Excited Atoms & Atomic Structure

1. Excited Atoms& Atomic Structure

2. The Quantum Mechanical Picture of the Atom Basic Postulates of Quantum Theory • Atoms and molecules can exist only in certain energy states. In each energy state, the atom or molecule has a definite energy. When an atom or molecule changes its energy state, it must emit or absorb just enough energy to bring it to the new energy state (the quantum condition). • Atoms or molecules emit or absorb radiation (light) as they change their energies. The frequency of the light emitted or absorbed is related to the energy change by a simple equation.

3. The Quantum Mechanical Picture of the Atom The allowed energy states of atoms and molecules can be described by sets of numbers called quantum numbers. • Quantum numbers are the solutions of the Schrodinger, Heisenberg & Dirac equations. • Four quantum numbers are necessary to describe energy states of electrons in atoms – n, , m, ms Schroedinger 3-dimensional time independent equation Heisenberg’s uncertainty Equation Dirac’s quantum mechanical model E. Schrodinger 1887-1961 W. Heisenberg 1901-1976

4. n = 1 n = 2 n = 3 Quantum Numbers – n n = 4 n = 5 n = 6 n = 7 • The Principal quantum number has the symbol – n. • n = 1, 2, 3, 4, ...... “shells” • n = K, L, M, N, ...... • The electron’s energy depends principallyon n and tells the average relative distance of the electron from the nucleus. • – As n increases for a given atom, so does the average distance of the electrons from the nucleus. • – Electrons with higher values of n are easier to remove from an atom.

5. Quantum Numbers –  • 2. The azimuthal quantum numberhas the symbol. • describes the shape of the region of space occupied by the electron • When linked with n defines the energy of the electron, All wave functions that have the same value of both n and l form a subshell • = 0, 1, 2, 3, 4, 5, .......(n-1) • = s, p, d, f, g, h, .......(n-1) • = 0 • = s • = 1 • = p n = 1 n = 2 • = 2 • = d n = 3 n = 4 n = 5 n = 6 n = 7 • = 3 • = f

6. Quantum Numbers – m • The symbol for the magnetic quantum number is m. m = -  , (-  + 1), (-  +2), .....0, ......., ( -2), ( -1),  • If = 0 (or an s orbital), then m = 0. • There is only 1 value of m. Thus there is one s orbital per n value. n  1 • If  = 1 (or a p orbital), then m = -1,0,+1. • There are 3 values of m. Thus there are three p orbitals per n value. n  2 • If  = 2 (or a d orbital), then m = -2,-1,0,+1,+2. • There are 5 values of m. Thus there are five d orbitals per n value. n  3 • If  = 3 (or an f orbital), then m = -3,-2,-1,0,+1,+2, +3. • There are 7 values of m. Thus there are seven f orbitals per n value, n • Theoretically, this series continues on to g,h,i, etc. orbitals. • Practically speaking atoms that have been discovered or made up to this point in time only have electrons in s, p, d, or f orbitals in their ground state configurations. • Each wave function with an allowed combination of n, l, and mlvalues describes an atomic orbital, a particular spatial distribution for an electron • For a given set of quantum numbers, each principal shell contains a fixed number of subshells, and each subshell contains a fixed number of orbitals

7. Atomic Orbitals • Atomic orbitals are regions of space where the probability of finding an electron about an atom is highest. • s orbital properties: • There is one s orbital per n level. •  = 0 • 1 value of m • = 0 • = s n = 1 n = 2 n = 3 n = 4 n = 5 n = 6 n = 7

8. Atomic Orbitals • p orbitals are peanut or dumbbell shaped. • They are directed along the axes of a Cartesian coordinate system. • The first p orbitals appear in the n = 2 shell. • There are 3 p orbitals per n level. • The three orbitals are named px, py, pz. • They have an= 1. • m= -1,0,+1 3 values of m

9. Atomic Orbitals • d orbital shapes

10. Atomic Orbitals • f orbital shapes

11. Quantum Numbers

12. Quantum Numbers – ms • The last quantum number is the spin quantum number which has the symbol ms. • The spin quantum number only has two possible values. • ms = +1/2 or -1/2

13. The Periodic Table and Electron Configurations Note that the 3d subshell is higher in energy than the 4s subshell so appears in the 4th period Day 1

14. Building up the Periodic Table • The Nucleus: • The Aufbau Process • – Used to construct the periodic table • – First, Build by adding the required number of protons (the atomic number) and neutrons (the mass of the atom) • – Second, Determine the number of electrons in the atoms then add electrons one at a time to the lowest-energy orbitals available without violating the Pauli principle • Electrons: • Hund’s Rule states that each orbital will be filled singly before pairing begins. The singly filled orbitals will have a parallel spin. • – Each of the orbitals can hold two electrons, one with spin up , which is written first, and one with spin down  • – A filled orbital is indicated by , in which the electron spins are paired • – The electron configuration is written in an abbreviated form, in which the occupied orbitals are identified by their principal quantum n and their value of l (s, p, d, or f), with the number of electrons in the subshell indicated by a superscript • Pauli’s Exclusion Principle states that paired electrons in an orbital will have opposite spins. • Neon - 2p • 2s • 1s

