P.A. Cox - Inorganic chemistry (793955), страница 3
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Other elements result from radioactive decay, including helium and argon andseveral short-lived radioactive elements coming from the decay of thorium and uranium (see Topic I2). Fig. 1 showshow 238U decays by a succession of radioactive α and β processes, generating shorter-lived radioactive isotopes of otherelements and ending as a stable isotope 206Pb of lead. Similar decay series starting with 232Th and 235U also generateshort-lived radioactive elements and end with the lead isotopes 208Pb and 207Pb, respectively.All elements beyond bismuth (Z=83) are radioactive, and none beyond uranium (Z=92) occur naturally on Earth. Withincreasing numbers of protons heavier elements have progressively less stable nuclei with shorter half-lives.
Elementswith Z up to 110 have been made artificially but the half-lives beyond Lr (Z=103) are too short for chemicalinvestigations to be feasible. Two lighter elements, technetium (Tc, Z=43) and promethium (Pm, Z=61), also have nostable isotopes.Radioactive elements are made artificially by bombarding other nuclei, either in particle accelerators or with neutronsin nuclear reactors (see Topic I2). Some short-lived radioactive isotopes (e.g. 14C) are produced naturally in smallamounts on Earth by cosmic-ray bombardment in the upper atmosphere.Section A—Atomic structureA2ATOMIC ORBITALSKey NotesWavefunctionsQuantum number andnomenclatureAngular functions:‘shapes’Radical distributonsEnergies in hydrogenHydrogenic ionsRelated topicsThe quantum theory is necessary to describe electrons. It predictsdiscrete allowed energy levels and wavefunctions, which giveprobability distributions for electrons.
Wavefunctions for electrons inatoms are called atomic orbitals.Atomic orbitals are labeled by three quantum numbers n, l and m.Orbitals are called s, p, d or f according to the value of l; there arerespectively one, three, five and seven different possible m values forthese orbitals.s orbitals are spherical, p orbitals have two directional lobes, whichcan point in three possible directions, d and f orbitals havecorrespondingly greater numbers of directional lobes.The radial distribution function shows how far from the nucleus anelectron is likely to be found. The major features depend on n butthere is some dependence on l.The allowed energies in hydrogen depend on n only. They can becompared with experimental line spectra and the ionization energyIncreasing nuclear charge in a one-electron ion leads to contraction ofthe orbital and an increase in binding energy of the electron.Many-electron atoms (A3)Molecular orbitals:homonuclear diatomics (C4)WavefunctionsTo understand the behavior of electrons in atoms and molecules requires the use of quantum mechanics.
This theorypredicts the allowed quantized energy levels of a system and has other features that are very different from ‘classical’physics. Electrons are described by a wavefunction, which contains all the information we can know about theirbehavior. The classical notion of a definite trajectory (e.g. the motion of a planet around the Sun) is not valid at amicroscopic level. The quantum theory predicts only probability distributions, which are given by the square of thewavefunction and which show where electrons are more or less likely to be found.Solutions of Schrödinger’s wave equation give the allowed energy levels and the corresponding wavefunctions.By analogy with the orbits of electrons in the classical planetary model (see Topic A1), wavefunctions for atoms areknown as atomic orbitals.
Exact solutions of Schrödinger’s equation can be obtained only for one-electron atoms andA2—ATOMIC ORBITALS7ions, but the atomic orbitals that result from these solutions provide pictures of the behavior of electrons that can beextended to many-electron atoms and molecules (see Topics A3 and C4–C7).Quantum numbers and nomenclatureThe atomic orbitals of hydrogen are labeled by quantum numbers. Three integers are required for a completespecification.• The principal quantum number n can take the values 1, 2, 3,….
It determines how far from the nucleus theelectron is most likely to be found.• The angular momentum (or azimuthal) quantum number l can take values from zero up to a maximum of n−1. It determines the total angular momentum of the electron about the nucleus.• The magnetic quantum number m can take positive and negative values from −l to +l. It determines thedirection of rotation of the electron. Sometimes m is written ml to distinguish it from the spin quantum number ms(see Topic A3).Table 1 shows how these rules determine the allowed values of l and m for orbitals with n=1−4. The values determinethe structure of the periodic table of elements (see Section A4).Atomic orbitals with l=0 are called s orbitals, those with l=1, 2, 3 are called p, d, f orbitals, respectively.
