Physics for Geologists, Second edition

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Atomic structure and age-dating 59 Neutrinos: particles, probably with no rest mass,l carrying no electric charge. Photon: discrete packets of energy (quanta) of electromagnetic radiation. The amount of energy depends on the frequency of the radiation and covers the full range of electromagnetic frequencies (page 65). They have no charge, and no rest mass. They travel at the speed of light. As a matter of interest, there is another aspect of atomic structure that is not intuitively obvious: Heisenberg's Uncertainty Principle or Indeterminacy Principle. This states that the position and speed of a particle cannot both be measured with precision at the same time. Strictly, it applies to all objects, but it is only significant with subatomic masses. The basic reasoning is that any observation involves a change of state - either the emission of photons if it is to be seen, or the bombardment by photons if it is to be illuminated. (See Feynman et al. 1963, vol. 1: 6-10.) Atoms An atom is very small:2 about 100 x 10-l2 m, or 100 pm. Each atom consists of a positively-charged nucleus surrounded by a cloud of negatively-charged electrons. The nucleus consists of two types of particles: neutrons and protons. Atoms as a whole have, in general, no charge, so the number of electrons must equal the number of protons. The simplest atom of all, hydrogen, consists of a nucleus of one proton accompanied by a single electron. The nucleus is very, very small compared to the size of the atom, the volume ratio being about 10-15, in spite of contributing most of its mass. Atoms have mass, and so weight, but common usage makes no distinction between the two, and weight and mass are used interchangeably. Atomic weights were originally expressed relative to hydrogen until it was found that hydrogen had three atoms that differed slightly from each other. These isotopes (to be explained below) made hydrogen unsuitable as a standard, so the definition of the unit was changed to one twelfth of the mass of the common carbon atom that has 12 neutrons and protons in its nucleus, the atomic weight of which is 12.011. The mass of an atom of carbon-12 is 19.924 x kg, so one atomic mass unit (amu) is 1.660 3 x kg. The electron 'cloud' around a nucleus must not be thought of as a minute model of the Solar System, with electrons in orbit around the nucleus. New- tonian mechanics is totally inadequate to describe the motion of electrons around their nucleus. The fundamental force between the nucleus and its electrons is electromagnetic. Unlike charges attract each other: like charges 1 Rest mass is the term mo in the equation m = mold1 - (vlc)' where v is the speed of the particle and c is the speed of light. 2 The old unit, the angstrom, named after the Norwegian physicist Anders Jonas angstrom (1814-74), was a good practical unit because most atoms are about 18 in diameter (100 x m). Copyright 2002 by Richard E. Chapman
60 Atomic structure and age-dating repel. So the electrons are attracted to the nucleus but repel each other. Moving charges generate a magnetic field. Particles have energy, and the unit is the electron volt, eV [ML~T-~]. This is the energy acquired by a particle carrying a single charge when acted on by a potential difference of one volt. 1 eV = 160.210 x joules (J). Be careful with units and dimensions here because the symbol is to be seen as a single symbol: eV, not e x V. An electric charge in coulombs [As] acted on by a volt [W A-l] gives an energy in watt-seconds which equals joules [W = J s-'1. The charge on an electron (e) is a fundamental and natural unit of electricity. Its value is 160.210 x lop2' coulombs (C), and all non-zero charges are a whole multiple of this. The number of protons is called the atomic number (Z, which is dimensionless). Elements are placed in the Periodic Table according to their atomic number because an element is determined by the charge of the protons in the nucleus, not by the neutrons. Neutrons and protons are much more massive than electrons (by factors of 1836.1 and 1838.63, respectively), and the total number of neutrons (N) and protons (Z) is called the atomic mass number (A). This is a whole number, dimensionless, that is very nearly equal to the mass of the atom because of the small mass of the electrons. The full notation is given by prefixes to the abbreviation of the element; the atomic number written subscript, and the atomic mass number written superscript, $. For example, '$ means that there are 6 protons, and 12 protons and neutrons (so, 6 neutrons) in the nucleus. The symbol is often abbreviated by leaving out the atomic number, for example, 12C. In older works you may find the superscript prefix after the element abbreviation, as c14. Isotopes Some atoms of simple elements have differing numbers of neutrons. Hydrogen is found in three forms. :H,:H and :H, which we call hydrogen, deuterium and tritium. These are isotopes of hydrogen. Another example is carbon, which also has three isotopes: ';c, ' 2 ~ and *:c. Isotopes of an element have the same general chemical properties (because protons, not neutrons, determine this) but differ slightly in mass and in some physical properties. They occupy the same place in the Periodic Table because they have the same atomic number. Isotopes are of two sorts: stable and unstable. Certain combinations of neutrons and protons are stable, others unstable. The unstable isotopes change spontaneously to a more stable form by emitting or capturing particles. These unstable isotopes are also called radioisotopes. It turns out that stable isotopes are those in which Z and N are nearly equal (or Z is about half A) - a small minority of the isotopes. Tritium, :H, is an unstable isotope of hydrogen. The decay of an unstable isotope also involves the emission of quanta of energy. The use of radioisotopes, such as ':c, in age-dating will be discussed below. Copyright 2002 by Richard E. Chapman
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Physics for Geologists Second editi
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Copyright 2002 by Richard E. Chapma
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... vlii Contents Polarization 47 L
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Figures Copyright 2002 by Richard E
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Tables Copyright 2002 by Richard E.