15. Building up the Periodic Table • Valence electrons – It is tedious to keep copying the configurations of the filled inner subshells – The notation can be simplified by using a bracketed noble gas symbol to represent the configuration of the noble gas from the preceding row – Electrons in filled inner orbitals are closer and are more tightly bound to the nucleus and are rarely involved in chemical reactions Now we can write a complete set of quantum numbers for all of the electrons in these three elements as examples. • Na • First for 11Na. • When completed there must be one set of 4 quantum numbers for each of the 11 electrons in Na (remember Ne has 10 electrons) [Ne] = 1s22s22p6

16. Building up the Periodic Table 11Na 1s22s22p63s1

17. Electron Configuration of the Elements l = 0 l = 1 l = 2 l = 3

18. Periodic Trends in Atomic Radii In the periodic table, atomic radii decrease from left to right across a row because of the increase in effective nuclear charge due to poor electron screening by other electrons in the same principal shell. Atomic radii increase from top to bottom down a column because the effective nuclear charge remains constant as the principal quantum number increases.

19. Ionization Energies • There are two reasons for It takes more energy to remove the second electron from an atom than the first, and so on. : 1. The second electron is being removed from a positively charged species rather than a neutral one, so more energy is required. 2. Removing the first electron reduces the repulsive forces among the remaining electrons, so the attraction of the remaining electrons to the nucleus is stronger.

20. Electron Affinities Electron affinity (EA) of an element E is defined as the energy change that occurs when an electron is added to a gaseous atom: E (g) + e--  E—(g) energy change = EA. • Electron affinities can be negative (in which case energy is released when an electron is added) or positive (in which case energy must be added to the system to produce an anion) or zero (the process is energetically neutral). • Halogens have the most negative electron affinities.

21. Ionic Radii and Isoelectronic Series When one or more electrons is removed from a neutral atom, two things happen: 1. Repulsions between electrons in the same principal shell decrease because fewer electrons are present. 2. The effective nuclear charge felt by the remaining electrons increases because there are fewer electrons to shield one another from the nucleus.

22. Electronegativity Increases Increases Increases The tendency of an element to gain or lose electrons is is called electronegativity (), defined as the relative ability of an atom to attract electrons to itself in a chemical compound.

23. An Overview of Chemical Bonding • Chemical bond — the force that holds atoms together in a chemical compound • Covalent bonding — electrons are shared between atoms in a molecule or polyatomic ion • Ionic bonding —positively and negatively charged ions are held together by electrostatic forces • Ionic compounds — dissolve in water to form aqueous solutions that conduct electricity • Covalent compounds — dissolve to form solutions that do not conduct electricity • Chemical bonding • 1. Ionic — one or more electrons are transferred completely from one atom to another, and the resulting ions are held together by purely electrostatic forces • 2. Covalent — electrons are shared equally between two atoms • 3. Polar covalent — electrons are shared unequally between the bonded atoms • 4. Polar bond — bond between two atoms that possess a partial positive charge (õ+) and a partial negative charge (õ-)

24. The Continuous Range of Bonding Types • Covalent and ionic bonding represent two extremes. • In pure covalent bonds electrons are equally shared by the atoms. • In pure ionic bonds electrons are completely lost or gained by one of the atoms. • Most compounds fall somewhere between these two extremes. • All bonds have some ionic and some covalent character. • For example, HI is about 17% ionic • The greater the electronegativity differences the more polar the bond. Day 2

25. OXIDATION NUMBERS • Guidelines for assigning oxidation numbers. • The oxidation number of any free, uncombined element is zero. • The oxidation number of an element in a simple (monatomic) ion is the charge on the ion. • In the formula for any compound, the sum of the oxidation numbers of all elements in the compound is zero. • In a polyatomic ion, the sum of the oxidation numbers of the constituent elements is equal to the charge on the ion. • Fluorine has an oxidation number of –1 in its compounds. • Hydrogen, H, has an oxidation number of +1 unless it is combined with metals, where it has the oxidation number -1. • Examples – LiH, BaH2 • Oxygen usually has the oxidation number -2. • Exceptions: • In peroxides O has oxidation number of –1. • Examples - H2O2, CaO2, Na2O2 • In OF2, O has oxidation number of +2. Use the periodic table to help with assigning oxidation numbers of other elements. • IA metals have oxidation numbers of +1. • IIA metals have oxidation numbers of +2. • IIIA metals have oxidation numbers of +3. • VA elements have oxidation numbers of –3 in binary compounds with H, metals or NH4+. • VIA elements below O have oxidation numbers of –2 in binary compounds with H, metals or NH4+.

