8 Periodic Table Contents 8-1 Electron Configurations 8-2 The Periodic Table and Electron Configurations 8-3 Using the Periodic Table to Write Electron Configurations 8-4 Atomic and Ionic Radii 8-5 Ionization Energy 8-6 Electron Affinity 8-7 Chemical Properties and the Periodic Table 8.1 Electron Configurations • Armed with knowledge of the relative energies of orbitals and the Pauli exclusion principle, we are in a position to consider the arrangements of electrons in atoms. • Electron configuration：The way electrons are distributed among the various orbitals of an atom. Three principles of electron configuration • Principle of the Lowest Energy：The orbitals are filled in order of increasing energy. • The Pauli exclusion principle：No more than two electrons per orbital. • Hund’s Rule：For degenerate orbitals, the lowest energy is attained when the number of electrons having the same spin is maximized. Orbitals and Their Energies • In hydrogen the energy of an orbital depends only on its principal quantum number, n. • For a one-electron hydrogen atom, orbitals on the same energy level have the same energy. • The 3s, 3p, and 3d subshells all have the same energy. 1 En RH 2 (n 1, 2,3, 4 ) n In a multi-electron atom the electron–electron repulsions cause the various subshells in a given shell to be at different energies. Notice also that all orbitals of a given subshell (such as the five 3d orbitals) have the same energy as one another. Orbitals with the same energy are said to be degenerate. The important idea is this: In a multi-electron atom, for a given value of n, the energy of an orbital increases with increasing value of l. General energy ordering of orbitals for a multi-electron atom Three-electron atom——lithium Li • The number of electrons in a neutral atom equals its atomic number. • The ls orbital can accommodate two of the electrons. The third one goes into the next lowest energy orbital, the 2s. • We can represent any electron configuration by writing the symbol for the occupied subshell and adding a superscript to indicate the number of electrons in that subshell. • 1s22s1 Orbital Diagram • We can also show the arrangement of the electrons as • In this representation, which we call an orbital diagram. • Each box represents one orbital. • Half-arrows represent the electrons, each electron by a half arrow . • The direction of the arrow represents the spin of the electron (ms = +½, －½). Paired and unpaired electron • Electrons having opposite spins are said to be paired when they are in the same orbital • An unpaired electron is one not accompanied by a partner of opposite spin. Hund’s Rule • Consider now how the electron configurations of the elements change as we move from element to element across the periodic table. • The choice of a spin-up electron here is arbitrary; It is customary to show unpaired electrons with their spins up. Electron Spin and the Pauli Exclusion Principle Electron Spin and the Pauli Exclusion Principle • Since electron spin is quantized, we define ms = spin quantum number = ½. • Pauli’s Exclusions Principle: no two electrons can have the same set of 4 quantum numbers. • Therefore, two electrons in the same orbital must have opposite spins. Electron Configurations: Hund’s Rule • Electron configurations tells us in which orbitals the electrons for an element are located. • Three rules: • electrons fill orbitals starting with lowest n and moving upwards; • no two electrons can fill one orbital with the same spin (Pauli); • for degenerate orbitals, electrons fill each orbital singly before any orbital gets a second electron (Hund’s rule). Energy of orbitals in a ____________ electron atom Energy depends only on principal quantum number n n=3 n=2 En = -RH ( 1 n2 ) n=1 7.7 Energy of orbitals in a ___________-electron atom Energy depends on n and l n=3 l = 2 n=3 l = 0 n=2 l = 0 n=3 l = 1 n=2 l = 1 n=1 l = 0 7.7 Fill lowest energy orbitals first (______________ principle) H 1 electron H 1s1 7.7 Fill lowest energy orbitals first (Aufbau principle) He 2 electrons He 1s2 7.7 Fill lowest energy orbitals first (Aufbau principle) Li 3 electrons Li 1s22s1 7.7 Fill lowest energy orbitals first (Aufbau principle) Be 4 electrons Be 1s22s2 7.7 Fill lowest energy orbitals first (Aufbau principle) B 5 electrons B 1s22s22p1 7.7 Fill lowest energy orbitals first (Aufbau principle) ? C 6 electrons C 1s22s22p2 7.7 ______________: The most stable arrangement of electrons in subshells is the one with the greatest number of parallel spins. C 6 electrons C 1s22s22p2 7.7 Hund’s rule: The most stable arrangement of electrons in subshells is the one with the greatest number of parallel spins. ? N 7 electrons N 1s22s22p3 7.7 Hund’s rule: The most stable arrangement of electrons in subshells is the one with the greatest number of parallel spins. N 7 electrons N 1s22s22p3 7.7 Hund’s rule: The most stable arrangement of electrons in subshells is the one with the greatest number of parallel spins. O 8 electrons O 1s22s22p4 7.7 Hund’s rule: The most stable arrangement of electrons in