Atomic Orbitals

1. Atomic Orbitals • Several mathematical relationships (when combined) describe the behavior of electrons in an atom • The math need not concern us—though we need to know what it tells us. • DeBroglie—light has wave and particle behavior • Schroedinger’s wave eq.s predict: • Wave functions (or an energy state of an atom) • the allowed energy of an electron AND • the probability of finding an electron in a particular region in space

2. More on the math • From Scrodinger • Also determined that three quantum numbers are needed to describe the 3-D coordinates of an electron’s motion. • Those numbers are n, l, and ml. • (note, the second/third “numbers” are L and mL

3. Atomic Orbitals, cont. • The region in space where an electron is most likely found is called an orbital • The way to visualize this region is to draw a picture that represents a 90% probability of finding an electron within • Using a set of four numbers (quantum numbers)…we can describe the location of electrons that surround an atom

4. Principal Quantum Number, n • Most informative quantum number—shows energy of electron (↑ n  higher energy (less attraction to the nucleus) • n is only an integral value, 1, 2, 3… • n also  number of different orbital types in a subshell • n2 total # of orbitals within n subshell

5. Second Quantum Number, l • Also very important, determines the SHAPE of the atomic orbital. • Has values from 0, to a maximum of n-1 • For n = 3, l can be either 0, 1, or 2 • These subshells are commonly given letter designations, s, p, d, f, g, etc…

6. More on second Q# • When l = 0,  s orbital • When l = 1,  p orbital • Energies of these subshells (or orbitals) are always s < p < d < f… (s is lowest energy, the most stable, greatest attraction to nucleus • Another note, as n increases, the orbitals become larger, and the number of different orbitals increases

7. Third Quantum Number, ml • Can have any integral value from –l to l. • For l = 3, then ml could be –3, -2, -1, 0, 1, 2, 3 • This gives the number of different types of orbitals (easier to see this…) • For n = 3, l = 1 (when l= 1, => p orbital), then ml = -1, 0, +1…three different types

8. Quantum number summary • n tells us the size of an atomic orbital • Size corresponds to energy • how many subshells there are (= to n) • n2 gives total number of orbitals within n shell • l tells us the shape of an atomic orbital • ml tells us how many orbitals there are (based on l, of course)

9. Visual representation of orbitals • recall that my artistry bites…so here’s what orbitals look like without me confusing things.

10. There is a fourth quantum number, ms, which is either ± ½. That’s the seat at the bottom. This is based on the Pauli Exclusion principle, which states that no two electrons may have the same 4 quantum #’s Another way to see this

11. Quantum Numbers: ml The magnetic quantum number (ml): • Determines the orientation in space of the orbitals of any given type in a subshell. • Can be any integer from –l to +l • The number of possible values for mlis (2l + 1), and this determines the number of orbitals in a subshell.

12. Notice: ones orbital in each principal shell threep orbitals in the second shell (and in higher ones) fived orbitals in the third shell (and in higher ones)

13. Considering the limitations on values for the various quantum numbers, state whether an electron can be described by each of the following sets. If a set is not possible, state why not. (a) n= 2, l= 1, ml= –1 (c) n= 7, l= 3, ml= +3 (b) n= 1, l= 1, ml= +1 (d) n= 3, l= 1, ml= –3 Consider the relationship among quantum numbers and orbitals, subshells, and principal shells to answer the following. (a) How many orbitals are there in the 4d subshell? (b) What is the first principal shell in which f orbitals can be found? (c) Can an atom have a 2d subshell? (d) Can a hydrogen atom have a 3p subshell?

14. The 1s Orbital • The 1s orbital (n = 1, l = 0, ml = 0) has spherical symmetry. • An electron in this orbital spends most of its time near the nucleus. Spherical symmetry; probability of finding the electron is the same in each direction. The electron cloud doesn’t “end” here … … the electron just spends very little time farther out.

15. Analogy to the 1s Orbital Highest “electron density” near the center … … but the electron density never drops to zero; it just decreases with distance.

16. The 2s Orbital • The 2s orbital has two concentric, spherical regions of high electron probability. • The region near the nucleus is separated from the outer region by a node—a region (a spherical shell in this case) in which the electron probability is zero.

17. The Three p Orbitals Three values of mlgives three p orbitals in the p subshell.

18. The Five d Orbitals Five values of ml(–2, –1, 0, 1, 2) gives five d orbitals in the d subshell.

19. Electron Spin: ms • The spin refers to a magnetic field induced by the moving electric charge of the electron as it spins. • The magnetic fields of two electrons with opposite spins cancel one another; there is no net magnetic field for the pair. • The electron spin quantum number (ms)explains some of the finer features of atomic emission spectra. • The number can have two values: +½ and –½.