It isnormal to specify the value of n as well, so that, for example, 1s denotes the orbital with n=1, l=0, and 3d the orbitalswith n=3, l=2. These labels are also shown in Table 1. For any type of orbital 2l+1 values of m are possible; thus thereare always three p orbitals for any n, five d orbitals, and seven f orbitals.Angular functions: ‘shapes’The mathematical functions for atomic orbitals may be written as a product of two factors: the radial wavefunctiondescribes the behavior of the electron as a function of distance from the nucleus (see below); the angularwavefunction shows how it varies with the direction in space.
Angular wavefunctions do not depend on n and arecharacteristic features of s, p, d,…orbitals.Table 1. Atomic orbitals with n=1–48SECTION A—ATOMIC STRUCTUREFig. 1. The shapes of s, p and d orbitals. Shading shows negative values of the wavefunction. More d orbitals are shown in Topic H2, Fig. 1.Diagrammatic representations of angular functions for s, p and d orbitals are shown in Fig. 1. Mathematically, they areessentially polar diagrams showing how the angular wavefunction depends on the polar angles θ and .
Moreinformally, they can be regarded as boundary surfaces enclosing the region(s) of space where the electron is mostlikely to be found. An s orbital is represented by a sphere, as the wavefunction does not depend on angle, so that theprobability is the same for all directions in space. Each p orbital has two lobes, with positive and negative values of thewavefunction either side of the nucleus, separated by a nodal plane where the wavefunction is zero. The threeseparate p orbitals corresponding to the allowed values of m are directed along different axes, and sometimes denotedpx, py and pz. The five different d orbitals (one of which is shown in Fig.
1) each have two nodal planes, separating twopositive and two negative regions of wavefunction. The f orbitals (not shown) each have three nodal planes.The shapes of atomic orbitals shown in Fig. 1 are important in understanding the bonding properties of atoms (seeTopics C4–C6 and H2).Radial distributionsRadial wavefunctions depend on n and l but not on m; thus each of the three 2p orbitals has the same radial form. Thewavefunctions may have positive or negative regions, but it is more instructive to look at how the radial probabilitydistributions for the electron depend on the distance from the nucleus. They are shown in Fig.
2 and have thefollowing features.• Radial distributions may have several peaks, the number being equal to n−l.• The outermost peak is by far the largest, showing where the electron is most likely to be found. The distance of thispeak from the nucleus is a measure of the radius of the orbital, and is roughly proportional to n2 (although it dependsslightly on l also).Radial distributions determine the energy of an electron in an atom. As the average distance from the nucleus increases,an electron becomes less tightly bound.
The subsidiary maxima at smaller distances are not significant in hydrogen, butare important in understanding the energies in many-electron atoms (see Topic A3).Energies in hydrogenThe energies of atomic orbitals in a hydrogen atom are given by the formula(1)A2—ATOMIC ORBITALS9Fig. 2. Radial probability distributions for atomic orbitals with n=1–3We write En to show that the energy depends only on the principal quantum number n.
Orbitals with the same n butdifferent values of l and m have the same energy and are said to be degenerate. The negative value of energy is areflection of the definition of energy zero, corresponding to n=∞ which is the ionization limit where an electron hasenough energy to escape from the atom. All orbitals with finite n represent bound electrons with lower energy.
TheRydberg constant R has the value 2.179×10−18 J, but is often given in other units. Energies of individual atoms ormolecules are often quoted in electron volts (eV), equal to about 1.602×10−19 J. Alternatively, multiplying the valuein joules by the Avogadro constant gives the energy per mole of atoms. In these unitsThe predicted energies may be compared with measured atomic line spectra in which light quanta (photons) areabsorbed or emitted as an electron changes its energy level, and with the ionization energy required to remove anelectron. For a hydrogen atom initially in its lowest-energy ground state, the ionization energy is the differencebetween En with n=1 and ∞, and is simply R.Hydrogenic ionsThe exact solutions of Schrödinger’s equation can be applied to hydrogenic ions with one electron: examples are He+ and Li2+. Orbital sizes and energies now depend on the atomic number Z, equal to the number of protons in thenucleus.
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