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Atomic structure Dr. Ayman H. Kamel Office:33 Contents 9-1 9-2 9-3 9-4 9-5 9-6 9-7 Electromagnetic Radiation Atomic Spectra Quantum Theory The Bohr Atom Two Ideas Leading to a New Quantum Mechanics Wave Mechanics Quantum Numbers and Electron Orbitals Contents 9-8 9-9 Quantum Numbers Interpreting and Representing Orbitals of the Hydrogen Atom 9-9 Electron Spin 9-11 Electron Configurations 9-12 Electron Configurations and the Periodic Table 9-1 Electromagnetic Radiation • Electric and magnetic fields propagate as waves through empty space or through a medium. • A wave transmits energy. EM Radiation Low High Frequency, Wavelength and Velocity • Frequency () in Hertz—Hz or s-1. • Wavelength (λ) in meters—m. • cm m nm (10-2 m) (10-6 m) (10-9 m) pm (10-10 m) (10-12 m) • Velocity (c)—3x 108 m s-1. c = λ λ = c/ = c/λ Electromagnetic Spectrum Red Orange Yellow 700 nm 450 nm Green Blue Indigo Violet Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 8 of 50 9-3 Quantum Theory Blackbody Radiation: Heated bodies emit light Blackbody Radiation Iαλ Classical theory predicts continuous increase of intensity with wavelength. 1900, Max Planck made the revolutionary proposal that ENERGY, LIKE MATTER, IS DISCONTINUOUS. Introduces the concept of QUANTA of energy. Max Planck, 1900: Energy, like matter, is discontinuous. E = h , h = 6.62607 x 10-34 J s. The Photoelectric Effect • Light striking the surface of certain metals causes ejection of electrons. • > o • e- I • ek threshold frequency • Photon strikes a bound electron which absorbs the energy, if binding energy (known as the work function) is less than photon energy, the e- is ejected. The Bohr Atom -RH E= 2 n RH = 2.179 10-18 J The Bohr Atom • Electrons move in circular orbits about the nucleus. • Motion described by classical physics. • Fixed set of stationary states (allowed orbits). – Governed by angular momentum: nh/2π, n=1, 2, 3…. • Energy packets (quanta) are absorbed or emitted when electrons change stationary states. • The integral values are allowed are called quantum numbers. Energy-Level Diagram -RH -RH – 2 ΔE = Ef – Ei = 2 nf ni 1 1 – = RH ( 2 ) = h = hc/λ 2 ni nf • In spite of its accomplishments, there are weaknesses in Bohr theory. Can’t explain 1. Spectra of species with more than one electron. 2. Effect of magnetic fields on emission spectra. • Modern quantum theory replaced Bohr theory in 1926. Emission and Absorption Spectroscopy Two Ideas Leading to a New Quantum Mechanics • Wave-Particle Duality. – Einstein suggested particle-like properties of light could explain the photoelectric effect. – But diffraction patterns suggest photons are wave-like. • deBroglie, 1924 – Small particles of matter may at times display wavelike properties. deBroglie and Matter Waves If matter waves exist for small particles, then beams of particles such as electrons should exhibit the characteristic properties of waves: diffraction. E = mc2 h = mc2 h/c = mc = p p = h/λ λ = h/p = h/mu X-Ray Diffraction 1927 Davisson aand Germer – Diffraction of slow electrons from a Ni crystal. 1927 Thomson- diffraction from thin metal foil Nobel prize shared by Davisson and Thomson in 1937. The Uncertainty Principle • Werner Heisenberg: It is difficult to determine the position and velocity of the electron in the same time. h Δx Δp ≥ 4π Schroedinger equation: • *Wave functions, are introduced to describe the allowed shapes and • Energies of electron waves (each is called orbital to distinguish it from Bohr’s orbits). • For the hydrogen atom, the square of the function ,2, is directly proportional to the probability of finding the electron in any point. • To understand this, see the figure, the depth of colour is proportional to the probability of finding the electron at a given point. The closer to the nucleus the higher the probability of finding the electron. 20 Quantum numbers • When schrodinger equation was solved, many wave functions (orbitals) were found to satisfy it. Each of these orbitals is characterized by a series of numbers called quantum numbers, which describes various properties of the orbital. The principal quantum number (n) n has integral value 1, 2, 3, …. The principal quantum number is related to the size and energy of the orbital. As n increases, the orbital becomes larger and the electrons spread more time further from the nucleus. An increase in n also means higher energy, because the electron is less tightly bound to the nucleus and the energy is less negative. An electron for which n=1 is said to be in the first principal level. If n= 2, we are dealing with the 2nd principal level and so on. 21 Wave Mechanics • Standing waves. – Nodes do not undergo displacement. 