In previous chapter we learned a new understanding of matter and energy which in turn led to the quantum mechanical model of the atom • In late 19th century chemists were exploring so many aspects of chemistry and became a major university subject in Europe and America • Superimposed on this activity was the accumulation of an enormous body of facts about the elements, which became organized into the periodic table. • The goal of this chapter is to show how the organization of the table was explained perfectly by the new quantum-mechanical atomic model • This model answers one of the central questions in chemistry; how does the electron configuration of an element – the distribution of electron within the orbitals of its atom – relate to its chemical and physical properties?
Development of the Periodic Table • The earliest organizing attempt was made by Johann Döbereiner, who placed groups of three elements with similar properties, such as calcium, strontium and barium into “triads” • John Newland noted similarities between every eighth element (arranged by atomic mass) and placed them in “octaves”. • The most successful organizing scheme was made by Russian chemist Dmitri Mendeleev, in 1870 he arranged the 65 elements then known into a periodic table and summarized their behavior in the periodic law, when arranged by atomic mass, the elements exhibit a periodic recurrence of similar properties. • German chemist Julius Lothar Meyer also arrived at virtually the same organization simultaneously yet independently
Mendeleev’s predicted properties of Germanium (Eka Silicon) and its actual properties
Characteristic of Many-Electron Atoms • The Schrödinger equation does not give exact solutions for many-electron atoms, however it gives very good approximate solution using modern computers • These solutions show that the atomic orbitals of many-electron atoms are hydrogen-like, that is they resemble those of the H atom
3 features that were not relevant in the case of Hydrogen • The need of a fourth quantum number • A limit on the number of electrons allowed in a given orbital, and • A more complex set of orbital energy levels
The Electron-spin Quantum Number • The three quantum numbers n, l and ml describe the size (energy), shape and orientation respectively of an atomic orbital • However additional quantum number is needed to describe a property of the electron itself, called spin which is not a property of the orbital
Observing the Effect of Electron Spin Beam of H atom Source of H atoms ms = - ½ N Detecting screen S ms = + ½ Direction of external nonuniform magnetic field Magnet
The spin quantum number (ms) indicates the direction of the electron spin about its own axis and can have one of two possible values +½ or -½ • So each electron in an atom is described completely by a set of four quantum numbers: the first three describe its orbital and the fourth describes its spin • The quantum number for the lone electron in hydrogen is n = 1, l = 0, ml = 0 and ms = +½. The spin quantum number for this electron could just as well have been –½ but, byconvention we assign + ½ for the first electron in an orbital
The Exclusion Principle • The first electron in the He ground state has the same set quantum numbers as the electron in the H atom, but the second electron does not • Based on observation of the excited state of atoms, Wolfgang Pauli formulated the exclusion principle: no two electrons in the same atom can have the same four quantum number • Each electron must have a unique “identity” as expressed by its set of quantum numbers • Because ms can have only two values, the major consequence of the exclusion principle is that an atomic orbital can hold a maximum of two electrons and they must have opposing spins.
Electrostatic effects and the splitting of energy levels • When opposite charges are far apart, the energy of the system is higher (less stable) than when they are close together, because the charges attract each other less strongly • When a large positive charge attracts a 1- charge, the energy of the system is lower (more stable) than when a small positive charge does so, because the charges attract each other more strongly • These effects lead to a more complex set of energy states than exists in the H atom. • The energy states of many electron atoms arise from two types of interaction: nucleus-electron attraction and electron-electron repulsion. • One major consequence is the splitting of energy levels into sub levels of differing energy (depends primarily on its n value and secondarily on its l value.
Factors that Affected Orbital Energy • The effect of nuclear charge (Z) on orbital energy: higher nuclear charge (Z) lowers orbital energy by increasing nucleus-electron attractions • The effect of electron repulsions on orbital energy: the shielding effect. Shielding (or screening) reduces the nuclear charge to an effective nuclear charge (Zeff) the nuclear charge an electron actually experiences, makes it easier to remove. Inner electrons shield outer electrons more effectively than do electrons in the same sublevel • The effect of orbital shape (l value) on orbital energy: the penetration effect. In general differences in radial probability distribution (orbital shape) lead to differences in penetration, which affect shielding. These factor cause an energy level to split into sublevels
Order of sublevel energies: s < p < d < f
The Quantum-Mechanical Model and The Periodic Table • A useful way to determine the electron configuration of the elements is to add one electron per element to the lowest energy orbital available. This approach called the aufbau principle (German aufbauen, “to build up”) • It results in ground state electron configuration. • There are two common ways to show the orbital occupancy: • The electron configuration • The orbital diagram
Building up periods 1 and 2 • The placement of electrons for carbon exemplifies Hund’s Rule: when orbitals of equal energy are available the electron configuration of lowest energy has the maximum number of unpaired electrons with parallel spins
Sample Problems • Write a set of quantum numbers for the third and eighth electrons added to F • Use the periodic table to identify the element with the electron configuration 1s22s22p4. Write its orbital diagram and give the quantum numbers of its sixth electron.