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xiv Preface waves diminishes with d
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xvi Preface provides. This book is
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xviii Acknowledgements to K. Whaler
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xx Symbols mass refractive index bu
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2 Basic concepts Table 1.1 Dimensio
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4 Basic concepts Table 1.2 Basic SI
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6 Basic concepts pascal (Pa) and si
Page 25 and 26: 8 Basic concepts all the relevant d
Page 27 and 28: 10 Basic concepts relating them by
Page 29 and 30: 2 Force The dimensions of force are
Page 31 and 32: 14 Force The ratio of the Moon's ac
Page 33 and 34: 16 Force Figure 2.1 The sum of the
Page 35 and 36: 18 Force When a motorcycle takes a
Page 37 and 38: 20 Force Figure 2.3 Torque is the p
Page 39 and 40: 22 Force How does momentum differ f
Page 41 and 42: 24 Force the weights - that is, the
Page 43 and 44: 26 Force Figure 2.6 Wall-sticking i
Page 45 and 46: 3 Gravity Universal gravity When di
Page 47 and 48: 30 Gravity are significant to geolo
Page 49 and 50: 32 Gravity Figure 3.2 The tractive,
Page 51 and 52: 34 Gravity Mean sea level It might
Page 53 and 54: 36 Gravity The benefits of space fl
Page 55 and 56: 38 Gravity Figure 3.6 Profile of th
Page 57 and 58: 40 Gravity Figure 3.8 The siphon at
Page 59 and 60: 4 Optics Light is an electromagneti
Page 61 and 62: 44 Optics Figure 4.2 Refraction. (a
Page 63 and 64: 46 Optics The coeficient of reflect
Page 65 and 66: 48 Optics only the light oscillatin
Page 67 and 68: 50 Optics called Iceland Spar. Two
Page 69 and 70: 52 Optics Diffraction If you shine
Page 71 and 72: 54 Optics Figure 4.7 Geometrical op
Page 73 and 74: 56 Optics Figure 4.9 The mirrors in
Page 75: 5 Atomic structure and age-dating P
Page 79 and 80: 62 Atomic structure and age-dating
Page 81 and 82: 64 Atomic structure and age-dating
Page 83 and 84: 66 Electromagnetic radiation radiat
Page 85 and 86: 68 Electromagnetic radiation Source
Page 87 and 88: Heat and heat flow The noun heat ha
Page 89 and 90: 72 Heat and heat flow Second Law: A
Page 91 and 92: 8 Electricity and magnetism Electri
Page 93 and 94: Electricity and magnetism 77 Figure
Page 95 and 96: Electricity and magnetism 79 rivett
Page 97 and 98: Electricity and magnetism 8 1 defin
Page 99 and 100: Electricity and magnetism 83 is kno
Page 101 and 102: 9 Stress and strain Pressure, p, is
Page 103 and 104: Stress and strain 87 than some natu
Page 105 and 106: These three elastic constants are r
Page 107 and 108: Stress and strain 91 Figure 9.1 New
Page 109 and 110: Stress and strain 93 Figure 9.2 Com
Page 111 and 112: Stress and strain 95 Figure 9.3 Ide
Page 113 and 114: Fracture Stress and strain 97 We fo
Page 115 and 116: Stress and strain 99 from which we
Page 117 and 118: 10 Sea waves The nature of water wa
Page 119 and 120: Sea waves 103 Figure 10.1 Wave moti
Page 121 and 122: Sea waves 105 refraction by islands
Page 123 and 124: Acoustics: sound and other waves 10
Page 125 and 126: Acoustics: sound and other waves 10
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12 Fluids and fluid flow Introducti
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Fluids and fluid flow 1 13 Figure 1
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Fluids and fluid flow 115 Figure 22
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Fluids and fluid flow 117 and the f
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water above a vertical thickness h
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Fluids and fluid flow 121 where V i
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Fluids and fluid flow 123 ardentes,
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Fluids and fluid flow 125 Figure 12
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- 14 $ 12 E 10 K .- 3 8 r cll + 6 0
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Fluids and fluid flow 129 the liqui
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Some dangers of mathematical statis
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Appendix 139 What would happen if y
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Notes 141 and since x is very large
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References Allum, J. A. E. (1966) P
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References 145 -(1950) 'Mechanism o
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Further reading 147 Trigg, G. L. an
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