subshells is the one with the greatest number of parallel spins. F 9 electrons F 1s22s22p5 7.7 Hund’s rule: The most stable arrangement of electrons in subshells is the one with the greatest number of parallel spins. Ne 10 electrons Ne 1s22s22p6 7.7 Order of orbitals (filling) in multi-electron atom 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s 7.7 What is the electron configuration of Mg? Mg 12 electrons 1s < 2s < 2p < 3s < 3p < 4s ___________________ 2 + 2 + 6 + 2 = 12 electrons Abbreviated as [Ne]______ [Ne] is 1s22s22p6 7.7 What are the possible quantum numbers for the last (outermost) electron in Cl? Cl 17 electrons 1s < 2s < 2p < 3s < 3p < 4s ____________________ 2 + 2 + 6 + 2 + 5 = 17 electrons Last electron added to 3p orbital n=3 l=1 ml = -1, 0, or +1 ms = ½ or -½ 7.7 8-2 The Periodic Table and Electron Configurations The Periodic Table Reading the Periodic Table • Columns in the periodic table are called groups (numbered from 1A to 8A or 1 to 18). • Rows in the periodic table are called periods. • Metals are located on the left hand side of the periodic table (most of the elements are metals). • Non-metals are located in the top right hand side of the periodic table. • Elements with properties similar to both metals and nonmetals are called metalloids and are located at the interface between the metals and non-metals. Properties of the Periodic Table • Some of the groups in the periodic table are given special names. • These names indicate the similarities between group members: Group 1A: Alkali metals. Group 2A: Alkaline earth metals. Group 6A: Chalcogens. Group 7A: Halogens. Group 8A: Noble gases. Description of the Modern Periodic Table • The vertical groups bring together elements with similar properties. • The horizontal periods of the table are arranged in order of increasing atomic number from left to right. The groups are numbered at the top. and the periods at the extreme left in the periodic table on the inside front cover. • The first two groups--the s block- and the last six groups--the p block-together constitute the main-group elements. • The d-block elements are known as the transition elements. The f-block elements, sometimes called the innertransition elements, would extend tile table to a width of 32 members if incorporated in the main body of the table. The table would generally be too wide to fit on a printed page, and so the f-block elements are extracted from the table and placed at the bottom. The 14 elements following lanthanum (Z = 57) are called the lanthanides, and the 14 following actinium ( Z = 89) are called the actinides. ns2np6 ns2np5 ns2np4 ns2np3 ns2np2 ns2np1 d10 d5 d1 ns2 ns1 Ground State Electron Configurations of the Elements 4f 5f 8.2 • The electron configurations of the elements correspond to their locations in the periodic table. • Elements in the same column of the table have related outer-shell (valence) electron configurations. • All 2A elements have an ns2 outer configuration, and all 3A elements have an ns2np1 outer configuration, with the value of n increasing as we move down each column. • As shown in figure, the periodic table can be divided into four blocks based on the filling order of orbitals. • Two blue columns of elements, known as the alkali metals (group 1A) and alkaline earth metals (group 2A), are those in which the valence s orbitals are being filled. These two columns make up the s block of the periodic table. • On the right is a block of six pink columns that comprises the p block, where the valence p orbitals are being filled. • The s block and the p block elements together are the representative elements (main-group elements). • The orange block has ten columns containing the transition metals. These are the elements in which the valence d orbitals are being filled and make up the d block. • These elements are known as either transition elements or transition metals. • The elements in the two tan rows containing 14 columns are the ones in which the valence f orbitals are being filled and make up the f block. • In most tables, the f block is positioned below the periodic table to save space: • The number of columns in each block corresponds to the maximum number of electrons that can occupy each kind of subshell. • s, p, d, and f subshells → the numbers of electrons. • The s block has 2 columns, the p block has 6, the d block has 10, and the f block has 14. • Recall also that ls is the first s subshell, 2p is the first p subshell, 3d is the first d subshell, and 4f is the first f subshell. • Using these facts, you can write the electron configuration of an element based merely on its position in the periodic table. • Let’s use the periodic table to write the electron configuration of selenium (Se, element 34). 