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Chapter 9
Electrons in Atoms
 
 
 
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 Flame tests illustrate the emission of light by metals
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 Demonstration: Flame Tests for Metals (*) When a metal is placed in a flame it absorbs energy causing its electrons to be promoted to higher energy levels. The characteristic colors observed result from the energy released as the electrons fall to lower energy levels. The frequency of the emitted light depends on the differences in energy between the energy levels of the specific metal. Li produces a red flame, Na produces a yellow flame, and K produces a blue flame.
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 The photoelectric effect is illustrated for light of different wavelengths and intensities.
Notes
 Animation: Photoelectric Effect (**) Light may cause electrons to be emitted from an electrode in a photocell. Long wavelength light does not have enough energy to cause the electron to escape, regardless of its intensity. When light of a shorter wavelength (higher energy) light strikes the electrode, electrons are released. The amount of current produced depends on the intensity of the light and the energy of the escaping electrons depends on the wavelength of the light.
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 Contour plots and plots of radial electron distribution for the 1s, 2s and 3s orbitals and He, Ne, and Ar
Notes
 Animation: Radial Electron Distribution (**) The s orbitals are spherically symmetrical. As the principal quantum number increases the size of the orbital and the number of nodes increases. The radial electron densities show that the 1s orbital of Ar is closer to the nucleus than the 1s orbitals of He and Ne. The electrons in the second energy level of Ar are closer to the nucleus than those of Ne.
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 Effect of shielding on effective nuclear charge
Notes
 Animation: Effective Nuclear Charge (*) The effective nuclear charge is the nuclear charge an electron actually feels. It depends on the actual nuclear charge and on shielding by the average number of electrons in the sphere that extends to the electron.The outermost electrons have more electrons to shield them so they feel a smaller effective nuclear charge.
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 This animation shows the order in which the orbitals of the first 12 elements are filled.
Notes
 Animation: Electron Configurations (**) In atoms with more than one electron the repulsions between electrons cause subshells in the same quantum level to have different energies. Electrons occupy the lowest available energy level first. Each orbital can hold a maximum of two electrons which have opposite spins. Electrons occupy individual degenerate orbitals with parallel spins before any electrons are paired.
9.2
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 9.02
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 Electromagnetic waves. This sketch of two different electromagnetic waves shows the propagation of mutually perpendicular oscillating electric and magnetic fields. For a given wave, the wavelengths, frequencies, and amplitudes of the electric and magnetic field components are identical. Note that the wave with the longer wavelength (a) has a lower frequency, and the wave with the shorter wavelength (b) has a higher frequency.
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9.3
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 9.03
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 The electromagnetic spectrum. The visible region, which extends from violet at the shortest wavelength to red at the longest wavelength, is only a small portion of the entire spectrum. The approximate wavelength and frequency ranges of some other forms of electromagnetic radiation are also indicated.
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9.5a
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 9.05
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 medium size waves in two boxes on left with arrow to no wave in box on right
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9.9
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 9.09
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 Production of an atomic, or line, spectrum
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9.11
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 9.11
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 Radiation graph in terms of intensity and wavelength
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9.12a
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 9.12
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 evacuated chamber with ammeter and voltmeter
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9.13
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 9.13
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 Bohr model of the hydrogen atom. A portion of the hydrogen atom is pictured. The nucleus is at the center, and the electron is found in one of the discrete orbits, n 5 1, 2, . . . . Excitation of the atom raises the electron to higher numbered orbits, as shown through black arrows. Light is emitted when the electron falls to a lower numbered orbit. Two transitions are shown that produce lines in the Balmer series of the hydrogen spectrum, in the approximate colors of the spectral lines.
Notes
  
9.14
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 9.14
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 Energy-level diagram for the hydrogen atom. If the electron acquires 2.179 3 10218 J of energy, it moves to the orbit n 5 •; ionization of the H atom occurs (black arrow). Energy emitted when the electron falls from higher numbered orbits to the orbit n 5 1 is in the form of ultraviolet light, which produces a spectral series called the Lyman series (gray lines). Electron transitions to the orbit n 5 2 yield lines in the Balmer series (recall Figure 9-9); three of the lines are shown here (in color). Transitions to n 5 3 yield spectral lines in the infrared.
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9.15a
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 9.15
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 Excited sample, film or detecotr, prism, and increasing wavelength emission spectrum
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9.16
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 9.16
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 The uncertainty principle. A photon of “light” strikes an electron and is reflected (left). In the collision the photon transfers momentum to the electron. The reflected photon is seen through the microscope, but the electron is out of focus (right). Its exact position cannot be determined.
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9.17
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 9.17
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 Standing waves in a string. The string can be set into motion by plucking it. The blue boundaries outline the range of displacements at each point for each standing wave. The relationships between the wavelength, string length, and the number of nodes-points that are not displaced-are given by Equation (9.10). The nodes are marked by bold dots.
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9.18a
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 9.18
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 a standing wave with an integral number of wavelengths
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9.19
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 9.19
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 the wavefunctions
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9.20
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 9.20
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 the probabilities
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9.21
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 9.21
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 spherical polar coordinates
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9.22
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 9.22
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 shells and subshells
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9.231
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 9.23 C
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 electron probability graphs for 1s, 2s, and 3s orbitals
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9.232
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 9.23 2
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 charge density pattern for 1s orbital
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9.233
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 9.23 2
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 charge density pattern for 2s orbital
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9.234
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 9.23 3
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 charge density pattern for 3s orbital
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9.24a
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 9.24
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 Value of cos
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9.25
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 9.25
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 Three representations of electron probability and charge density for a 2p orbital. (a) The value of c2 is zero at the nucleus, rises to a maximum on either side, and then falls off with distance (r) along a line through the nucleus (i.e., along the x, y, or z axis). (b) The dots represent electron probability and charge density in a plane passing through the nucleus, for example, the xz plane. (c) Electron probabilities and charge densities represented in three dimensions. The greatest probability of finding an electron is within the two lobes of the dumbbell-shaped region. Note that this region is not spherically symmetric. Note also that the probability drops to zero in the shaded plane-the nodal plane (the yz plane).
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9.26
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 9.26
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 Representations of the three 2p orbitals. The p orbitals are usually represented as directed along the perpendicular x, y, and z axes, and the symbols px, py, and pz are often used. The pz orbital has m, 5 0. The situation with px and py is more complex: Each of these orbitals has contributions from both m, 5 1 and m, 5 21. Our main concern is just to recognize that p orbitals occur in sets of three and can be represented in the orientation shown here. In higher numbered shells p orbitals have a somewhat different appearance, but we will use these general shapes for all p orbitals.
Notes
  