26. OXIDATION NUMBERS NH3 ClO- H3PO4 MnO4- Cr2O72- C3H8

27. Formal Charges • The most likely formula for a molecule or ion is usually the one in which the formal charge on each atom is zero or as near zero as possible • Negative formal charges are more likely to occur on the more electronegative elements • Lewis dot formulas in which adjacent atoms have formula charges of the same sign are usually not accurate Cl=N-O O=N-Cl

28. Formal Charges - + H H Cl Cl Al H H N B H H Cl H H ∙∙ ∙∙ ∙∙ + O N H H H S H H H ∙∙ H H

29. Covalent Bonding • Covalent bonds are formed when atoms share electrons. • If the atoms share 2 electrons a single covalent bond is formed. • If the atoms share 4 electrons a double covalent bond is formed. • If the atoms share 6 electrons a triple covalent bond is formed. • The attraction between the electrons is electrostatic in nature • The atoms have a lower potential energy when bound. • Covalent bonds in which the electrons are shared equally are designated as nonpolar covalent bonds. • Nonpolar covalent bonds have a symmetrical charge distribution. • To be nonpolar the two atoms involved in the bond must be the same element to share equally.

30. Polar and Nonpolar Covalent Bonds • Covalent bonds in which the electrons are not shared equally are designated as polar covalent bonds • Polar covalent bonds have an asymmetrical charge distribution • To be a polar covalent bond the two atoms involved in the bond must have different electronegativities. • Some examples of polar covalent bonds. • HF

31. Polar and Nonpolar Covalent Bonds • Compare HF to HI. 2.1 2.5

32. Polar and Nonpolar Covalent Bonds • Polar molecules can be attracted by magnetic and electric fields.

33. Dipole Moments • Molecules whose centers of positive and negative charge do not coincide, have an asymmetric charge distribution, and are polar. • These molecules have a dipole moment. • The dipole moment has the symbol . •  is the product of the distance,d, separating charges of equal magnitude and opposite sign, and the magnitude of the charge, q. • There are some nonpolar molecules that have polar bonds. • There are two conditions that must be true for a molecule to be polar. • There must be at least one polar bond present or one lone pair of electrons. • The polar bonds, if there are more than one, and lone pairs must be arranged so that their dipole moments do not cancel one another.

34. Molecular Dipole Moments • In complex molecules that contain polar covalent bonds, the three-dimensional geometry and the compound’s symmetry determine if there is a net dipole moment • Mathematically, dipole moments are vectors; they possess both a magnitude and a direction • Dipole moment of a molecule is the vector sum of the dipole moments of the individual bonds in the molecule • If the individual bond dipole moments cancel one another, there is no net dipole moment • Molecular structures that are highly symmetrical (tetrahedral and square planar AB4, trigonalbipyramidal AB5, and octahedral AB6) have no net dipole moment; individual bond dipole moments completely cancel out • In molecules and ions that have V-shaped, trigonal pyramidal, seesaw, T-shaped, and square pyramidal geometries, the bond dipole moments cannot cancel one another and they have a nonzero dipole moment • Polar Molecules must meet two requirements: • One polar bond or one lone pair of electrons on central atom. • Neither bonds nor lone pairs can be symmetrically arranged that their polarities cancel.

35. Polar Covalent Bonds

36. Polar Covalent Bonds Ionic Polar Covalent Covalent Determine Inductive effect Count the number of electrons the element should have Determine how equally electrons are shared (DEN) >1.7 consider it ionic Oxidation number Formal charge Day 3

37. Writing Lewis Formulas: The Octet Rule • The octet rule states that representative elements usually attain stable noble gas electron configurations in most of their compounds. • Lewis dot formulas are based on the octet rule. • We need to distinguish between bonding (or shared) electrons and nonbonding (or unshared or lone pairs) of electrons. • N - A = S rule • Simple mathematical relationship to help us write Lewis dot formulas. • N = number of electrons needed to achieve a noble gas configuration. • N usually has a value of 8 for representative elements. • N has a value of 2 for H atoms. • A = number of electrons available in valence shells of the atoms. • A is equal to the periodic group number for each element. • A is equal to 8 for the noble gases. • S = number of electrons shared in bonds. • A-S = number of electrons in unshared, lone, pairs.