8-4 Atomic and Ionic Radii General definition Atomic Radii The covalent radius is one-half the distance between the nuclei oftwo identical atoms joined by a single covalent bond. The ionic radius is based on the distance between the nuclei of ions joined by an ionic bond. The metallic radius is one-half the distance between the nuclei of two atoms in contact in the crystalline solid metal. Covalent radius 186pm Na Na Metallic radius 99pm Na- Cl- Ionic radius 8.3 Ionic Radius A comparing of atomic and ionic sizes Metallic radii are shown for Na and Mg and ionic radii for Na+ and Mg2+. Na 186pm Mg 160pm Na+ Mg2+ 99pm 72pm 8-5 Ionization Energy The first ionization energy (I1) of magnesium is 738 kJ/mol. The second ionization energy (I2) is 1450 kJ/mol. The amount of energy required increased for the second ionization. It is more difficult to remove an electron from a positively charged ion than it is to remove one from a neutral atom. This is a direct consequence of Coulomb's law, which states, in part, that the force of attraction between oppositely charged particles is directly proportional to the magnitudes of the charges. First ionization energies (I1) for many of the elements are plotted in the following figure. In general, the farther an electron is from the nucleus, the more easily it can be extracted. General Trend in First Ionization Energies Increasing First Ionization Energy Increasing First Ionization Energy 8.4 8-7 Chemical Properties and the Periodic Table Atomic Properties Electron affinity Atomic radius Atomic properties and the periodic table—a summary Electron affinity Atomic radius Ionization energy Ionization energy 8-6 Electron Affinity Electron Affinity Electron affinity, EA, is a measure of the energy change that occurs when a gaseous atom gains an electron. Example F(g) + e- → F-(g) EA = -328kJ/mol When a F atom gains an electron, energy is given off. The process is exothermic, the electron affinity is a negative quantity. Why When a F atom gains an electron to become F-, the F atom acquires the very stable electron configuration of the noble gas neon (Ne). That is, F(ls22s22p5) + e- → F- (ls22s22p6) Even metal atoms can form negative ions in the gaseous state, for example, where the added electron enters the half-filled 2s orbital. Li(g) + e- → Li- (g) EA = -59.6 kJ/mol For some atoms, there is no tendency to gain an electron The noble gases In considering the gain of a second electron by a nonmetal atom, Positive electron affinities can be encountered. CHAPTER SUMMARY AND KEY TERMS INTRODUCTION AND SECTION 7.1 • The electronic structure of an atom describes the energies and arrangement of electrons around the atom. Much of what is known about the electronic structure of atoms was obtained by observing the interaction of light with matter. Visible light and other forms of electromagnetic radiation (also known as radiant energy) move through a vacuum at the speed of light, c = 3.00×108 m/s. Electromagnetic radiation has both electric and magnetic components that vary periodically in wavelike fashion. The wave characteristics of radiant energy allow it to be described in terms of wavelength,λ, and frequency,ν, which are interrelated: c SECTION 7.2 • Planck proposed that the minimum amount of radiant energy that an object can gain or lose is related to the frequency of the radiation: E h. This smallest quantity is called a quantum of energy. The constant h is called Planck’s constant: h = 6.626×10-34Js. In the quantum theory, energy is quantized, meaning that it can have only certain allowed values. Einstein used the quantum theory to explain the photoelectric effect, the emission of electrons from metal surfaces when exposed to light. He proposed that light behaves as if it consists of quantized energy packets called photons. Each photon carries energy, E h. SECTION 7.3 • Dispersion of radiation into its component wavelengths produces a spectrum. If the spectrum contains all wavelengths, it is called a continuous spectrum; if it contains only certain specific wavelengths, the spectrum is called a line spectrum. The radiation emitted by excited hydrogen atoms forms a line spectrum. • Bohr proposed a model of the hydrogen atom that explains its line spectrum. In this model the energy of the electron in the hydrogen atom depends on the value of a quantum number, n. The value of n must be a positive integer (1, 2, 3, . . .), and each value of n corresponds to a different specific energy, En. • The energy of the atom increases as n increases. The lowest energy is achieved for n = 1; this is called the ground state of the hydrogen atom. Other values of n correspond to excited states. Light is emitted when the electron drops from a higher-energy state to a lower-energy state; light is absorbed to excite the electron from a lower energy state to a higher one. • The frequency of light emitted or absorbed is such that h rrrrrrequals the difference in energy between two allowed states. • De Broglie proposed that matter, such as electrons, should exhibit wavelike properties——Wave-Particle Duality. This hypothesis of matter waves was proved experimentally by observing the diffraction of electrons. An object has a characteristic wavelength that depends on its momentum, mv: . h / mv • Discovery of the wave properties of the electron led to Heisenberg’s uncertainty principle, which