POLYELECTRONIC ATOMS PERIODICITY OF ELEMENTS (Part 2; Sec 9-13) Electronic Configurations Periodic Trends

POLYELECTRONIC ATOMS We will extend the 1-electron results (energy eqn, quantum numbers, AO shapes, etc) to the polyelectronic atom (atoms with > 1 electron). Electrostatic forces in the poly-e atom include nucleus-electron attractions and electron-electron repulsions.

POLYELECTRONIC ATOMS The e-e repulsions prevent the exact solution of the Schrodinger Eqn for helium and above. (Electron Correlation Problem) The presence of > 1 electron results in partial shielding of the nuclear charge. I.e. Z eff = Z actual – electron shielding

POLYELECTRONIC ATOMS (2) Also, because of the difference in AO shape for different ℓ values, electrons with the same n but in different subshells (ℓ) experience different attractive forces to the nucleus. As the electron spend more time near the nucleus, its energy becomes more negative (is held more tightly).

POLYELECTRONIC ATOMS (3) For the 1-e atom, AO energy depends only on n. As n increases, energy increases (becomes less positive). So AOs can be ordered from low to high energy: 1s < [2s, 2p] < [3s, 3p, 3d]... Fig 7.18 (note degeneracy). For the many-electron atom, energy depends on n and ℓ: 1s < 2s < 2p < 3s < 3p, etc. See Fig 7.22 (note that the degeneracy is partially lifted).

Figure 7.22 The Orders of the Energies of the Orbitals in the First Three Levels of Polyelectronic Atoms

Figure 7.18 Orbital Energy Levels for the Hydrogen Atom

PERIODIC TABLE Most powerful tool in the study of chemistry. Elements are placed in order by Z. Used to predict undiscovered elements and their properties. Tables 7.3, 7.4 Quantum mechanics explains the appearance of the PT and also periodicity of atomic properties

Table 7.3 Comparison of the Properties of Germanium as Predicted by Mendeleev and as Actually Observed

Table 7.4 Predicted Properties of Elements 113 and 114

From H to Polyelectronic Atoms In H, AOs with the same n have the same E. In multielectron atoms, –For a given set of QNs, orbital energies are lower than in H (larger Z value). –AOs with the same n value but different ℓ have different energies (nondegenerate). –orbitals with the same n and ℓ have the same E. –3d and 4s have similar energies

DETERMINING ELECTRONIC CONFIGURATIONS What is the arrangement of electrons in the atom? What rules govern these arrangements or electronic configurations? There are four quantum numbers [n, ℓ, m ℓ, m s ] that have defined relationships to each other and that are used to define a set of atomic orbitals (AOs) that electrons fill.

ELECTRON CONFIG. (2) Aufbau (building-up) Principle determines the order of filling AOs; i.e. the electronic configuration of the atom. The electrons fill the AOs in order of lowest energy (most negative) to highest energy. The atom’s ground state is the one that has the lowest energy. All others are called excited states.

ELECTRON CONFIG. (3) Pauli Exclusion Principle: The maximum number of electrons per orbital is 2 because no two electrons can have the same 4 q.n. values in an atom. Since there are two spin states (up/down; α/β; ↑/↓), the max AO occupancy number is 2.

ELECTRON CONFIG. (4) Hund’s Rule: When filling orbitals of identical energy, fill the empty orbitals with one electron before pairing them up; I.e. maximize number of unpaired spins. This produces the lowest energy configuration. There are exceptions: e.g. 4s fill before 3d; Cr, Cu have a single 4s electron and fully- or half-filled 3d orbitals (extra stability).

ELECTRON CONFIG. (5) Electron configs. of cations (remove from largest n AO) and anions (add according to Aufbau Prin.) Ways to depict electronic config: –AO list with # electrons as superscripts –orbital diagram –noble gas core for [core electrons] + valence electrons (VE). Fig 7.25

ELECTRON CONFIG. (6) Valence electrons are the outermost electrons and the most important ones in chemical bonding. Atoms in the same group have the same VE configuration.

ELECTRON CONFIG. (7) Learn electron config.s through Kr; use PT to identify VEs of atoms beyond Kr. Count unpaired electrons Fig 7.27 shows how the Periodic Table can be used to determine electron config. – Main Group: s- and p- block elements –Transition Group: d-block elements –Lanthanide and Actinide: f-block element

Problems 65, 68, 70, 72, 74, 76, 80, 82

Figure 7.27 The Orbitals Being Filled for Elements in Various Parts of the Periodic Table

Figure 7.28 The Periodic Table with Atomic Symbols, Atomic Numbers, and Partial Electron Configurations

PERIODIC LAW Now we can see how the electronic configurations of atoms lead to periodicity of elements and form the basis for chemical and physical properties of elements. PERIODIC LAW: When the elements are arranged according to Z, their physical and chemical properties vary periodically, regularly and predictably.

PERIODIC LAW (2) Elements in the nth A-Group (Main Group) have n electrons in the valence (outermost occupied) shell. Elements in the nth period have n as the principal QN of its valence shell.

PERIODICITY OF ATOMIC PROPERTIES Ionization Energy: energy required to remove one electron from gaseous atom or ion (kJ/mol) – Fig , 7.31; Table 7.5, 7.6 –Atom (g) -----> Ion + (g) + electron, I 1 –Across row, I 1 increases WHY? –Down group, I 1 decreases WHY? –I 1 is highest in upper RH corner

Figure 7.30 The Values of First Ionization Energy for the Elements in the First Six Periods

Table 7.5 Successive Ionization Energies in kJ/mol for the Elements in Period 3

PERIODICITY OF ATOMIC PROPERTIES (2) Electron Affinity: energy associated with addition of electron to gaseous species (kJ/mol) – Fig 7.32, Table 7.7 –Atom (g) + electron -----> Ion - (g) –Note most EA values are negative (exothermic) –Trend across row and down group? And WHY? –EA is highest in upper RH corner

Figure 7.32 The Electron Affinity Values for Atoms Among the First 20 Elements that Form Stable, Isolated X- Ions

PERIODICITY OF ATOMIC PROPERTIES (3) Atomic Radius: measure of atomic size –Atomic radii based on covalent or metallic bond distances (pm) –Figs 7.34 –Trend across row and down group? And WHY? –Atomic size is largest in lower LH corner –Note that size of cation < size of neutral atom –But size of anion > size of neutral atom

Figure 7.34 Atomic Radii (in Picometers) for Selected Atoms

PERIODICITY OF ATOMIC PROPERTIES (4) Metallic Character –Form cations, small I –lower LH corner –alkali metals Nonmetallic Character –Form anions, large I –upper RH corner

Problems 85, 90, 96,