9.28
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 9.28
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 Representations of the five d orbitals. The designations xy, xz, yz, and so on are related to the values of the quantum number m,, but this is a detail that we will not pursue in the text. The number of nodal surfaces for an orbital is equal to the , quantum number. For d orbitals there are two such surfaces. The nodal planes for the dxy orbital are shown here. (The nodal surfaces for the dz2 orbital are actually cone-shaped.)
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9.29
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 9.29
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 electron spin visualized
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9.30
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 9.30
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 The Stern-Gerlach experiment. Ag atoms vaporized in the oven are collimated into a beam by the slit, and the beam is passed through a nonuniform magnetic field. The beam splits in two. (The beam of atoms would not experience a force if the magnetic field were uniform. The field strength must be stronger in certain directions than in others.)
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9.31
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 9.31
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 Dartboard analogy to a 1s orbital. Imagine that a single dart (electron) is thrown at a dartboard 1500 times. The board contains 90% of all the holes; it is analogous to the 1s orbital. Where is a thrown dart most likely to hit? The number of holes per unit area is greatest in the “50” region-that is, the “50” region has the greatest probability density. The most likely score is “30,” however. Even though the density of holes is not as great, the total area, and hence the total number of hits, is greater in the “30” ring than in the “50” ring. The probability of scoring “30” is greater than that of scoring “50.” We consider the dartboard analogy again in Feature Problem C on page 312.
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9.32aC
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 9.32
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 radial probability densities - 1s
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9.33
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 9.33
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 Orbital energy diagram for the first three electronic shells. Energy levels are shown for a hydrogen atom (left) and three typical multielectron atoms (right). Each multielectron atom has its own energy level diagram. Note that for the hydrogen atom orbital energies within a principal shell-for example, 3s, 3p, 3d-are alike (degenerate), but in a multielectron atom they become rather widely separated. Another feature of the diagram described in the text is the steady decrease in all orbital energies with increasing atomic number.
Notes
  
9.34
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 9.34
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 The order of filling of electronic subshells. Beginning with the top line, follow the arrows and the order obtained is the same as in expression (9.14).
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9.34.4UN
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 9.34.04
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 3d, 4s boxes with arrows
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9.35
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 9.35
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 Electron configurations and the periodic table. To use this figure as a guide to the Aufbau process, locate the position of an element in the table. Subshells listed ahead of this position are filled. For example, germanium (Z 5 32) is located in Group 4A of the blue 4p row. The filled subshells are 1s2, 2s2, 2p6, 3s2, 3p6, 4s2, and 3d10. At Z 5 32, a second electron has entered the 4p subshell. The electron configuration of Ge is [Ar]3d104s24p2. Exceptions to the orderly filling of subshells suggested here are found among a few of the d-block and some of the f-block elements
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9.36
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 9.36
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 Spontaneous and stimulated light emission by Ne atoms. (a) The waves a, b, c, and d, although having the same frequency and wavelength, are emitted in different directions. Waves a and b are out of phase. The crests of one wave line up with the troughs of the other. The two waves cancel and they transmit no energy at all. (b) Photon (1) interacts with a Ne atom in a metastable energy state and stimulates it to emit photon (2). Photon (2) stimulates another Ne atom to emit photon (3), and so on. The waves are coherent, or in phase. The crests and troughs of the waves match perfectly.
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9.37
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 9.37
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 Operation of a He-Ne laser. Pictured here is a hypothetical laser tube arbitrarily divided into three sections representing the same portion of the tube at different times. At the top left a 633-nm photon (n) stimulates light emission from an excited Ne atom. Now there are two photons, and one of them in turn stimulates emission of a third photon. The photons are reflected by the mirror on the right, and their transit of the tube in the opposite direction is shown in the center. Three photons are amplified to five. At the bottom, the five photons are amplified to seven, and so on. A small portion of the photons is drawn off as the laser beam.
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9.37.3UN
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 9.37.03
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 exercise #83
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9.37.4
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 9.37.04
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Table 9.1
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 Table 9.1
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Table 9.2
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 Table 9.2
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