20. Orbital Energy Diagrams Increasing nuclear charge, (done by increasing # protons!), LOWERS energy (forces of attraction are negative) of the orbitals and “separates” them Remember l (letter between k and m?), it differentiated energy of orbitals s > p > d > f etc Orbital energies are lower in a multielectron atom …

21. Electron Configurations • An electron configurationdescribes the distribution of electrons among the various orbitals in the atom. • Electron configuration is represented in two ways. Or even three… The spdf notation uses #’s for n and letters for l (s, p, d, f-and we already know this!!); a superscript indicates the number of electrons in a designated subshell. --most common method!!

22. Electron Configurations Part 2 In anorbital (box) diagrama box represents each orbital within subshells, and arrows represent electrons. The arrows’ directions represent electron spins; opposing spins are paired. This is not nearly as ‘convenient’ as the spdf… N:

23. Rules—Electron Configurations • Electrons ordinarily occupy orbitals of the lowest energy available. • Lowest energy = closest to nucleus • Just think of it as Electrons are lazy… • No two electrons in the same atom may have all four quantum numbers alike. • Pauli exclusion principle: one atomic orbital can accommodate no more than two electrons, and these electrons must have opposing spins. • In orbitals of identical energy, electrons enter empty orbitals whenever possible (Hund’s rule). • Electrons in half-filled orbitals have parallel spins (same direction).

24. Now we know the rules…next? • A couple of ways to remember which orbitals get filled first • Simply use the Periodic Table • Start at the top and work left to right • Reach the end and work your way down • Must know what ‘groups’ are…we’ll get to that • Use the “follow the arrow” strategy • List the orbital types in columns • Orbitals are filled in according to diagonals… • ALWAYS easier to see this

25. Order of Subshell Energies • Follow the arrows from the top: • 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, etc. • Subshells that are far from the nucleus may exhibit exceptions to the filling order.

26. The Aufbau Principle • The Aufbau principledescribes a hypothetical “building-up” of an atom from the one that precedes it in atomic number. (Z = 1) H 1s1 (Z = 2) He 1s2 (Z = 3) Li 1s2 2s1 To get He, add one electron to H. To get Li, add one electron to He. • Noble-gas-core abbreviation: we can replace the portion that corresponds to the electron configuration of a noble gas with a bracketed chemical symbol. It’s easier to write … this is the third way I eluded to earlier • (Z = 3) Li [He]2s1 • (Z = 22) Ti [Ar]4s2 3d2

27. Using the Periodic Table to Write Electron Configurations

28. A couple of examples… • Write electron configurations for MY favorite element, phosphorus--using both the spdf notation and an orbital diagram (using noble gas config?) • What about sodium—potassium? • note their electron configurations look very much alike…hence their being in the same group

29. Main Group andTransition Elements • The main group elements are those in which the LAST orbital being filled in the aufbau process is an s or a p orbital. In transition elements, or transition METALS the subshell being filled in the aufbau process is in an inner principal shell.

30. Revisiting the Periodic Table for Electron Configurations The electron configuration of Rh ends with 5s2 4d7

31. Give the complete ground-state electron configuration of a strontium atom (a) in the spdf notation and (b) in the noble-gas-core abbreviated notation. • Some exceptions to the Aufbau principle…not every atom behaves. This is more pronounced towards the heavier elements…but a couple of 3d elements don’t follow the rules either… • and we’ll get into the difference between valence and core electrons.

32. Exceptions to the Aufbau Principle Half-filled d subshell plus half-filled s subshell has slightly lower in energy than s2 d4. Filled d subshell plus half-filled s subshell has slightly lower in energy than s2 d9. More exceptions occur farther down the periodic table. They aren’t always predictable, because energy levels get closer together.

