1	Chapter 6 Electronic Structure of the atom
2	Electronic Structure Constructed on the basis of the similarity of chemical properties of elements in the same group. Why are their properties similar? Chemical properties are a result of electronic interactions between different atoms. The nature of these interactions depend on the arrangement of the electrons in the atom. The arrangement of the electrons in an atom is called the electronic structure of the atom.
3	Electrons Negatively charged particles. Very small particles Move about in the empty space of the atom at fairly large speeds (about 10⁶ m/s) Very small particles do not tend to behave like everyday ordinary objects In order to understand an electron’s nature, you must first know something about the nature of light.
4	Light Light is called electromagnetic radiation. It consists of a traveling packet of energy that consists of perpendicular electric and magnetic fields which consists of waves.
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7	Waves A wave is a traveling repeating pattern of hills and valleys. Velocity of wave: v, Speed of light: c Length of one repeating unit is called the wavelength, l. Units: m, cm, mm, nm, etc. The number of repeating units that pass a stationary point per second is called the frequency, n. Units: 1/s(s^-1) also known as a Hz (Hertz) For any wave (sound, water) v = l´n. For light: c = l´n. c = speed of light in a vacuum = 2.998 ´ 10⁸ m/s
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9	Light What is the wavelength, in nanometers, of light having a frequency of 8.6 ´ 10¹³ Hz? What is the frequency of light with a wavelength of 25.4 mm?
10	Light’s Interaction with matter Light interacts with matter in ways that classical physics cannot explain. Blackbody radiation: analyze the light emanated from very energetic substances. For example, hot iron glows red and then glow white just before it melts. Classical physics would predict that an excited object would emit higher frequencies as well as lower frequencies (called the “Ultraviolet Catastrophe”)
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12	Planck’s Law Max Planck (1858-1947) solved this problem. Assumed that light was emitted in small portions called “quanta.” The energy of one quantum of light is given by: Planck’s constant: h = 6.626 ´ 10^-34 J·s
13	Photoelectric Effect
14	Photoelectric Effect Experimental observations: Electrons were not emitted at all until a certain minimum frequency, called the threshold frequency, was reached. The average kinetic energy of emitted electrons increased with the frequency of light, not the intensity of the light. The intensity of light increased the number of emitted electrons but their average kinetic energy remained the same.
15	Photoelectric Effect Explained by Einstein in 1905 Assume that light consists of small particles called photons. The energy of one photon of light is given by Planck’s Law When a photon strikes an electron at the surface, the electron absorbs its energy. If this energy is larger than the energy holding the electron to the surface, called the work function, W, then the electron is emitted.
16	Photoelectric Effect (cont) The kinetic energy of emitted photon is equal to the difference between the energy of the photon minus the work function: K. E. = hn – W Increasing the intensity of light will increase the number of photons but not their energy. Therefore, more electrons will be emitted but their kinetic energies remain constant.
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18	Planck’s Law Blue light has a frequency of about 7.5 ´ 10¹⁴ Hz. What is the energy of a photon of this light? A photon has a wavelength of 624 nm (1 nm = 10^-9 m). What is the energy of this photon?
19	Spectra
20	Spectra Pass white light through a prism (or a refracting grating) and it separates into its frequencies creating a “rainbow” called a spectrum. A spectrum with no breaks in it is called a continuous spectrum.
21	Atomic spectra When you excite a low pressure of gaseous atoms, the atoms emit only particular frequencies of light depending on the identity of the atom. This is called a discontinuous or line spectrum. Also, a low pressure of gaseous atoms will absorb the same frequencies of light when white light passes through it producing the “negative” of the emission spectrum.
22	Atomic spectra
23	Atomic spectra Hydrogen: 410.2 nm, 434.1 nm, 486.1 nm, 656.3 nm Neon: emits in the orange-red region Argon: emits in the blue region. Sodium: emits in the yellow region
24	Hydrogen’s atomic spectrum 4 emissions in visible region: 410.2 nm; 434.1 nm; 486.1 nm; 656.3 nm (called the Balmer series). There are other series in the ultraviolet region (called the Lyman series) and in the infrared region.
25	Bohr Model (1913) In hydrogen, the electron is allowed only certain values of energy. The energy of the electron is quantized. A electron can increase its energy by absorbing a photon. The energy of the photon is equal to the difference in the allowed energy values.
26	Bohr model (continued) An electron increases its energy by moving to a higher n level (or orbit) while absorbing a photon An electron decreases its energy by moving to a lower n level (or orbit) while emitting a photon.
27	Bohr Model Niels Bohr Introduces the concept of quantization of energy to the electron. Model works only for hydrogen and other ions with only one electron. Won Nobel Prize in 1922 for this model.
28	Bohr Model Calculate the wavelength (in nanometers) of the photon emitted when its electron drops from the n = 5 state to the n = 3 state.
