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Transcript

6.5-6.9 Reading: sections 6.5-6.6 As you read this material, ask yourself the following questions: What are wave functions and orbitals, how do orbitals differ from orbits? What can we learn about an electron from a wave function? What properties of the electron do the principal quantum number(n), the angular momentum quantum number(l) and the magnetic quantum number determine(ml). What values can each of these quantum numbers have, how are their values related? What are the shapes of the orbitals for different values of the angular momentum quantum number (different subshells)? Sketch these shapes. What labels do we give these subshells? How do the energy levels differ in many electron atoms? What is the fourth quantum number (ms) and what values can it have? When assigning energies to electrons, what are the implications of the Pauli Exclusion principle? Chem 101 1 6.5 Quantum Mechanics and Atomic Orbitals Erwin Schrödinger proposed an equation containing both wave and particle terms. The solution of the equation is known as a wave function, Ψ (psi). describes the behavior of a quantum mechanical object, like an electron Ψ2 is the probability density Ψ2 gives the electron density for the atom A region of high electron density = high probability of finding an electron Orbitals and quantum numbers If we solve the Schrödinger equation we get wave functions and corresponding energies. These wave functions are called orbitals 1 6.5-6.9 For interest only: do not need to memorise Wavefunctions: Chem 101 4 2 6.5-6.9 Probability function (Ψ2) analogy: compare probability of dart landing here vs. there Chem 101 5 6.6 Representations of Orbitals The s orbitals ( to memorize) (l=0) • All s orbitals are spherical • As n increases, the s orbitals get larger • As n increases, the number of nodes increases height of graph indicates electron density node = probability of finding an electron is 0 For an s orbital the number of nodes is given by n – 1 3 6.5-6.9 s orbitals (ℓ = 0) [4πr2Ψ(r)2] n = 1, ℓ = 0 1s orbital node n = 2, ℓ = 0 2s orbital pg 230-231 (a closer look)7 Chem 101 The p orbitals: (l=1) to memorize • p orbitals are dumbell-shaped two lobes and a node at the nucleus • 3 values of mℓ 3 different orientations (x,y,z) pz px py 4 6.5-6.9 The d orbitals : to be aware of 5 values of mℓ so 5 different orientations 3 d orbitals lie in a plane bisecting the x-, y-, and z-axes 2 d orbitals lie in a plane aligned along the x-, y-, and z-axes 4 of the d orbitals have 4 lobes each 1 d orbital has 2 lobes and a “donut” To memorise 5 6.5-6.9 To be aware of (ie: draw a d orbital) f orbitals (Lanthanides and Actinides: for interest only) 6 6.5-6.9 6.7 Many electron atoms n+ ℓ = 5 n+ ℓ = 4 n+ ℓ = 4 n+ ℓ =3 n+ ℓ =3 n+ ℓ =2 n+ ℓ =1 1 electron system (H,or He+ etc..) Multi- electron system (all atoms but H) Chem 101 13 Electron Spin and the Pauli Exclusion Principle .Stern and Gerlach designed an experiment to determine why line splitting occurs. A beam of atoms was passed through a slit and into a magnetic field and the atoms were detected: Beam of atoms Beam collector plate Slit Magnet electron spin is quantized 7 6.5-6.9 6.8 Electron configuration Chem 101 15 6.9 Electron Configurations and the Periodic Table The periodic table can be used as a guide for electron configurations. the period number is the value of n d-block s-block transition metals alkali and alkaline earth metals p-block main group elements f-block lanthanides and actinides 8 6.5-6.9 6.9 Electron Configurations and the Periodic Table 9