Chapter 4: Introduction to Quantum Theory and Atomic Properties - PDF

Chapter 4 Introduction to quantum theory and properties of atoms 1  Electromagnetic Radiation (light) - Wave like Wavelength, l, is the distance from one crest to the next in the wave. Measured in units of distance. Frequency, n, is the number of com...

Chapter 4 Introduction to quantum theory and properties of atoms 1  Electromagnetic Radiation (light) - Wave like Wavelength, l, is the distance from one crest to the next in the wave. Measured in units of distance. Frequency, n, is the number of complete cycles per sec., expressed in s-1 or Hz Speed of Light, C, same for all electromagnetic radiation. C= 3 x 108 m/s in vacuum n = c/l Practice: The yellow light given by sodium lamp has l = 589 nm. What is the frequency of this radiation? C = 3 × 108 m/s Answer: l = 589 nm = 589 × 10-9 m u = C/l = 3 × 108 / (589 x 10-9) = 5.09 x 1014 s-1 2 The continuous spectrum of light Continuous spectrum of light in the visible region The line spectrum of hydrogen The spectrum of hydrogen element is a discontinuous spectrum (line spectrum) Why? 3  The wave-particle duality of light q Planck: Atoms can gain or lost only certain quantities of energy, DE = nhn (where n is a positive integer, 1, 2, 3, etc) by absorbing or emitting radiation. This means energy is quantized. q The wave-particle duality of light (proposed by Einstein): Light consisted of packets of energy called photons (particle-like) that had wave-like properties as well. Ephoton = hn =hc/l=DEatom Planck's constant h= 6.62x10-34 Js 4  Bohr Model of the Hydrogen Atom q Hydrogen atom has only certain allowable energy levels for the electron orbits. (quantized energy) Ground state: the lowest possible energy level an electron can be at (n=1). Excited state: an energy level higher than the ground state (n>1). The energy level En = - RE / n2 = - 2.18 x 10-18 / n2 where n = 1, 2, 3,....¥ The energy constant RE = 2.18 x 10-18 J DE Ground state (lowest energy) qThe electron traveled in circular orbits. Each orbit has certain radius rn rn = 0.5 x n2 Å Example: For n=3, rn = 0.5 × 32 = 4.5 Å 5 qWhen the electron moves from one orbit to another, it absorbs or emits a photon whose energy equals the difference in energy between the two orbits. Electron moves from a -2.18 x 10-18 / (ninitial)2 (In Joule) higher energy level orbit to a lower energy level orbit -2.18 x 10-18 / (nfinal)2 Emits a photon Electron moves from a lower energy level orbit -2.18 x 10-18 / (nfinal)2 to a higher energy level orbit -2.18 x 10-18 J / (ninitial)2 absorbs a photon 6 Practice: Calculate the wavelength (l) of the line corresponding to the transition of an electron from n = 4 to n = 2 in the hydrogen atom. C= 3 x 108 m/s and h = 6.63 x 10-34 Js ni = 4 E4 = -2.18 x 10-18 / (42) nf = 2 E2 = -2.18 x 10-18 / (22) DE= Efinal – Einitial = E2 – E4 = -2.18 x 10-18 [ (1 / 4) – (1 / 16 ) ] = - 4.1 x 10-19 J. The sign (-) indicates a lose of energy since light is emitted from an atom when the electron moves from a higher level to a lower level (nfinal< ninitial) DE = h C/l l =h C/ DE, The wavelength of the light emitted is l= (6.63 x 10-34 x 3 x 108) / 4.1 x 10-19 = 4.86 x 10-7 m = 486 nm (green light) 7  Explanation of the line spectrum of hydrogen The lines of the hydrogen spectrum correspond to the transition of electrons from a higher energy level to a lower energy level: for the visible series, nf = 2 and ni = 3, 4, 5,... And l =h C/ DE 8 de Broglie hypothesis:The Wave-Particle Duality of Matter qde Broglie hypothesizes particles could have a wave behavior. qThe electrons have wave-like properties qThe de Broglie relation: l = h/mv = h/p h: Planck’s constant: h= 6.62x10-34 Js m: mass of the particle v: velocity of the particle p: momentum of the particle (p = mv) q Every particle has a wave nature as well but it is only truly evident when a particle is very light such as an electron (m = 9.11 ×10-28 g). q However, we cannot observe both the wave nature and the particle nature of the electron at the same time. q According to the Heisenberg Uncertainty Principle, we cannot know both the position and the speed of the electron at a given time. 9  Quantum Numbers and Atomic Orbitals Atomic Orbital: