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Quantum Mechanical Model of the Atom • Many scientists contributed to the development of the quantum mechanical model of the atom. – Bohr – Planck – DeBroglie – Heisenberg – Schrodinger – Pauli 2 What was already known.. • Early 1900’s…believed that – Energy is quantized – Electrons have both wave and matter properties – Electrons can be at a variety of specific energy levels in an atom • Energy levels are called orbits (Bohr model) – Proposed that electron had both wave and matter properties 3 Next round of research • Goal was to describe electrons in atoms • Ultimately describe for each electron: – Energy level & size of the region it occupies (n) – 3-D shape of the region it occupies (l) – Orientation of the region/orbital (ml) – Spin on the electron (ms) 4 Schrodinger & deBroglie • S & deB pictured the electron bound to the atom in a standing wave 5 Schrodinger • Sch.. Proposed that electrons move around the nucleus in standing waves – Each orbit represents some whole number multiple of a wavelength – Schrodinger analyzed the hydrogen data based on the assumption that the electrons behaved as standing waves. 6 Standing Waves 7 Schrodinger – Schrodinger’s equation takes into account: • The position of the electron in 3D space (its x,y,z coordinates) • Potential energy of the atom due to the attraction between electrons and protons • Kinetic energy of the electron 8 Schrodinger’s Equation! 9 Schrodinger • Schrodinger’s equation has many solutions – Each solution is called a wave function (y) and is correlated to a specific amount of energy • Each wave function is more commonly called an orbital. 10 Orbitals Each solution to Schrodinger’s equation describes a specific wave function (y) /orbital – The square of a wave function, (y)2, generates a probability distribution for an electron in that orbital • Also called an electron density map for a given orbital • (y)2 describes the shape, size, and orientation of the orbital 11 Orbitals • Orbitals are regions in space where an electron is likely to be found – 90% of the time the electron is within the boundaries described by the electron density map • Can describe its energy, shape, and orientation – The exact path of an electron in a given orbital is not known! 12 Heisenberg • Heisenberg uncertainty principle states that we cannot know both the position and the momentum of an electron at the same time. – Therefore, we do not know the exact path of the electron in an orbital. 13 Orbitals – The lowest energy solution to Sch..’s equation for an electron in a hydrogen atom describes what is known as the 1s orbital. 14 Describing Orbitals • Use quantum numbers to describe orbitals. A given orbital can be described by a set of 3 quantum numbers: 1. Principal quantum number (n) 2. Angular momentum quantum number (l) 3. Magnetic quantum number (ml) 15 Principal Quantum Number (n) • (n) describes the size and energy of the oribital – Possible values: whole number integer • 1, 2, 3, … – As “n” increases so does the size and energy of the orbital 16 Angular momentum quantum number (l) • (l) is related to the shape of the orbital – Possible values: (l) is an integer between 0 and n-1 – Each (l) value is also assigned a letter designation 17 Angular momentum quantum number (l) (l) Value Letter Designation 0 s 1 p 2 d 3 f 18 n Possible l values 1 2 0 0 1 0 1 2 1s 2s 2p 3s 3p 3d 0 1 2 3 4s 4p 4d 4f 3 4 Designation 19 Magnetic quantum number (ml) • (ml) is related to the orientation of the orbital in 3-D space – Possible values: - l to + l 20 Magnetic quantum number (ml) • Consider the p orbital…it has an l value of 1 and thus the possible ml values are -1, 0, +1 – These 3 ml values correspond to the 3 possible orientations of the p orbital 21 Ml and Orbitals l ml # orbitals 0 (s) 0 1 1 (p) -1, 0, 1 3 2 (d) -2, -1, 0, 1, 2 5 3 (f) -3, -2, -1, 0, 1, 2, 3 7 22 23 Quantum Number Summary • See page 256 and board. – A set of 3 quantum numbers describes a specific orbital • Energy and size - n • Shape - l • Orientation – ml 24 4th Quantum Number! • A 4th quantum number was added to describe the spin on a given electron. – Called the electron spin quantum number - ms • Possible values: +1/2 and -1/2 25 More on electron spin. • Each orbital can hold a maximum of 2 electrons of opposite spin. • Pauli exclusion principle states that no two electrons in an atom can have the same set of 4 quantum numbers 26 Summary • Three quantum numbers describe a specific orbital – Energy and size, shape, and orientation • Four quantum numbers describe a specific electron in an atom 27 7.9 Polyelectronic atoms • The Schrodinger model was based on H and works in principle for atoms with more than one electron. – The shapes and possible orientations of the hydrogen based orbitals holds true for polyelectronic atoms. – However, the size and energy of the orbitals in polyelectronic atoms differ from those calculated for hydrogen. 