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6.5-6.9 6.5 Quantum Mechanics and Atomic Orbitals Reading: sections 6.5-6.6 Erwin Schrödinger proposed an equation containing both wave and particle terms. The solution of the equation is known as a wave function, Ψ (psi). As you read this material, ask yourself the following questions: What are wave functions and orbitals, how do orbitals differ from orbits? describes the behavior of a quantum mechanical object, like an electron 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? Ψ2 is the probability density Ψ2 gives the electron density for the atom 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? A region of high electron density = high probability of finding an electron How do the energy levels differ in many electron atoms? Orbitals and quantum numbers 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 If we solve the Schrödinger equation we get wave functions and corresponding energies. These wave functions are called orbitals For interest only: do not need to memorise Wavefunctions: Chem 101 4 6.6 Representations of Orbitals Probability function (Ψ2) 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 analogy: compare probability of dart landing here vs. there Chem 101 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 5 1 6.5-6.9 s orbitals (ℓ = 0) [4πr2Ψ(r)2] The p orbitals: (l=1) to memorize two lobes and a node at the nucleus • p orbitals are dumbell-shaped • 3 values of m ℓ 3 different orientations (x,y,z) n = 1, ℓ = 0 pz 1s orbital node n = 2, ℓ = 0 px py 2s orbital pg 230-231 (a closer look)7 Chem 101 The d orbitals : to be aware of To memorise 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 be aware of (ie: draw a d orbital) f orbitals (Lanthanides and Actinides: for interest only) 2 6.5-6.9 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: 6.7 Many electron atoms Beam of atoms n+ ℓ = 5 n+ ℓ = 4 n+ ℓ = 4 Beam collector plate n+ ℓ =3 Slit n+ ℓ =3 n+ ℓ =2 Magnet n+ ℓ =1 1 electron system (H,or He+ etc..) Multi- electron system (all atoms but H) Chem 101 electron spin is quantized 13 6.8 Electron configuration 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 main group elements f-block Chem 101 p-block lanthanides and actinides 15 6.9 Electron Configurations and the Periodic Table 3