Excited Atoms & Atomic Structure

The Quantum Mechanical Picture of the Atom Basic Postulates of Quantum Theory Atoms and molecules can exist only in certain energy states. In each energy state, the atom or molecule has a definite energy. When an atom or molecule changes its energy state, it must emit or absorb just enough energy to bring it to the new energy state (the quantum condition). Atoms or molecules emit or absorb radiation (light) as they change their energies. The frequency of the light emitted or absorbed is related to the energy change by a simple equation.

The Quantum Mechanical Picture of the Atom The allowed energy states of atoms and molecules can be described by sets of numbers called quantum numbers. Quantum numbers are the solutions of the Schrodinger, Heisenberg & Dirac equations. Four quantum numbers are necessary to describe energy states of electrons in atoms – n, , m, ms Schroedinger 3-dimensional time independent equation Heisenberg’s uncertainty Equation Dirac’s quantum mechanical model E. Schrodinger 1887-1961 W. Heisenberg 1901-1976

Quantum Mechanics Based on the wave properties of the atom Schrodinger’s equation is  = wave function = mathematical operator E = total energy of the atom A specific wave function is often called an orbital. This equation is based on operators – not simple algebra. This is a mathematical concept you will not have dealt with yet.

Heisenberg Uncertainty Principle x = position mv = momentum h = Planck’s constant The more accurately we know a particle’s position, the less accurately we can know its momentum. Both the position and momentum of a particle can not be determined precisely at a given time. The uncertainty principle implies that we cannot know the exact motion of the electron as it moves around the nucleus.

Radial Probability Distribution

Quantum Numbers – n n = 1 n = 2 n = 3 n = 4 n = 5 n = 6 n = 7 The Principal quantum number has the symbol – n. n = 1, 2, 3, 4, ...... “shells” n = K, L, M, N, ...... The electron’s energy depends principally on n and tells the average relative distance of the electron from the nucleus. – As n increases for a given atom, so does the average distance of the electrons from the nucleus. – Electrons with higher values of n are easier to remove from an atom. n = 1 n = 2 n = 3 n = 4 n = 5 n = 6 n = 7

Quantum Numbers –  2. The azimuthal quantum number has the symbol .  describes the shape of the region of space occupied by the electron When linked with n defines the energy of the electron, All wave functions that have the same value of both n and l form a subshell  = 0, 1, 2, 3, 4, 5, .......(n-1)  = s, p, d, f, g, h, .......(n-1) = 0 = s = 1 = p = 2 = d = 3 = f n = 1 n = 2 n = 3 n = 4 n = 5 n = 6 n = 7

Quantum Numbers – m The symbol for the magnetic quantum number is m. If  = 1 (or a p orbital), then m = -1,0,+1. There are 3 values of m. Thus there are three p orbitals per n value. n  2 If  = 2 (or a d orbital), then m = -2,-1,0,+1,+2. There are 5 values of m. Thus there are five d orbitals per n value. n  3 If  = 3 (or an f orbital), then m = -3,-2,-1,0,+1,+2, +3. There are 7 values of m. Thus there are seven f orbitals per n value, n Theoretically, this series continues on to g,h,i, etc. orbitals. Practically speaking atoms that have been discovered or made up to this point in time only have electrons in s, p, d, or f orbitals in their ground state configurations. Each wave function with an allowed combination of n, l, and ml values describes an atomic orbital, a particular spatial distribution for an electron For a given set of quantum numbers, each principal shell contains a fixed number of subshells, and each subshell contains a fixed number of orbitals

Atomic Orbitals n = 1 n = 2 n = 3 n = 4 n = 5 n = 6 n = 7 Atomic orbitals are regions of space where the probability of finding an electron about an atom is highest. s orbital properties: There is one s orbital per n level.  = 0 1 value of m = 0 = s n = 1 n = 2 n = 3 n = 4 n = 5 n = 6 n = 7

Atomic Orbitals The three orbitals are named px, py, pz. p orbitals are peanut or dumbbell shaped. They are directed along the axes of a Cartesian coordinate system. The first p orbitals appear in the n = 2 shell. There are 3 p orbitals per n level. The three orbitals are named px, py, pz. They have an  = 1. m = -1,0,+1 3 values of m

Atomic Orbitals d orbital shapes

Atomic Orbitals f orbital shapes

Quantum Numbers

Quantum Numbers – ms The last quantum number is the spin quantum number which has the symbol ms. The spin quantum number only has two possible values. ms = +1/2 or -1/2

