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

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

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)

Schrodinger & deBroglie S & deB pictured the electron bound to the atom in a standing wave

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.

Standing Waves

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

Schrodinger’s Equation!

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.

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

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!

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.

Orbitals The lowest energy solution to Sch..’s equation for an electron in a hydrogen atom describes what is known as the 1s orbital.

Describing Orbitals Use quantum numbers to describe orbitals. A given orbital can be described by a set of 3 quantum numbers: Principal quantum number (n) Angular momentum quantum number (l) Magnetic quantum number (ml)

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

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

Angular momentum quantum number (l) (l) Value Letter Designation s 1 p 2 d 3 f

n Possible l values Designation 1 1s 2 2s 2p 3 3s 3p 3d 4 4s 4p 4d 4f

Magnetic quantum number (ml) (ml) is related to the orientation of the orbital in 3-D space Possible values: - l to + l

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

Ml and Orbitals l ml # orbitals 0 (s) 1 1 (p) -1, 0, 1 3 2 (d) 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

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

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

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

Summary Three quantum numbers describe a specific orbital Energy and size, shape, and orientation Four quantum numbers describe a specific electron in an atom

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.

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)

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

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.

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.

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:

Periodic Table and Electron Configurations

1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s…

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:

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

CH 7: Atomic Structure and Periodicity Sections 7.10 -7.13

Periodic Trends Models explain observed behavior. The better the model the fewer the exceptions Consider computer weather models vs. kinetic molecular theory

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

Atomic Radius Measuring/defining atomic radius Metals: atomic radius is half the distance between nuclei in a solid Nonmetals; atomic radius is half the distance between the nuclei of atoms in a diatomic molecule Cu H H

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

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

Atomic Radius Consider the 2nd period…filling n = 2 Li Be B C N O F Ne  decreasing atomic radius

Atomic radius Atomic radius remains ~same across a row of transition metals Why?

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

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.

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.

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.

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 IE1 = 495 kJ/mole Na+ (g)  ____ + e IE2 = 4560 kJ/mol

Trends in Successive IE IE jumps when the first core electron is removed. Why? Na(g)  Na+ (g) + e IE1 = 495 kJ/mole (val. e) Na+ (g)  ____ + e IE2 = 4560 kj/mol (core e)

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)

EA Trends MANY EXCEPTIONS! In general, EA becomes less negative down a group. In general, EA becomes more negative across a period.

Periodic Trends Atomic radius Ionization Energy (>0) First IE and successive IE 3A and 6A exceptions Electron Affinity (<0)