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30	Wave Nature of Particles Louis deBroglie (1892-1987) proposed that for a particle of mass, m, traveling at a velocity, v, a wavelength can be calculated with the following equation. Nobel Prize: 1929
31	deBroglie wavelengths Protons can be accelerated to speeds near that of light in particle accelerators. Estimate the wavelength of such a proton moving at 2.90 ´ 10⁸ m/s. The mass of a proton is 1.675 ´ 10^-27 kg.
32	Heisenberg Uncertainty Principle It is impossible to simulatneously and exactly determine a particle’s position and its momentum. (Heisenberg won Nobel Prize in 1932 for this) Because of this principle, cannot locate an electron precisely. The probability of finding the electron in space is talked about instead.
33	Quantum Mechanics Developed about 1926 simultaneously by Erwin Schrodinger and Heisenberg. Main assumption: An electron is not a particle but a wave. The electron is described by a wave function, y. This function is a mathematical function. It contains all the information about the electron. y² is proportional to the probability of finding the electron in space.
34	Quantum Mechanics Wave function is obtained by solving the Schrodinger equation: This equation is a differential equation which can be solved to obtain a mathematical function for y. When solved for the hydrogen atom, certain parameters with certain limits come out of the solutions. These parameters are called quantum numbers.
35	Quantum Numbers Principal quantum number, n: allowed values are any positive integer. n = 1, 2, 3, 4, 5,… For the hydrogen atom, energy increases with n number only. The higher the n number, the greater the average distance of the electron from the nucleus.
36	Quantum Numbers Azimuthal quantum number, l: allowed values are any integer between 0 and the value of n–1. For n = 0: l = 0 For n = 1: l = 0, or 1 For n = 2: l = 0, 1, or 2 The l quantum number is associated with the shape of the region in which the electron is likely to be found (called the orbital).
37	Orbitals Region in which the electron is likely to be found Letter designations for orbitals: l = 0: s orbital: spherical shape l = 1: p orbital: dumbbell shape l = 2: d orbital: 4-lobed shape l = 3: f orbital: 6-lobed shaped l = 4: g orbital: 8-lobed shape
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40	Orbitals Allowed orbitals For n =1, l = 0: 1s orbital For n = 2, l = 0 or 1: 2s and 2p orbitals For n = 3, l = 0, 1, or 2: 3s, 3p, and 3d orbitals For n =4, l = 0, 1, 2, or 3: 4s, 4p, 4d, and 4f orbitals Combinations that are not allowed do not exist (such as 1p, 2d, or 3f)
41	Quantum Numbers Electrons with the same value of n are said to be in the same shell. Electrons with the same value of n and l are said to be in the same subshell. n = 1, l = 0: 1s subshell n = 3, l = 2: 3d subshell
42	Quantum Numbers Magnetic quantum number, m_l: allowed values of m_l depends on the value of l: m_l is an integer that lies between the values of –l and +l. –l ≤ m_l ≤ +l For l = 0: m_l = 0 For l = 1: m_l = –1, 0, or 1 l number gives the orientation in space of the orbital. Number of m_l values for a given l value is the number of orbitals in the given subshell.
43	Quantum Numbers A particular l value has 2l + 1 values of m_l. l = 0, m_l = 0: an s subshell has 1 orbital l = 1, m_l = -1, 0, +1: a p subshell has 3 orbitals l = 2, m_l = -2, -1, 0, +1, +2: a d subshell has 5 orbitals l = 3, m_l =-3,-2, -1, 0, +1, +2, +3: an f subshell has 7 orbitals
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46	s orbitals
47	"Node" Node: place where the value of the wave function equals zero. 1s orbital: no nodes (Only atomic orbital that has no nodes !!) 2s orbital: average distance from the nucleus larger than 1s. There is 1 radial node. 3s orbital: average distance from nucleus larger than 2s. There are 2 radial nodes.
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49	p orbitals Since a np subshell have 3 allowed m_l values (-1, 0, 1), there are 3 orbitals in a np subshell 2p: one planar node in the plane perpendicular to the p orbital through the nucleus. 3p: larger than 2p, one planar node plus one radial node. 4p: larger than 3p, one planar node plus two radial nodes.
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51	d orbitals d orbitals: Since there are 5 allowed ml values (2,1,0,–1,–2), there will be 5 orbitals in a nd subshell. 3d: two planar nodes between the 4 lobes of the d orbital. 4d: two planar nodes plus one radial node.
52	Observations An n shell has n subshells. An l subshell has 2l + 1 orbitals. The total number of orbitals in an n shell is equal to n². For hydrogen, the energy depends only on the n quantum number Orbitals of equal energy are called degenerate. For hydrogen, all orbitals in a given n shell are degenerate.
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54	Wave functions An electron in a hydrogen atom is described by picking a set of allowed quantum numbers which is actually describing the wave function. Lowest energy set of quantum numbers is called the ground state electron configuration. All other sets of quantum numbers are called excited state electron configurations.
55	Hydrogen Ground state electron configuration Lowest energy state: n = 1 is the lowest energy shell available. For n =1, the allowed value of l is 0 and the allowed value of m_l is 0. The electron is in a 1s orbital. Configuration is expressed as “1s¹”.