A region in space in which there is high probability of finding an electron. Quantum numbers specify the properties of atomic orbitals and their electrons, i.e., an atomic orbital is specified by three quantum numbers (n, l, ml). The spin of the electron is specified by the quantum number ms (or s) Principal Quantum Number, n Indicates main energy levels: n = 1, 2, 3, 4… Each main energy level has sub-levels A main energy level 10  Orbital Quantum Number, ℓ (Angular Momentum Quantum Number/ Azimuthal quantum number) ℓ indicates the shape of orbital sublevels ℓ = 0, 1, …., (n-1) Example: When n=4, ℓ = 0, 1, 2 and 3. ℓ=0 ℓ=1 ℓ=2 ℓ=3 s p d f 4 sublevels for N=4 A sublevel 11  Magnetic Quantum Number, mℓ Indicates the orientation of the orbital in space. Equals to integer values, including zero ranging from - ℓ to +ℓ An orbital The sublevel s contains one orbital, p contains 3 orbitals, d contains 5 orbitals and f contains 7 orbitals. In a main energy level n, there are n2 orbitals, i.e., for n = 4 there are 42 = 16 orbitals. For each main energy level n, the number of mℓ values represents the number of orbitals. 12  Electron Spin Quantum Number, (ms or s) Indicates the direction in which an electron spins in an orbital (clockwise or counterclockwise). Values of ms = -1/2, +1/2 PRACTICE Q1. When the principle quantum number n=4, the orbital quantum number ℓ takes the values a) 0,1,2,3,4 b) -4,-3,-2,-1, 0, 1,2,3,4 c) 0,1,2,3 d) -1/2, 1/2 Q2. The name of the sub-level with n= 3 and l = 2 is a) 2d b) 3d c) 3p d) 2s Q3. When the orbital quantum number ℓ = 1, the magnetic quantum number mℓ takes the values a) 0,1 b) -1, 0, 1 c) 0 d) -1/2, 1/2 Q4. The quantum number that takes only the values -1/2 and 1/2 is the magnetic quantum number (mℓ). 13 a) True b) False  Electronic configurations Electronic configuration is how the electrons are distributed among the various atomic orbitals in an atom. There are 3 rules to build up electronic configurations: 1. Aufbau (building up) Principle Electrons enter the orbitals in order of ascending energy. üIncreased n+ ℓ, increased energy üSame value of n+ ℓ, lowest energy for lowest n orbital 1s 2s 2p 3s 3p 4s 3d n +ℓ 1+0 2+0 2+1 3+0 3+1 4+0 3+2 Energy 2p and 3s have the same value of n+ ℓ, 2p has a lower energy than 3p General pattern for filling the sublevels 1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s 4f 5d 6p 7s … 14 2. Hund’s Rule : When in orbitals of equal energy, electrons will try to remain unpaired. The electrons occupy degenerate orbitals singly to the maximum extent possible and with their spins parallel. Placing two electrons in one orbital means that, as they are both negatively charged, there will be some electrostatic repulsion between them. Placing each electron in a separate orbital reduces the repulsion and the system is more stable. YES No 2 electrons 2p 3 electrons 2p 15 3. Pauli’s exclusion principle : No two electrons in the same atom have the same set of the four quantum numbers (n , ℓ, mℓ , ms). This means that: Orbitals of the same energy must be occupied singly and with the same spin before pairing up of electrons occurs. Electrons occupying the same orbital must have opposite spins. An orbital is occupied au maximum by 2 electrons. An orbital containing paired electrons is presented as : YES No 4 electrons 2p 5 electrons 2p 6 electrons 2p 16  Practice 1: Determine the electronic configurations of 4Be, 17Cl, 26Fe, and 35Br. 4Be: 1s22s2 17Cl: 1s22s22p63s23p5 26Fe: 1s22s22p63s23p64s23d6 35Br: 1s22s22p63s23p64s23d104p5 Practice 2: How many unpaired electrons are there in 10Ne , 8O, and 15P? 10Ne: 1s2 2s2 2p6 zero unpaired electrons 8O: 1s2 2s2 2p4 2 unpaired electrons 15P: 1s2 2s2 2p6 3s2 3p3 3 unpaired electrons 17  Exceptions in some transition metals: Cr and Cu 1 electron q Chromium 24Cr: Expected electronic configuration:1s2 2s2 2p6 3s2 3p6 4s2 3d4 ØReal electronic configuration: 1s2 2s2 2p6 3s2 3p6 4s1 3d5 1 electron q Copper 29Cu: Expected electronic configuration:1s2 2s2 2p6 3s2 3p6 4s2 3d9 ØReal electronic configuration: 1s2 2s2 2p6 3s2 3p6 4s1 3d10 The reason for these anomalies is the greater stablity of d subshells that are either half-filled (d5) or completely filled (d10) 18  Valance-Shell and Valence