28 Polyelectronic Atoms • In general, find that in a given principal quantum number (n) – S is lower energy than p, which is lower energy than d….. • s<p<d<f – Already know that 1s < 2s < 3s… and 2p < 3p < 4p…. (in terms of size and energy) 29 7.11 The Aufbau Principle • Putting electrons in to orbitals… – Aufbau means “building up” in German – Electrons always enter the lowest energy orbital with room 30 Hund’s Rule • The orbitals of a given sublevel (e.g. p, or d, or f) are degenerate (of the same energy). • The lowest energy state occurs with the maximum number of unpaired electrons. – Meaning…..electrons enter an empty orbital of a given sublevel before pairing up. 31 Goals • To be able to write for any atom: – Electron configuration – Box/energy diagram – Lewis dot symbol • State the quantum numbers for each electron in an atom. • To relate the electron configuration of an atom to its location on the periodic table and its properties. 32 Goals Elaborated • Electron configuration – shows the number of electrons in each sublevel – Format: 1s22s22p4 or [He] 2s22p4 • Box/energy diagram – shows electrons as arrows and each orbital as a box. Electrons of opposite spin are indicated by up and down arrows. – Format: 33 Periodic Table and Electron Configurations 34 1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s… 35 Goals Elaborated • Lewis Dot Symbol – shows valence electrons as dots around the symbol for the atom – Maximum of 2 electrons per side of the symbol – Valence electrons are all of the electrons in the highest occupied principle quantum level (n) – Format: 36 The fun part - practice! • Representative elements – IA – 8A – Ions formed by above • Transition metals – Iron • Ion formation – Exceptions • Cr – expect ___ electrons in 3d – Actually….. • Cu – expect ___ electrons in 3d – Actually….. 37 CH 7: Atomic Structure and Periodicity Sections 7.10 -7.13 38 Periodic Trends • Models explain observed behavior. – The better the model the fewer the exceptions – Consider computer weather models vs. kinetic molecular theory 39 Periodic Trends • The quantum mechanical model of the atom explains many trends in the properties observed for the elements. – Trends in physical properties • Atomic radius • Size of the ion vs. the “parent” atom – Trends in reactivity: • Charge on the ion formed • Ease of removing or adding an electron to an atom 40 Atomic Radius • Measuring/defining atomic radius – Metals: atomic radius is half the distance between nuclei in a solid Cu – Nonmetals; atomic radius is half the distance between the nuclei of atoms in a diatomic molecule H H 41 Atomic radius trends (pg 276) • Atomic radius increases down a group – Valence electrons are in higher (larger) principal quantum levels with increased shielding. • • • • H 1s1 Li …..2s1 Na ……......3s1 K ………………..4s1 42 Atomic radius trends • Atomic radius decreases across a period of representative elements – Valence shell (PEL) remains the same across a period, same shielding across the period……however… – The # protons increases across a period • The increased nuclear charge “pulls” shells closer to the nucleus 43 Atomic Radius Consider the 2nd period…filling n = 2 Li Be B C N O F Ne # p 3 4 5 6 7 8 9 10 decreasing atomic radius 44 Atomic radius • Atomic radius remains ~same across a row of transition metals – Why? 45 Ionization Energy • Ionization Energy – energy needed to remove the highest energy electron from an atom in its gaseous state. – See page 272/273, IE > 0 Na(g) Na+ (g) + e IE1 = 495 kJ/mole 46 IE Trends • First IE (IE1 ) becomes less endothermic (less +) down a group – See table 7.5 on page 272 – Why? • As you go down a group, the electron being removed is farther from the nucleus and shielded by more core electrons from the attractive forces of the nucleus. • Therefore, it’s easier to remove. 47 IE Trends • In general, first IE (IE1 )increases across a period. – See figure 7.31 on page 273 – Why? • Atoms become smaller across a period and the # core electrons (shielding) remains the same while nuclear charge increases. • Electron to be removed is held more tightly to the nucleus across a period. 48 Exceptions to IE Trends • A dip in IE1 is observed for elements in group 3A and 6A. – 3A elements are all ns2p1 • Hypothesized that the s2 electrons shield the first p electron – 6A elements are all ns2p4 • Hypothesized that the first pairing of p electrons increases repulsions and thus this electron is easier to remove. 49 Trends in Successive IE • IE increases as additional electrons are removed from a given element – see table 7.5 on page 272 Na(g) Na+ (g) + e Na+ (g) ____ + IE1 = 495 kJ/mole e IE2 = 4560 kJ/mol 50 Trends in Successive IE • IE jumps when the first core electron is removed. – Why? Na(g) Na+ (g) + e (val. e) Na+ (g) (core e) ____ + e IE1 = 495 kJ/mole IE2 = 4560 kj/mol 51 Electron Affinity • EA – energy change associated with the addition of an electron to a gaseous atom. – In this text, EA < 0 (convention varies) – See page 275 X (g) + e X-(g) 52 EA Trends • MANY EXCEPTIONS! • In general, EA becomes less negative down a group. • In general, EA becomes more negative across a period. 53 Periodic Trends 1. Atomic radius 2. Ionization Energy (>0) • • First IE and successive IE 3A and 6A exceptions 3. Electron Affinity (<0) 54