Answers • The third electron is in the 2s orbital. n = 2. l = 0, ml = 0, ms = + ½ • The eighth electron is in the first 2p orbital n = 2, l = 1, ml = -1, ms = - ½ • The element has eight electron so Z = 8 oxygen 1s 2s 2p n = 2, l = 1, ml = 0, ms = + ½
Electron Configuration within Groups • One of the central points in all chemistry is that similar outer electron configurations correlate with similar chemical behavior • Example in group 1A, lithium and sodium have the condensed electron configuration ns1 as do all the other alkali metals. All are highly reactive metals that form ionic compounds with non metals. • Restating the general theme: within a group similarities in chemical behavior reflect similarities in the distribution of electrons in the highest energy orbitals • Thus two major connections between quantum mechanics and chemical periodicity are: orbital filling occurs in order of increasing energy; properties recur periodically because electron configurations recur periodically
Categories of electrons • Inner (core) electrons are those in the previous noble gas and any completed transition series. They fill all the lower energy levels of an atom • Outer electron are those in the highest energy level (highest n value). They spent most of their time farthest from nucleus • Valence electron are those involved in forming compounds. Among the main group elements, the valence electrons are the outer electrons. Among the transition elements, some inner d electrons are also often involved in bonding and are counted among the valence electrons.
Sample Problems • Give the (1) full and condensed electron configurations, (2) partial orbital diagrams for the valence electrons and (3) number of inner electrons for the following element: • Potassium (K: Z = 19) • Molybdenum (Mo: Z = 42) • Lead (Pb: Z = 82) • Give full and condensed electron configurations, a partial diagrams for valence electrons and the number of inner electrons for the following element: • Ni (Z = 28) • Sr (Z = 38) • Po (Z = 84)
Answers • K (Z = 19) Full: 1s2 2s2 2p6 3s2 3p6 4s1 Condensed: [Ar] 4s1 • Mo (Z = 42) Full: 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s1 4d5 Condensed : [Kr] 5s1 4d5 • Pb (Z = 82) Full: 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2 4f14 5d10 6p2 Condensed: [Xe] 6s2 4f14 5d10 6p2
Trends in Atomic Size • Size goes UP on going down a group. • Because electrons are added further from the nucleus, there is less attraction. • Size goes DOWN on going across a period.
Atomic Size • Size decreases across a period owing to increase in Z*. • Each added electron feels a greater and greater + charge. Na Mg Al Si P S Cl Ar 186 160 143 118 110 103 100 98
Sample Problem • Using only the periodic table, rank each set of main-group elements in order of decreasing atomic size: • Ca, Mg, Sr • K, Ga, Ca • Br, Rb, Kr • Sr, Ca, Rb • Sr > Ca > Mg • K > Ca > Ga • Rb > Br > Kr • Rb > Sr > Ca
Ion Sizes • CATIONS are SMALLER than the atoms from which they come. • The electron/proton attraction has gone UP and so size DECREASES. • 3- > 2- > 1- > 1+ > 2+ > 3+
Ion Sizes • ANIONS are LARGER than the atoms from which they come. • The electron/proton attraction has gone DOWN and so size INCREASES. • Trends in ion sizes are the same as atom sizes.
Sampel problems • Rank the ions in order of increasing size • Na+, Mg2+, F- • Ca2+, Sr2+, Mg2+ Answers : • Mg2+< Na+ < F- • Mg2+ < Ca2+ < Sr2+
Ionization Energy • IE = energy required to remove an electron from an atom in the gas phase. Mg (g) + 735 kJ ---> Mg+ (g) + e- Mg+ (g) + 1451 kJ ---> Mg2+ (g) + e- Mg2+ (g) + 7733 kJ ---> Mg3+ (g) + e- • Energy cost is very high to dip into a shell of lower n. This is why ox. no. = Group no.
Trend in Ionization Energy • IE increases across a period because Z* increases. • Metals lose electrons more easily than nonmetals. • Metals are good reducing agents. • Nonmetals lose electrons with difficulty. • IE decreases down a group because size increases • Reducing ability generally increases down the periodic table.
Sample Problem • Using the periodic table only, rank the elements in each of the following sets in order of decreasing IE • Kr, He, Ar • Sb, Te, Sn • K, Ca, Rb • I, Xe, Cs • Rank in order of increasing IE • Sb, Sn, I • Sr, Ca, Ba
Answers • Decreasing IE • He > Ar > Kr • Te > Sb > Sn • Ca > K > Rb • Xe > I > Cs • Rank in order of increasing IE • Sn < Sb < I • Ba < Sr < Ca
Electron Affinity • A few elements GAIN electrons to form anions. • Electron affinity is the energy accompanying the addition of 1 mol electrons to 1 mol gaseous atoms or ions. A(g) + e- Ion-(g) ∆E = EA1 • In most cases energy is release when the first electron is added because it is attracted to the atom’s nuclear charge, thus EA1 is usually negative • Factors other than Zeff and atomic size affect electron affinities, so trends are not as regular as those the previous two properties
Despite irregularities, three key points emerge when examine ionization energy and electron affinity values: • Elements in groups 6A and especially 7A have high ionization energy and highly negative (exothermic) electron affinities. These elements lose electrons difficulty but attract them strongly so they form negative ions • Elements in groups 1A and 2A have low ionization energy and either slightly negative or positive (endothermic) electron affinities. These elements lose electron readily but attract them weakly, therefore in their ionic compounds they form positive ions • The noble gases, group 8A have very high ionization energy and highly positive electron affinities, therefore these elements do not tend to lose or gain electron.