Electrons qThe most outer sublevels (for the highest n) are called valence-shell qElectrons in the most outer sublevels are called valence electrons qTransition metal: metal whose atom has an incomplete d subshell or which can give rise to cations with an incomplete d subshell. For transition metals, the valence shell is ns (n-1)d Examples: Elements Valence shell Valence electrons 9F: 1s2 2s2 2p5 2s 2p 7 11Na: 1s2 2s2 2p6 3s1 3s 1 18Ar: 1s2 2s2 2p6 3s2 3p6 3s 3p 8 35Br: 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p5 4s 4p 7 Transition metals Valence shell Valence electrons 26Fe: 1s2 2s2 2p6 3s2 3p6 4s2 3d6 4s 3d 8 28Ni : 1s2 2s2 2p6 3s2 3p6 4s2 3d8 4s 3d 10 19  ELECTRONIC CONFIGURATION OF IONS Electrons are removed first from the highest occupied orbitals (except for transition metals). SODIUM 11Na 1s2 2s2 2p6 3s1 1 electron removed from the 3s orbital 11Na 1s2 2s2 2p6 + CHLORINE 17Cl 1s2 2s2 2p6 3s2 3p5 1 electron added to the 3p orbital 17Cl 1s2 2s2 2p6 3s2 3p6 - Isoelectronic configuration Atoms or ions having the same electronic configuration Example: 8O2-, 11Na+, 9F- 2-: 1s2 2s2 2p6 8O + 2 2 6 11Na : 1s 2s 2p - 2 2 6 9F : 1s 2s 2p 20  Electronic configuration of transition metal ions Electrons in the ns orbital are removed before any electrons in the (n-1)d orbitals. Examples: TITANIUM 22Ti: 1s2 2s2 2p6 3s2 3p6 4s2 3d2 Ti+: 1s2 2s2 2p6 3s2 3p6 4s1 3d2 (1 electron is removed from 4s) Ti2+: 1s2 2s2 2p6 3s2 3p6 3d2 (2 electrons are removed from 4s) Ti3+: 1s2 2s2 2p6 3s2 3p6 3d1 (1 electron is removed from 3d) Ti4+: 1s2 2s2 2p6 3s2 3p6 (2 electrons are removed from 3d) Practice. Determine the electronic configurations of Fe, Fe2+ and Fe3+ Answer: Iron 26Fe: 1s2 2s2 2p6 3s2 3p6 4s2 3d6 Fe2+:1s2 2s2 2p6 3s2 3p6 3d6 (2 electron are removed from 4s) Fe3+: 1s2 2s2 2p6 3s2 3p6 3d5 (1 electron is removed from 3d) 21  Short cut for writing electronic configuration Noble gases: [2He], [10Ne], [18Ar], [36Kr], [54Xe] [86Rn], [118Og] Short cut electronic configuration 10Ne: 1s2 2s2 2p6 17Cl: [Ne] 3s2 3p5 17Cl: 1s 2s 2p 3s 3p 2 2 6 2 5 18Ar: 1s2 2s2 2p6 3s2 3p6 28Ni: [Ar] 4s2 3d8 2 2 6 2 6 2 8 28Ni : 1s 2s 2p 3s 3p 4s 3d 22  Periodic table of elements and properties of atoms The vertical columns of the table (Numbered from 1 to 18 ) are called groups or families. Element in the same group have similar but not identical characteristics. Elements in the same group have the same outer shell electron configuration (same number of outer shell electrons), and hence similar chemical properties. The horizontal rows of the table (Numbered from 1 to 7) are called periods. Each period contains elements with electrons in the same outer shell. 23  Effective nuclear charge (Zeff) The effective nuclear charge (Zeff) is the net positive charge experienced (felt) by an electron in a multi-electron atom Zeff: The effective nuclear charge, Zeff = Z - S Z: Atomic number of the atom, S: Number of inner electrons (in the core) ELEMENTS OF THE SAME PERIOD ELEMENTS OF THE SAME GROUP Element S Zeff=Z-S Element S Zeff=Z-S 11Na:1s 10 1 3Li:1s 2 1 22s22p63s1 22s1 13Al:1s 10 3 11Na:1s 10 1 22s22p63s23p1 22s22p63s1 Elements in63s P:1s22s22p the23psame period 10 2 2Elements 6 in1 the same group 5 19K:1s 2s 2p 3s 3p 4s 18 1 3 6 2 15 17Cl:1s 10 7 37Rb:1s 36 1 22s22p63s23p5 22s22p63s23p64s23d104p65s1 q When we move from the left to the right along a period, in the periodic table, Zeff increases q When we move along a group in the periodic table, Zeff remains constant Practice: Calculate Zeff for 11Na and for 11Na+ Answer: 11Na: 1s22s22p63s1 Z=11 and S= 10 so Zeff = 11-10 = 1 11Na : 1s 2s 2p Z=11 and S= 2 so Zeff = 11-2 = 9 + 2 2 6 24  Atomic size or Radius The atomic size (or radius) is the half distance of closest approach between two identical atoms. q When we move from the left to the right along a period, in the periodic table, the atomic size decreases since there is an increase in core charge (Zeff increases), the outer shell electrons are attracted closer to the nucleus (it’s the same shell but there are more electrons in the shell as you move across the period). q When we move from the top to the bottom along a group in the periodic table, the atomic size increases since there is an increase in the