Chapter 6: Electronic Structure of AtomsConcept CheckSo electrons are found in Orbitals…Classification of OrbitalsPractice ProblemShapes of the OrbitalsHydrogen Atom in the Ground State: Where is the Electron?Shapes of the S OrbitalsShapes of the P OrbitalsShapes of the D OrbitalsPractice ProblemsOrbitals SummaryEnergies of OrbitalsEnergies of Orbitals: The Hydrogen AtomEnergies of Orbitals: Many Electron AtomsWhy do the Energies Differ? (Qualitatively)Why do the Energies Differ? (Quantitatively)What You Should KnowWhat You Should KnowWhat You Should KnowChapter 6: Electronic Structure of AtomsCH110 FA10 SAS 1By the end of Lecture 6 you should know:wavelength and frequency of light, dual nature of light, electronic transitions and line spectraBohr modelMatter acts as wavesHeisenberg Uncertainty PrincipleElectronic transitions of orbitalsQuantum numbers (n, , m, ms)Orbitals: their shapes and energiesOrbitals and atoms with many electronsSpin quantum number (ms): Pauli Exclusion Principle and Hunds RuleElectron Configurations using the periodic tableWhat is the structure of an atom?What are the properties of atoms?Remember: structure affects function!Where are the electrons located? What is the energy of an electron?KEY QUESTIONS: THE BIG PICTUREConcept CheckCH110 FA10 SAS 2Understanding electromagnetic energy led toquantum theory(it explains what we observe) which led toatomic structureand predictselectron configurationsand explainsperiodic trends of the elementsSo electrons are found in Orbitals…CH110 FA10 SAS 31. Principal quantum number: _________n=2. Azimuthal quantum number : _________=3. Magnetic quantum number : _________m=Symbols used for the  quantum numbers:l valuesubshell namen = 1 l = 0 (ml= 0) n = 2 l = 0 (ml= 0) n = 2 l = 1 (ml= –1,0,1) n = 3 l = 0 (ml= 0) # ofelectronsTwo electrons fit in each orbital(more on this next time!)Some Examples:Classification of OrbitalsCH110 FA10 SAS 4Orbitals are defined by a set of n, , mThere are n2orbitals in the nthshell.nsizeshapemldirectionOrbitals insubshellOrbitals inshell1234Practice ProblemCH110 FA10 SAS 5Which of the following shows the correct n, , and mquantum numbers for an electron in a 3p subshell?A. n = 3 = 0 m= 0 B. n = 3  = 2 m= 0 C. n = 3  = 1 m= 0D. n = 3  = 1 m= -2E. n = 3  = 2 m= 1Shapes of the OrbitalsCH110 FA10 SAS 6Determined by the __________ (ψ2) of finding an electron at a certain distance (r) from the nucleus.Example: s orbitals• 2s is ____________ than 1s• Size of s orbital ________ as n increases• Shape: ________ symmetry, meaning…r0Ψ2(1s)at nucleus, r = 0electron densityor probability (Ψ2)Hydrogen Atom in the Ground State:Where is the Electron?CH110 FA10 SAS 7• We ________ know precisely where e-is• Dense dots indicate where we are _________ to find e-Shapes of the S OrbitalsCH110 FA10 SAS 8S Orbitals  = 0• Size determined by:• Shape is:Shapes of the P OrbitalsCH110 FA10 SAS 9The first p orbitals ( = 1) are found when n=2n = 2 = 1m= –1, 0, 1 same different Two “lobes” with_______ in betweenEnergies of the threeorbitals are __________(meaning _____________ )Shapes of the D OrbitalsCH110 FA10 SAS 10The first d orbitals ( = 2) are found when n=3n = 3 = 2m=samePractice ProblemsCH110 FA10 SAS 111. Which quantum numbers are needed to define the subshell?A. n onlyB. n and C.  onlyD. monlyE. n, , and m2. Which picture or pictures represent an orbital with a value of  = 2?1 2 3 4 5A. 1B. 3C. 4D. 2 and 5E. 1 and 3Orbitals SummaryCH110 FA10 SAS 12Orbitals• Allowed ____________ for electrons in atoms (all atoms, not just hydrogen).• Describes _______________________ of electrons in these energy states.Orbital number shape?name of orbitals?spdfQuantum Numbersdefines? provides?n (principal) (azimuthal) m(magnetic)Energies of OrbitalsCH110 FA10 SAS 13One electron cases: E ∝1n2not dependenton  or mTwo or more electrons:E depends on ______ (but not _____ )Therefore:E2s E2pE3sE3pE3d• Value of n determines shell• Same n and  means same ________…and….• Same subshell means same _______Energies of Orbitals: The Hydrogen AtomCH110 FA10 SAS 14Energies of Orbitals:Many Electron AtomsCH110 FA10 SAS 151s2s 2p3s 3p 3d4s 4p 4d 4f5s 5p 5d 5f6s 6p 6d1st2nd3rd4th5th6th“Typical” OrbitalEnergy SequenceWhy do the Energies Differ?(Qualitatively)CH110 FA10 SAS 16Forces act on Electrons in Orbitals• Electrons in outer orbitals “see” nucleus and also the _____ electrons.(electrons in a lower energy _______ )• s and p orbitals have different _______ , which impacts the average ________from the nucleus• s orbital has density at the nucleus, but p, d, and f orbitals have a _____ there• s electrons see more of “Z”: the _____________, have lower ______ , and are more _______• p electrons see less of Z,have higher _______ , are less _______Why do the Energies Differ?(Quantitatively)CH110 FA10 SAS 17Recall orbital energy is the energy released when an electron goes into the empty orbital (negative) or needed to remove it (positive).• H atom: Energy does not depend on  or m• 1 e-atom with nuclear charge Z (He+, Li+2)• Multi-electron atom where Zeff= effective nuclear charge reduced by “screening”21)(−=nRnEH2)(−=nZRnEH2),(−=nZRnEeffHWhat You Should KnowCH110 FA10 SAS 18Orbitals• Describe the probability density for finding an electron in a given region of space (why can’t we know it exactly?)• The surfaces we draw to represent orbitals enclose 90% of the electron density (another term for the probability density).• Orbitals specify the energy of the electron (differ in E, some degenerate, increase in energy and size as average distance from nucleus increases).• Characterized by 3 quantum numbersWhat You Should KnowCH110 FA10 SAS 19Quantum Numbers• n must be a positive integer and describes the size of the orbital and its average distance from the nucleus•  is an integer from 0 to n-1, defines shape. What is the common one letter name attached to  = 0, 1, 2, 3?• mis an integer from - to  and defines the orientation of the orbital in space• What is a shell? What is a subshell?What You Should KnowCH110 FA10 SAS 20Orbital Shapes• s orbitals are radially (spherically) symmetric and