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
2.2 Breathing air A swimming elephant can breathe by holding the end of its trunk out of the water, but if it tried to find its food under the surface, like the desman, it would have to hold its breath. Neither the mammalian lung nor the skin can extract enough oxygen from water to sustain life, so aquatic mammals must come to the surface at intervals to breathe; and all of them – pinnipeds, sirenians and cetaceans – drown if they are prevented from doing so for prolonged periods. Lungs form 7% of th
6.3 Valence-shell electron-pair repulsion theory The theory of molecular shape that we have been working towards is called valence-shell electron-pair repulsion theory (VSEPR theory). When applied to molecules and ions of the typical elements, its success rate is high. Here is a stepwise procedure that you can follow when applying this theory. It is illustrated with the molecule XeF4 and the ion C1O3−. Xenon tetrafluoride is one of the select band of noble gas compounds that were unknown before 1962
6.1 Introduction Structural formulae of, for example, hexan-1-ol (Structure 6.1) and PF5 (Structure 5.13) merely tell us the immediate neighbours of any particular atom. They are two-dimensional drawings, which ignore the three-dimensional shapes of the molecules. But in studying the structures obtained by X-ray crystallography in Sectio
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. 3.4 Outer electronic configurations and the Periodic Table The essential message of Figure 22 is that the Groups of elements that appear in columns of the Periodic Table usually have atoms with similar outer electronic configurations. Figure 23 incorporates these configurations into our mini-Periodic Table of typical elements; they appear at the top of each Group. They imply that the typi 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 3.2 The electronic configurations of atoms The quantum theory of the atom tells us that we cannot say exactly where an electron in an atom will be at any particular moment; we can speak only of the probability of finding an electron at a particular point. So the precise orbits shown in the Rutherford model of Figure 1 misrepresent the arrangement of electrons about 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:
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. 4.4 Further exercises In this exercise, take
2.1 The four rules of arithmetic You are now going to use the four operation keys (on the bottom right-hand side of the TI-84 keyboard): Does it make sense? 1.1 Mathematics and you Many people's ideas about what mathematics actually is are based upon their early experiences at school. The first two activities aim to help you recall formative experiences from childhood. Read 4.4 Self-assessment questions and problems Find the distance between the numbers 2 − i and 1 + 3i. 2.3 Section summary In this section we have seen that the complex number system is the set R × R together with the operations + and × defined by From this, one can justify the performance of ordinary algebraic operations on expressions of the form a + ib
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Exercise 29
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Example 3
Activity 1 Carl Jung's school days
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