2L λ= , n = 1, 2, 3… n Wave Functions • ψ, psi, the wave function. – Should correspond to a standing wave within the boundary of the system being described. • Particle in a box. ψ 2 n x sin L L Probability of Finding an Electron Wave Functions for Hydrogen • Schrödinger, 1927 Eψ = H ψ – H (x,y,z) or H (r,θ,φ) ψ(r,θ,φ) = R(r) Y(θ,φ) R(r) is the radial wave function. Y(θ,φ) is the angular wave function. Quantum numbers (cont.) The angular momentum quantum number (ℓ) Has integral values from 0 to n-I for each value of n. ℓ = 0, 1, 2, …(n-1) This quantum number is related to the shape of atomic orbitals. The value of ℓ for a particular orbital is commonly assigned a letter: ℓ =0 is called s, ℓ = 1 is called p; ℓ = 2 is called d; ℓ = 3 is called f……. If n= 1, there is only one possible value of ℓ namely 0. This means that in the first principal level there is only one sublevel (s). If n=2, two values of ℓ are possible, 0 and 1. (s, p) If n= 3, ℓ = 0, 1, 2 (three sublevels) (s, p, d) If n=4, ℓ = 0, 1, 2, 3 (four sublevels) (s, p, d, f) In general, in the nth principal level, there are n different sublevels. 26 Quantum numbers (cont.) The magnetic orbital quantum number (mℓ) Has integral values between ℓ and -ℓ, including zero. mℓ = ℓ,….,+1, 0, -1,…., - ℓ The value of mℓ is related to the orientation of the orbital in space relative to the other orbitals in the atom. For s sublevel (ℓ=0), mℓ can have only one value 0. This means that an s sublevel contains only one orbital referred to as an s orbital. For p sublevel (ℓ=1), mℓ =1, 0, -1. This means that the p sublevel has three orbitals . For d sublevel (ℓ=2), mℓ = 2, 1, 0, -1, -2 (five orbitals) For f sublevel (ℓ=3), mℓ = 3, 2, 1, 0, -1, -2, -3 (seven orbitals) 27 Quantum numbers (cont.) Magnetic spin quantum number (ms) • This is related to electron spin. An electron has magnetic properties that correspond to those of a charged particle spinning on its axis. Either of two spin is possible cw or ccw. • This quantum number is not related to any of the previous ones but it can only have one of two values ms = +1/2 or –1/2 • Electrons that have the same value of ms are said to have parallel spin and those of different values of ms are said to be of opposed spins. 28 29 Pauli exclusion principal • Principal that relates the four quantum numbers to each other. It states that, no two electrons in an atom can have the same set of four quantum number. • It requires that only two electrons can fit into an orbital. Since there are only two values of ms. Moreover, if two electrons occupy the same orbital, they must have opposed spins. Otherwise they would have the same set of four quantum numbers. • Example Consider the following sets of quantum numbers (n, ℓ, mℓ , ms ). Which ones could not occur? For the valid identify the orbital involved. 3, 1, 0, +1/2 Valid, 3p 1, 1, 0, -1/2 not valid, ℓ cannot equal n 2, 0, 0, +1/2 Valid, 2s 4, 3, 2, +1/2 Valid, 4f 2, 1, 0, 0 not valid, ms cannot be zero 30 Atomic orbitals, shapes and sizes P orbitals S orbitals D orbitals 31 F orbitals Electron configuration in atoms • Given the rules stated before , it is possible to assign quantum numbers to each electron in an atom. Electrons can be assigned to specific principal level, sublevels and orbitals. • The simplest way to describe the arrangement of electrons in an atom is to give its electronic configuration, which shows the number of electrons, indicated by a superscript, in each sublevel. • Remember that, electrons enter the available sublevels in order of increasing sublevel energy. Ordinarily, a sublevel is filled to capacity before the next one starts to fill. The order of increasing energy for the sublevels is This means that the order of filling orbitals is 1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 4f 32 5d 5f….. and so on Orbital Filling )n=1( Complete shell Hund’s Rule: When several orbitals of equal energy are available, electrons enter singly with parallel spins. )n=2( Complete shell complete subshell (n=3) Exception to Hund’s Rule (half filled d subshell) Exception to Hund’s Rule filled d subshell) Filled subshell )n=4( Compact form of electron configuration )n=1( غالف مكتمل )n=2( غالف مكتمل Ar (Z=18) 1s22s22p63s23p6 3s 3p تحت غالف مكتمل )n=3( Hund’s rule of orbital filling (cont.) • Based on Hund’s rule, it is possible to determine the number of unpaired electrons in an atom. • With solids, this is done by studying their behaviour in a magnetic field. • If there are unpaired electrons present, the solid will be attracted into the field. Such a substance is said to be paramagnetic. • If the atoms in the solid contain only paired electrons, it is slightly repelled by the field and is called diamagnetic. • With gaseous atoms, the atomic spectrum can be also used to establish the presence and number of unpaired electrons. 38 Aufbau Process and Hunds Rule Filling p Orbitals Electon Configurations of Some Groups of Elements Electron Configurations and the Periodic Table