56	4^th Quantum Number Later, relativity was introduced into the wave equation and a fourth quantum number was added. Spin quantum number, m_s Electrons possess an angular momentum (or a spin) as a property. They can spin either clockwise or counterclockwise. Allowed values of m_s are ½ or –½.
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58	Hydrogen atom Complete set of 4 quantum numbers for electron in hydrogen atom: n = 1; l = 0; m_l = 0; m_s = ½ (or –½) Written as “1s¹”
59	Many electron atoms Atoms with more than one electron will have electron-electron repulsions in addition to electron-nuclear attractions. These repulsions make the Schrodinger impossible to solve exactly. Make an approximation that the orbitals obtained in the solution to the hydrogen atom applies to many electron atoms.
60	Shielding The repulsion between electrons will cause outer lying electrons to be “shielded” from the attraction for the nucleus. This reduces the nuclear charge to an “effective nuclear charge”: Z_eff = Z – S. Shielding causes the energy to depend on the l number in addition to the n number: s < p < d < f in the same shell
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62	Pauli Exclusion Principle No two electrons in an atom can have the same set of 4 quantum numbers. Two electrons cannot occupy the same space. As a result, one orbital can accommodate no more than two electrons with opposite spins.
63	Ground State Electron Configurations for atoms Count the number of electrons in the atom (equal to the atomic number). Give each electron a set of 4 quantum numbers obeying the Pauli exclusion principle starting with the lowest energy set and moving up. Aufbau procedure: Order of filling orbitals 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p…
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65	Ground state electron configurations Helium: 2 electrons 1^st electron: n = 1, l = 0, m_l = 0, m_s = ½ 2^nd electron: n = 1, l = 0, m_l = 0, m_s = –½ 1s²_:s shell is now full.
66	Electon Configurations (cont) Lithium: 3 electrons 3^rd electron: n = 2; l = 0; m_l = 0; m_s = ½ 1s²2s¹ Be: 4 electrons 4^th electron: n = 2 ; l = 0; m_l = 0; m_s = –½ 1s²2s² 2s subshell is now full
67	Electron configurations (cont.) Boron: 5 electrons 5^th electron: n = 2; l = 1; m_l = –1, m_s = ½ 1s²2s²2p¹ Carbon: 6^th electron 6^th electron: which p orbital does the 6^th electron goes into with which spin??
68	Hund’s Rule For a set of degenerate orbitals (such as the orbitals in a subshell), the lowest energy configuration is the one with the maximum spin. In a subshell, electrons are placed in each orbital singly, with the same spin, until each orbital has one electron in it. Then, the electrons are paired up.
69	Hund’s Rule 2 electrons in 2p subshell
70	Electron configurations Carbon: 6 electrons 6^th electron: n = 2; l = 1; m_l = 0, m_s = ½ 1s²2s²2p²(2 unpaired electrons) Nitrogen: 7 electrons 7^th electron: n = 2; l = 1; m_l = 1, m_s = ½ 1s²2s²2p³(3 unpaired electrons) Oxygen: 8 electrons 8^th electron: n = 2; l = 1; m_l = –1, m_s = –½ 1s²2s²2p⁴ (2 unpaired electrons)
71	Electron configurations Fluorine: 9 electrons 9^th electron: n = 2; l = 1; m_l = 0, m_s = –½ 1s²2s²2p⁵ Neon: 10 electrons 10^th electron: n = 2; l = 1; m_l = 1, m_s = –½ 1s²2s²2p⁶ n=2 shell is now full s and p subshells full: called a closed shell.
72	Ground state electron configurations Should be able to come up with these for elements up to Kr (atomic number 36). Shorthand notation: Noble gas electron configurations can be used to replace long configurations: [He] = “1s²” [Ne] = “1s²2s²2p⁶” [Ar] = “1s²2s²2p⁶3s²3p⁶” [Kr] = “1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p⁶”
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74	Ground State Electron Configurations Fill orbitals with the assigned number of electrons obeying the Aufbau procedure Obey Pauli’s Exclusion principle and Hund’s Rule. Two exceptions to Aufbau procedure concern half-filled and completely filled d subshells Cr: [Ar]3d⁵4s¹ instead of [Ar]3d⁴4s² Cu: [Ar]3d¹⁰4s¹ instead of [Ar]3d⁹4s²
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76	Figure 06.30
77	Electron Configurations Determine the ground state electron configurations for the following atoms: P, Ti, K, S, Cl, Cr. How many unpaired electrons, if any, are there in each of the atoms above?
78	Paramagnetism A species is paramagnetic if it contains unpaired electrons Paramagnetic objects behave differently in a magnetic field. Degree of paramagnetism increases with the number of unpaired electrons.
79	Electron configurations Example: Ca: [Ar]4s² [Ar] are the inner shell or core electrons. Electrons in the outer n shell are called the valence electrons. Calcium has two valence electrons. For “A” groups, number of valence electrons equals the group number.
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