states that there is an inherent limit to the accuracy with which the position and momentum of a particle can be measured simultaneously. • In the quantum mechanical model of the hydrogen atom, the behavior of the electron is described by mathematical functions called wave functions, denoted with the Greek letter Ψ. Each allowed wave function has a precisely known energy, but the location of the electron cannot be determined exactly; rather, the probability of it being at a particular point in space is given by the probability density, Ψ2. The electron density distribution is a map of the probability of finding the electron at all points in space. • The allowed wave functions of the hydrogen atom are called orbitals. An orbital is described by a combination of an integer and a letter, corresponding to values of three quantum numbers. • n, l, and ml, to describe an orbital. • The principle quantum number——the energy of the orbital, and the distance from the nucleus • The azimuthal quantum number defines the shape of the orbital. • The magnetic quantum number describes the orientation of the orbital in space. • Contour representations are useful for visualizing the shapes of the orbitals. Represented this way, s orbitals appear as spheres that increase in size as n increases. • The radial probability function tells us the probability that the electron will be found at a certain distance from the nucleus. • The wave function for each p orbital has two lobes on opposite sides of the nucleus. They are oriented along the x, y, and z axes. • Four of the d orbitals appear as shapes with four lobes around the nucleus; the fifth one, the orbital, is represented as two lobes along the z axis and a “doughnut” in the xy plane. • Regions in which the wave function is zero are called nodes. There is zero probability that the electron will be found at a node. • In many-electron atoms, different subshells of the same electron shell have different energies. For a given value of n, the energy of the subshells increases as the value of l increases: ns＜np＜nd ＜nf. Orbitals within the same subshell are degenerate, meaning they have the same energy. • Electrons have an intrinsic property called electron spin, which is quantized. The spin magnetic quantum number, ms, can have two possible values, +1/2 and -1/2, which can be envisioned as the two directions of an electron spinning about an axis. The Pauli exclusion principle states that no two electrons in an atom can have the same values for n, l, ml, and ms. This principle places a limit of two on the number of electrons that can occupy any one atomic orbital. These two electrons differ in their value of ms. • The drawing below shows part of the orbital diagram for an element. • (a) As drawn, the drawing is incorrect. Why? • (b) How would you correct the drawing without changing the number of electrons? • (c) To which group in the periodic table does the element belong? KEY SKILLS • Calculate the wavelength of electromagnetic radiation given its frequency or its frequency given its wavelength. • Order the common kinds of radiation in the electromagnetic spectrum according to their wavelengths or energy. • Explain what photons are and be able to calculate their energies given either their frequency or wavelength. • Calculate the wavelength of a moving object. • Relate the quantum numbers to the number and type of orbitals and recognize the different orbital shapes. • Draw an energy-level diagram for the orbitals in a manyelectron atom and describe how electrons populate the orbitals in the ground state of an atom, using the Pauli exclusion principle and Hund’s rule. • Use the periodic table to write condensed electron configurations and determine the number of unpaired electrons in an atom. KEY EQUATIONS c E h h mv 1 En RH 2 (n 1, 2,3, 4 ) n 1 1 hc E E final Einitial RH 2 2 h n n f i Homework 1. State where in the periodic table these elements appear: • (a) elements with the valence-shell electron configuration ns2np5 • (b) elements that have three unpaired p electrons • (c) an element whose valence electrons are 4s24p1 • (d) the d-block elements • (a) Calculate the energy of a photon of electromagnetic radiation whose frequency is 6.75×1012 s-1. • (b) Calculate the energy of a photon of radiation whose wavelength is 322 nm. • (c) What wavelength of radiation has photons of energy 2.87×10-18J? • The visible emission lines observed by Balmer all involved nf = 2. • (a) Explain why only the lines with were observed in the visible region of the electromagnetic spectrum. • (b) Calculate the wavelengths of the first three lines in the Balmer series—those for which ni = 3, 4, and 5—and identify these lines in the emission spectrum of H atom • Sketch the shape and orientation of the following types of orbitals: (a) s, (b) pz, (c) dxy, (d) , (e) d 2 . z d x2 y 2 • Write the condensed electron configurations for the following atoms, using the appropriate noble-gas core abbreviations: (a) Cs(55), (b) Ni(28), (c) Se(34), (d) Cd(48), (e) Pb(82), (f) Cu(29), (g) Cr(24).