33. Five valence electrons, for which n = 4 28 core electrons Valence Electrons and Core Electrons • The valence shell is the outermost occupied principal shell. The valence shell contains the valence electrons. • For main group elements, the number of valence shell electrons is the same as the periodic table group number (2A elements: two valence electrons, etc.) The period number is the same as the principal quantum number n of the electrons in the valence shell. • Electrons in inner shells are called core electrons. Example: As [Ar]4s23d104p3

34. Electron Configurations of Ions • To obtain the electron configuration of an anion by the aufbau process, we simply add the additional electrons to the valence shell of the neutral nonmetal atom. • The number added usually completes the shell. • A nonmetal monatomic ion usually attains the electron configuration of a noble gas atom. O2– : [Ne] Br– : [Kr]

35. Electron Configurations of Ions • A metal atom loses electrons to form a cation. • Electrons are removed from the configuration of the atom. • The first electrons lost are those of the highest principal quantum number. • If there are two subshells with the same highest principal quantum number, electrons are lost from the subshell with the higher l. • This simply means an atom loses p elec before s.

36. Electron Configurations of Ions(cont’d) Atom Ion (or) F 1s2 2s22p5 F–1s2 2s22p6 [Ne] S [Ne] 3s2 3p4 S2–[Ne] 3s2 3p6[Ar] Sr [Kr] 5s2 Sr2+[Kr] 5s2[Kr] Ti [Ar] 4s2 3d2 Ti4+[Ar] 4s2 3d2[Ar] Fe [Ar] 4s2 3d6 Fe2+[Ar] 4s2 3d6[Ar] 3d6 What would be the configuration of Fe3+? Of Sn2+? Valence electrons are lost first.

37. Example 8.3 • Write the electron configuration of the Co3+ ion in a noble-gas-core abbreviated spdf notation. • How about same thing for Cr3+, P3-. • How likely is the formation of Na2+?

38. Periodic Properties • Certain physical and chemical properties recur at regular intervals, and/or vary in regular fashion, when the elements are arranged according to increasing atomic number. • Melting point, boiling point, hardness, density, physical state, and chemical reactivity are periodic properties. • We will examine several periodic properties that are readily explained using electron configurations.

39. A Summary of Trends

40. Periodic Properties: Atomic Radius • Half the distance between the nuclei of two atoms is the atomic radius. Covalent radius: half the distance between the nuclei of two identical atoms joined in a molecule. Metallic radius: half the distance between the nuclei of adjacent atoms in a solid metal.

41. Periodic Properties: Atomic Radius • Atomic radius increases from top to bottom within a group. • The value of n increases, moving down the periodic table. • The value of n relates to the distance of an electron from the nucleus.

42. Periodic Properties: Atomic Radius • Atomic radius decreases from left to right within a period. • Why? The effective nuclear charge increases from left to right, increasing the attraction of the nucleus for the valence electrons, and making the atom smaller. Mg has a greater effective nuclear charge than Na, and is smaller than Na.

43. Atomic Radii of the Elements

44. Ionic Radii The ionic radiusof each ion is the portion of the distance between the nuclei occupied by that ion. VERY much dependent on + and – attractions cations/anions loss/gain of e’s

45. Ionic Radii • Cations are smaller than the atoms from which they are formed; there is less electron–electron repulsion. Fewer e’s, same + charge, contracts

46. Ionic Radii • Anions are larger than the atoms from which they are formed. • Effective nuclear charge is unchanged, but additional electron(s) increase electron–electron repulsion. • Isoelectronic species have the same electron configuration; size decreases with effective nuclear charge. • arrange the following species in the expected order of increasing radius: Ca2+, Fe3+, K+, S2–, Se2–

47. Ionization Energy • Ionization energy (I) is the energy required to remove an electron from a ground-state gaseous atom. • I is usually expressed in kJ per mole of atoms. Metals normally give up e’s… M(g)  M+(g) + e–ΔH = I1 M+(g)  M2+(g) + e–ΔH = I2 M2+(g)  M3+(g) + e–ΔH = I3

48. Ionization Energy Trends • I1 < I2 < I3 • Removing an electron from a positive ion is more difficult than removing it from a neutralatom. • A large jump in I occurs after valence electrons are completely removed (why?). • I1 decreasesfrom top to bottom on the periodic table. • n increases; valence electron is farther from nucleus. • I1 generally increases from left to right, with exceptions. Goes back to AR trend…+ and – • Greater effective nuclear charge from left to right holds electrons more tightly.

49. Comparing Ionization Energies Compare I2 to I1 for a 2A element, then for the corresponding 1A element. Why is I2 for each 1A element so much greater than I1? Why don’t we see the same trend for each 2A element? I2 > I1 … but only about twice as great …

50. Selected Ionization Energies General trend in I1: An increase from left to right, but … The electron being removed is now a p electron (higher energy, easier to remove than an s). …I1 drops, moving from 2A to 3A. I1 between N/O, P/S is inconsistent!