Introduction

In this chapter we shall consider some general principles for making measurements. These are principles which should be borne in mind, first in selecting a particular method and second in getting the most out of it. By the latter we mean making the method as precise or reproducible as possible, and – even more important – avoiding its inherent systematic errors.

We shall illustrate the various points by describing some specific examples of instruments and methods. Though chosen from several branches of physics, they are neither systematic nor exhaustive. The idea is that, having seen how the principles apply in these cases, you will be able to apply them yourselves in other situations. As always there is no substitute for laboratory experience. But experience without thought is a slow and painful way of learning. By concentrating your attention on certain aspects of measurement making we hope to make the experience more profitable.

Metre rule

We start with almost the simplest measuring device there is – a metre rule. Its advantages are that it is cheap to make and convenient to use. It can give results accurate to about ⅕ mm. However, to achieve this accuracy certain errors must be avoided.

Parallax error. If there is a gap between the object being measured and the scale, and the line of sight is not at right angles to the scale, the reading obtained is incorrect (Fig. 6.1a).

The system of units used throughout this book is known as SI, an abbreviation for Système International d'Unités. It is a comprehensive, logical system, designed for use in all branches of science and technology. It was formally approved in 1960 by the General Conference of Weights and Measures, the international organization responsible for maintaining standards of measurement. Apart from its intrinsic merits, it has the great advantage that one system covers all situations – theoretical and practical.

A full account of SI will be found in a publication of the National Physical Laboratory (Bell 1993). The following are the essential features of the system.

(1) SI is a metric system. There are seven base units (see next section), the metre and kilogram replacing the centimetre and gram of the old c.g.s. system.

(2) The derived units are directly related to the base units. For example, the unit of acceleration is 1 m s-2. The unit of force is the newton, which is the force required to give a body of mass 1 kg an acceleration of 1 m s-2. The unit of energy is the joule, which is the work done when a force of 1 N moves a body a distance of 1 m.

The use of auxiliary units is discouraged in SI. Thus the unit of pressure, the pascal, is 1 N m-2; the atmosphere and the torr are not used. Similarly the calorie is not used; all forms of energy are measured in joules.

In our experience, an understanding of the laws of physics is best acquired by applying them to practical problems. Frequently, however, the problems appearing in textbooks can be solved only through long, complex calculations, which tend to be mechanical and boring, and often drudgery for students. Sometimes, even the best of these students, the ones who possess all the necessary skills, may feel that such problems are not attractive enough to them, and the tedious calculations involved do not allow their ‘creativity’ (genius?) to shine through.

This little book aims to demonstrate that not all physics problems are like that, and we hope that you will be intrigued by questions such as:

• How is the length of the day related to the side of the road on which traffic travels?

• Why are Fosbury floppers more successful than Western rollers?

• How far below ground must the water cavity that feeds Old Faithful be?

• How high could the tallest mountain on Mars be?

• What is the shape of the water bell in an ornamental fountain?

• How does the way a pencil falls when stood on its point depend upon friction?

• Would a motionless string reaching into the sky be evidence for UFOs?

• How does a positron move when dropped in a Faraday cage?

• What would be the high-jump record on the Moon?

• Why are nocturnal insects fatally attracted to light sources?

• How much brighter is sunlight than moonlight?

• How quickly does a fire hose unroll?

• […]

The following chapter contains the problems. They do not follow each other in any particular thematic order, but more or less in order of difficulty, or in groups requiring similar methods of solution. In any case, some of the problems could not be unambiguously labelled as belonging to, say, mechanics or thermodynamics or electromagnetics. Nature's secrets are not revealed according to the titles of the sections in a text book, but rather draw on ideas from various areas and usually in a complex manner. It is part of our taskt o find out what type of problem we are facing. However, for information, the reader can find a list of topics, and the problems that more or less belong to these topics, on the following page. Some problems are listed under more than one heading. The symbols and numerical values of the principal physical constants are then given, together with astronomical data and some properties of material.

The majority of the problems are not easy; some of them are definitely difficult. You, the reader, are naturally encouraged to try to solve the problems on your own and, obviously, if you do, you will get the greatest pleasure. If you are unable to achieve this, you should not give up, but turn to the relevant page of the short hints chapter. In most cases this will help, though it will not give the complete solution, and the details still have to be worked out.

P1 Three small snails are each at a vertex of an equilateral triangle of side 60 cm. The first sets out towards the second, the second towards the third and the third towards the first, with a uniform speed of 5 cm min−1. During their motion each of them always heads towards its respective target snail. How much time has elapsed, and what distance do the snails cover, before they meet? What is the equation of their paths? If the snails are considered as point-masses, how many times does each circle their ultimate meeting point?

P2 A small object is at rest on the edge of a horizontal table. It is pushed in such a way that it falls off the other side of the table, which is 1 m wide, after 2 s. Does the object have wheels?

P3 A boat can travel at a speed of 3 m s−1 on still water. A boatman wants to cross a river whilst covering the shortest possible distance. In what direction should he row with respect to the bank if the speed of the water is (i) 2 m s−1, (ii) 4 m s−1? Assume that the speed of the water is the same everywhere.

P4 A long, thin, pliable carpet is laid on the floor. One end of the carpet is bent back and then pulled backwards with constant unit velocity, just above the part of the carpet which is still at rest on the floor.