number of shells. § Cation is smaller than atom from which it is formed. Excess of protons in the ion draws the outer electrons closest to nucleus. § Anion is larger than atom from which it is formed. More repulsion between electrons and the ionic radius increases. Å Å 25  Ionization energy The ionization energy is the amount of energy it takes to detach one electron from a gas neutral atom If it is easy to detach an electron, it has low ionisation energy. If it is hard to detach an electron, it has a high ionisation energy The larger the atom the easier it is to detach an electron. The smaller the atom the harder to detach an electron q When we move from the left to the right along a period, in the periodic table, the ionization energy increases since there is an increase in core charge, the attraction is greater between the outer shell electrons and the nucleus. Therefore, electrons are harder to remove. q When we move from the top to the bottom along a group in the periodic table, the ionization energy decreases since there is an increase in the number of shells so the size of the atom is increasing, the attraction is weaker between the outer shell electrons and the nucleus. Therefore, electrons are easier to remove. 26  Electronegativity Electronegativity is the ability of an atom to attract a pair of electrons towards itself in a chemical bond. Same electronegativity A:A B is more electronegative than A A :B q When we move from the left to the right along a period, in the periodic table, the electronegativity increases since there is an increase in core charge, there is a greater attraction of the outer shell electrons to the nucleus. q When we move from the top to the bottom along a group in the periodic table, the electronegativity decreases since the electrons are further from the nucleus, there is a weaker attraction Electronegativity 27 Overview Number of shells increases, Zeff increases, attraction increases attraction decreases Practice: Arrange the following elements 12Mg, 16S, 13Al and 17Cl from the highest to the lowest 1. atomic radius 2. ionization energy 3. Electronegativity 4. Effective nuclear charge (Zeff) Answer: 1. decreasing atomic radius: Mg > Al > S >Cl 2. decreasing ionization energy: Cl > S > Al > Mg 3. decreasing electronegativity: Cl > S > Al > Mg 4. decreasing Zeff: Cl > S > Al > Mg 28  Practice on chapter 4 Q1. The wave-particle duality of light means that a)light consisted of particles called photons that had wave-like properties b) electrons behave as a wave b) light shinning on certain metal plates caused a flow of electrons. d) all of these Q2. The wavelength (l) of the line corresponding to the transition of an electron from n = 3 to n = 2 is (RE = 2.18 × 10-18 J) a) 486 nm b) 656 nm c) 1250 nm d) 32 nm Q3. Which of the following sets of quantum numbers (n, l, ml, ms) describes an electron in an orbital a)(2, 3, 1, 1/2) b) (3, 2, 3, 1/2) c) (2, 1, 1, -1/2) d) (3, 1, 0, -1/4) Q4. Choose the correct order of the following sublevels from the lowest to the highest energy. a) 3p < 4p < 3d < 4s b) 3p < 3d < 4s < 4p c) 3d < 3p < 4s < 4p d) 3p < 4s < 3d < 4p Q5. Which one of the followings about d orbitals is correct a) they are found in all principal energy levels. b) there are 5 types of d orbitals c) they are spherical in shape d) each d orbital can hold up to 3 electrons Q6. What is the number of sublevels associated with n = 2 a)1 b) 2 c) 4 d) 9 Q7. What is the number of orbitals associated with n = 2 a)1 b) 2 c) 4 d) 9 Q8. The electronic configuration of copper 29Cu is a)1s22s22p63s23p64s23d9 b) 1s22s22p63s23p64s13d5 c) 1s22s22p63s23p64s13d10 d) s22s22p63s23p64s13d54p3 Q9. The electronic configuration of 17Cl is a) 1s22s22p63s23p6 b) 1s22s22p63s23p5 c) 1s22s22p63p53s2 d) 1s22p62s23p53s2 Q10. Iron (Fe) is a transition metal. The electronic configuration of 26Fe2+ is a) 1s22s22p63s23p64s23d6 b) 1s22s22p63s23p64s23d4 c) 1s22s22p63s23p64s13d5 d) 1s22s22p63s23p63d6 Q11. How many unpaired electrons are there in 20Ca2+? a)0 b) 2 c) 10 d) 20 Q12. The ions 8O2-, 11Na+ and 9F- a)are isotopes b) have isoelectronic configurations c) are compounds d) are called sublevels Q13. The effective nuclear charge (Zeff) of oxygen (8O) is a) 2 b) 4 c) 6 d) 8 29