseases Obesity and being overweight are well-known as risk factors for cardiovascular diseases. Carrying excess body fat predisposes individuals to developing elevated blood cholesterol and diabetes. You will begin to appreciate that many of the modifiable risk factors for cardiovascular diseases are interlinked. This means that influencing one, such as reducing the amount of stored lipids in the body, may have a positive effect in reducing the risk associated with high blood cholesterol levels and Introduction You may be studying this unit because you – or a member of your family or a friend – have been personally affected by cardiovascular diseases in some way. You may be professionally involved in looking after people with one of these diseases. Perhaps you are interested in health issues in general. Whatever your motivation or underlying reasons for studying this unit, you will gain valuable insights into the extent of cardiovascular diseases and their treatment in the early twenty-first cen 2.12 How likely are particular results? In real experiments, as opposed to hypothetical ones, it is very rare that scientists make a sufficiently large number of measurements to obtain a smooth continuous distribution like that shown in Figure 7d. However, it is often convenient to assume a particular mathematical form for typically distributed measurements, and the form that is usually 2.11 Using a calculator for statistical calculations
Table 3 shows all the values for each step in the process of calculating a standard deviation, so that you can see what the operations encapsulated by Equation 7 actually entail, but you will probably be relieved to hear that it is not usually necessary to carry out such detailed calculations. Scientific and graphics calculators (or computer sp 2.8 Descriptive statistics Scientists collect many different types of information, but sets of data may be very loosely classified into two different types. In the first type, so-called ‘repeated measurement’, an individual quantity is measured a number of times. An astronomer wanting to determine the light output of a star would take many measurements on a number of different nights to even out the effects of the various possible fluctuations in the atmosphere that are a cause of stars ‘twinkling’. In the seco 2.6 Combining probabilities The probabilities described in Section 2.3 and Section 2.4 related to the outcomes of a single process, such as repeatedly tossing one coin. Now suppose you were to toss three separate coins simultaneously. What is the prob 1.4 How precise are the measurements? Scientists are always trying to get better and more reliable data. One way of getting a more precise measurement might be to switch to an instrument with a more finely divided scale. Figure 4 shows parts of two thermometers placed side by side to record the air temperature in a room. Introduction Many problems are best studied by working with real functions, and the properties of real functions are often revealed most clearly by their graphs. Learning to sketch such graphs is therefore a useful skill, even though computer packages can now perform the task. Computers can plot many more points than can be plotted by hand, but simply ‘joining up the dots’ can sometimes give a misleading picture, so an understanding of how such graphs may be obtained remains important. The object of t
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