Tools for applications

This chapter will introduce radionuclides and the emitted radiations as tools for applications. We shall begin with the well known α, β and γ radiations followed by a few characteristics of extranuclear electrons and X rays. Additional comments about neutrons (see Section 1.3.6), will follow in Section 5.4.4.

Properties of alpha particles

The nature and origin of alpha particles

Alpha particles are here called primary radiations because their emission is the first evidence of nuclear disintegrations which turn parent atoms into daughter atoms belonging to a different chemical element. Alpha particles are emitted either as a single branch, i.e. all with the same energy, or as several branches each with its own energy. A typical case is the α particle decay of americium-241. Close to 13% of the decays occur at an α particle energy of 5.44 MeV and close to 85% at 5.48 MeV, leaving three minor branches each with its own energy, overall exactly one α particle emitted per decay.

Properties of a particles were summarised in Table 1.2. With Z = 2 and A=4, α particles are physically identical to the nuclei of helium atoms. As calculated by Rutherford (Section 1.2) the diameter of α particles is about 10−14 m, or some 104 times smaller than the 10−10 m atomic diameters.

Introduction

Radioactivity, from the 1890s to the 1990s

Radioactivity is a characteristic of the nuclei of atoms. The nuclei, and with them the atoms as a whole, undergo spontaneous changes known as radio-active or nuclear transformations and also as decays or disintegrations. The energy released per nuclear transformation and carried away as nuclear radiation is, as a rule, some 103 to 106 times greater than the energy released per atom involved in chemical reactions.

Radioactivity was discovered in 1896 by the Frenchman H. Becquerel. The discovery occurred while he was experimenting with phosphorescence in compounds of uranium, an investigation aiming only at knowledge for its own sake. However, practical applications of radioactivity appeared not long after its discovery and have multiplied ever since.

Radioactivity could not have been discovered much before 1896 because at naturally occurring intensities it is undetectable by the unaided human senses. The photographic technique which contributed to its discovery was not adequately developed until well into the nineteenth century. But by the end of that century it played a major part in two discoveries which changed the path of science and of history: Röntgen's discovery of X rays in Germany in late 1895, followed by Becquerel's discovery of radioactivity in France in early 1896. These completely unexpected events opened the doors to totally new physical realities, to the emerging world of the nuclei of atoms and the high-energy nuclear radiations emitted by these nuclei.

Following Becquerel's discovery, it took about 35 years of intense scientific work before radioactive atoms could be produced from stable atoms by man-made procedures.

Electronic data exchange has become routine. Large research institutes are making their data widely available via the Internet as a cost-free service to the scientific community.

Nuclear reference data are particularly extensive and well suited for electronic distribution, as was noted in Section 4.2.1 where a brief reference was made to data from the web site of the Nuclear Data Center of the US Brookhaven National Laboratory (www.nndc.bnl.gov). The information at present available to users is the product of the combined efforts of the US National Nuclear Data Centre (NNDC) with other data centres and other interested groups which have an interest in such data, not only in the United States but world-wide. Sites linked to the NNDC are listed at http://www.nndc.bnl.gov/usndp.

The use of electronic data sources is not without its problems by virtue of the enormity of the resource. To be supplied with an excess of data can cause confusion to those who are not sufficiently expert in their use. When applying nuclear techniques to practical problems, the importance of a sound understanding of the scientific principles cannot be over stated. Scientific understanding is the foundation of a knowledge structure while data are the building blocks. A balance must be struck between the two. Nevertheless, electronic data centres represent an almost limitless store of information, making it advisable to refer readers to the World Wide Web, specially so for the latest published data, though the latest data are not necessarily the most useful data.

It is of course necessary to exercise care to ensure that electronically transmitted information is of adequate quality. Clearly National Laboratories and major universities are a first-class source of information.

An introduction to radioactivity measurements

Problems

Many comments in preceding chapters made it clear that accurate radio-activity measurements require specialised instruments and attention to numerous details, in particular an adequate knowledge of the decay data of the radionuclides of interest.

Highly accurate radioactivity measurements are rarely of interest outside standard laboratories, but two facts require attention: (a) all work with radioactivity relies ultimately on internationally established activity standards (Section 2.2.1), and (b) laboratories working with radioactivity must have facilities for at least moderately accurate radioactivity measurements since radiation protection authorities will not permit radioactive materials to be used unless their activity is known with sufficient accuracy, often within ±10%.

Since most nuclear decays are signalled by the emission of either an α or a β particle, the measurement of these decay rates could be expected to be straightforward: one counts the emitted particles for a known time and states the result as decays per second or becquerel (see Eq. (2.1)).

To proceed in this way could cause serious errors. For example, there are the β particle decays via excited states de-excited by conversion electrons (Section 3.6.2) which the detector treats like β particles, adding them to their number. Furthermore, to account for all emitted particles, counting must be done in exactly 4π or another accurately known geometry requiring appropriate detector arrangements and the source must be thin enough to permit all particles emitted from within its atoms to escape to be counted. In addition, there are uncertainties due to imperfections of the signal processing equipment (Section 4.5), the possible presence of unwanted radiations (Section 4.6) and ambiguities in interpretation of results (yet to be discused).