Building up the Periodic Table The Nucleus: The Aufbau Process – Used to construct the periodic table – First, Build by adding the required number of protons (the atomic number) and neutrons (the mass of the atom) – Second, Determine the number of electrons in the atoms then add electrons one at a time to the lowest-energy orbitals available without violating the Pauli principle Electrons: Hund’s Rule states that each orbital will be filled singly before pairing begins. The singly filled orbitals will have a parallel spin. – Each of the orbitals can hold two electrons, one with spin up , which is written first, and one with spin down  – A filled orbital is indicated by , in which the electron spins are paired – The electron configuration is written in an abbreviated form, in which the occupied orbitals are identified by their principal quantum n and their value of l (s, p, d, or f), with the number of electrons in the subshell indicated by a superscript Pauli’s Exclusion Principle states that paired electrons in an orbital will have opposite spins. No two electrons can have the same set of four quantum numbers (n, l, ml, ms). Neon - 2p    2s  1s 

Energy Diagram for Hydrogen Atom The energy of a particular orbital is determined by its value of n. All orbitals with the same value of n have the same energy and are said to be degenerate. Hydrogen single electron occupy the lowest energy state, the ground state. If energy is put into the system, the electron can be transferred to higher energy orbital called excited state. Orbital Energy Levels for the Hydrogen Atom

The Electron Configurations in the Type of Orbital Occupied Last for the First 18 Elements

Electron Configuration of the Elements

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

Valence Electrons The electrons in the outermost principle quantum level of an atom. Valence electron is the most important electrons to us because they are involved in bonding. Elements with the same valence electron configuration show similar chemical behavior. Inner electrons are called core electrons.

Building up the Periodic Table Valence electrons – It is tedious to keep copying the configurations of the filled inner subshells – The notation can be simplified by using a bracketed noble gas symbol to represent the configuration of the noble gas from the preceding row – Electrons in filled inner orbitals are closer and are more tightly bound to the nucleus and are rarely involved in chemical reactions Now we can write a complete set of quantum numbers for all of the electrons in these three elements as examples. Na First for 11Na. When completed there must be one set of 4 quantum numbers for each of the 11 electrons in Na (remember Ne has 10 electrons) [Ne] = 1s22s22p6

Electron Configurations for Potassium Through Krypton

Broad Periodic Table Classifications Representative Elements (main group): filling s and p orbitals (Na, Al, Ne, O) Transition Elements: filling d orbitals (Fe, Co, Ni) Lanthanide and Actinide Series (inner transition elements): filling 4f and 5f orbitals (Eu, Am, Es)

Periodic Trends in Atomic Radii In the periodic table, atomic radii decrease from left to right across a row because of the increase in effective nuclear charge due to poor electron screening by other electrons in the same principal shell. Atomic radii increase from top to bottom down a column because the effective nuclear charge remains constant as the principal quantum number increases.

The Radius of an Atom

Atomic Radii for Selected Atoms

Ionization Energies • There are two reasons for It takes more energy to remove the second electron from an atom than the first, and so on. : 1. The second electron is being removed from a positively charged species rather than a neutral one, so more energy is required. 2. Removing the first electron reduces the repulsive forces among the remaining electrons, so the attraction of the remaining electrons to the nucleus is stronger.

Electron Affinities Electron affinity (EA) of an element E is defined as the energy change that occurs when an electron is added to a gaseous atom: E (g) + e--  E—(g) energy change = EA. • Electron affinities can be negative (in which case energy is released when an electron is added) or positive (in which case energy must be added to the system to produce an anion) or zero (the process is energetically neutral). • Halogens have the most negative electron affinities.

Ionic Radii and Isoelectronic Series When one or more electrons is removed from a neutral atom, two things happen: 1. Repulsions between electrons in the same principal shell decrease because fewer electrons are present. 2. The effective nuclear charge felt by the remaining electrons increases because there are fewer electrons to shield one another from the nucleus.

Electronegativity Increases Increases Increases The tendency of an element to gain or lose electrons is is called electronegativity (), defined as the relative ability of an atom to attract electrons to itself in a chemical compound.

Information Contained in the Periodic Table 1. Each group member has the same valence electron configuration. Group elements exhibit similar chemical properties. 2. The electron configuration of any representative element can be obtained from periodic table. Transition metals – two exceptions, chromium and copper. Certain groups have special names (alkali metals, halogens, etc). Metals and nonmetals are characterized by their chemical and physical properties. Many elements along the division line exhibit both metallic and non metallic properties which are called metalloids or semimetals.

Special Names for Groups in the Periodic Table