38. Writing Lewis Formulas: The Octet Rule • For ions we must adjust the number of electrons available, A. • Add one e- to A for each negative charge. • Subtract one e- from A for each positive charge. • The central atom in a molecule or polyatomic ion is determined by: • The atom that requires the largest number of electrons to complete its octet goes in the center. • For two atoms in the same periodic group, the less electronegative element goes in the center. • Select a reasonable skeleton • The least electronegative is the central atom • Carbon makes 2,3, or 4 bonds • Nitrogen makes 1(rarely), 2,3, or 4 bonds • Oxygen makes 1, 2(usually), or 3 bonds • Oxygen bonds to itself only as O2 or O3, peroxides, or superoxides • Ternary acids (those containing 3 elements) hydrogen bonds to the oxygen, not the central atom, except phosphates • For ions or molecules with more than one central atom the most symmetrical skeleton is used • Calculate N, S, and A

39. Writing Lewis Dot Formulas N ever Have a Full Octet Always Have a Full Octet Sometimes Have a Full Octet Sometimes Exceed a Full Octet

40. Writing Lewis Dot Formulas • Count the number of electrons brought to the party (element’s group number) • For ions we must adjust the number of electrons available. • Add one e- for each negative charge. • Subtract one e- for each positive charge. • Select a reasonable skeleton • The least electronegative is the central atom • See prior periodic table for number of electrons involved in bonding • Group I 2 electrons or 1 bond • Group II 4 electrons or up to 2 bonds • Group III Al and B, 6 or 8 electrons up to 3 or 4 bonds • C,N,O,F must have 8 electrons (up to 4 bonds for C, 3 for N, 2 for O, and 1 bond for F). • All others must have at least 8 electrons (up to 4 bonds), but may have more. • When a choice for the central atom in a molecule or polyatomic ion is unclear: • For ions or molecules with more than one central atom the most symmetrical skeleton is used • The atom that requires the largest number of electrons to complete its octet goes in the center. • For two atoms in the same periodic group, the less electronegative element goes in the center. • Calculate Formal charges, adjust bonds for lowest numbers (zero preferred) and allow for resonance structures

41. Writing Lewis Formulas: • Write Lewis dot and dash formulas for hydrogen cyanide, HCN. • Write Lewis dot and dash formulas for sulfur trioxide, SO3. • Write Lewis dot and dash formulas for the sulfite ion, SO32-. • There are three possible structures for SO32-. • The double bond can be placed in one of three places. When two or more Lewis formulas are necessary to show the bonding in a molecule, we must use equivalent resonance structures to show the molecule’s structure. Double-headed arrows are used to indicate resonance formulas. • Write dot and dash formulas for BBr3. • Write dot and dash formulas for AsF5.

42. Stereochemistry • Stereochemistry is the study of the three dimensional shapes of molecules. • Valence Shell Electron Pair Repulsion Theory • Commonly designated as VSEPR • Principal originator • R. J. Gillespie in the 1950’s • Valence Bond Theory • Involves the use of hybridized atomic orbitals • Principal originator • L. Pauling in the 1930’s & 40’s

43. VSEPR Theory • Regions of high electron density around the central atom are arranged as far apart as possible to minimize repulsions. • There are five basic molecular shapes based on the number of regions of high electron density around the central atom. • Lone pairs of electrons (unshared pairs) require more volume than shared pairs. • Consequently, there is an ordering of repulsions of electrons around central atom. • Criteria for the ordering of the repulsions: • Lone pair to lone pair is the strongest repulsion. • Lone pair to bonding pair is intermediate repulsion. • Bonding pair to bonding pair is weakest repulsion. • Mnemonic for repulsion strengths • lp/lp > lp/bp > bp/bp • Lone pair to lone pair repulsion is why bond angles in water are less than 109.5o. • Valence-shell electron-pair repulsion (VSEPR) model predicts the shapes of many molecules and polyatomic ions but provides no information about bond lengths or the presence of multiple bonds

44. VSEPR Theory • Frequently, we will describe two geometries for each molecule. • Electronic geometryis determined by the locations of regions of high electron density around the central atom(s). • Molecular geometrydetermined by the arrangement of atoms around the central atom(s). Electron pairs are not used in the molecular geometry determination just the positions of the atoms in the molecule are used.

45. VSEPR Theory • Two regions of high electron density around the central atom. • Three regions of high electron density around the central atom. • Four regions of high electron density around the central atom.

46. VSEPR Theory • Five regions of high electron density around the central atom. • Six regions of high electron density around the central atom.

47. VSEPR Theory • An example of a molecule that has different electronic and molecular geometries is water - H2O. • Electronic geometry is tetrahedral. • Molecular geometry is bent or angular. • An example of a molecule that has the same electronic and molecular geometries is methane - CH4. • Electronic and molecular geometries are tetrahedral.

48. The VSEPR Model

49. The VSEPR Model • The same basic approach will be used in every example of molecular structure prediction:

50. The VSEPR Model Day 4