CHEM111_Ch6 PDF - Electronic Structure and Periodic Properties

Chapter 6 ELECTRONIC STRUCTURE AND PERIODIC PROPERTIES OF ELEMENTS Chapter Outline 6.1 Electromagnetic Energy 6.2 The Bohr Model 6.3 Development of Quantum Theory 6.4 Electronic Structure of Atoms (Electron Configurations) 6.5 Periodic Variations in Element Properties Electromagnetic (E...

Chapter 6 ELECTRONIC STRUCTURE AND PERIODIC PROPERTIES OF ELEMENTS Chapter Outline 6.1 Electromagnetic Energy 6.2 The Bohr Model 6.3 Development of Quantum Theory 6.4 Electronic Structure of Atoms (Electron Configurations) 6.5 Periodic Variations in Element Properties Electromagnetic (EM) Radiation Energy can move through space as waves called EM radiation. All waves are characterized by the following: Wavelength (λ): Distance between two consecutive peaks or troughs in a wave. Frequency (n): Number of waves (cycles) per second (Hertz, Hz). Amplitude: One-half the distance between the peaks and troughs One-dimensional sinusoidal waves show the relationship among wavelength, frequency, and speed. The wave with the shortest wavelength has the highest frequency. Amplitude is one-half the height of the wave from peak to trough. Wavelength, Frequency, and Speed The product of a wave's wavelength (λ) and its frequency (ν), λν, is the speed of the wave. Thus, EM radiation travels in a vacuum at 3.0 × 108 m/s = λν (C, the speed of light). Wavelength and frequency are inversely proportional: As the wavelength increases, the frequency decreases and vice versa. The EM spectrum is the range of all types of EM radiation. Visible light makes up only a small portion of the EM spectrum. Each of the various colors of visible light has specific frequencies and wavelengths associated with them. FIGURE Portions of 6.3 Whitney; work by Jane the electromagnetic credit spectrum “AM radio": modiecation of are workshown in order by Dave of decreasing frequency and increasing Clausen) wavelength. (credit “Cosmic ray": modiecation of work by NASA; credit “PET scan": modiecation of work by the National Institute of Health; credit “X-ray": modiecation of work by Dr. Jochen Lengerke; credit “Dental curing": Example 6.1 EXAMPLE EXAMPLE modiecation 6.1 of work by the6.1 Department of the Navy; credit “Night vision": modiecation of work by the Department of the Army; credit Determining the“Remote": Frequency modiecation of work by Emilian and Wavelength Robert Vicol; credit “Cell phone": modiecation of work of Radiation Determining the“Microwave by Brett Jordan; credit Frequency oven":and Wavelength modiecation of work by of BillyRadiation Mabray; credit “Ultrasound": modiecation of A sodium streetlight gives off yellow light that has a wavelength of 589 nm (1 nm = 1 10−9 m). What is the work A by Janestreetlight sodium Whitney; credit “AM radio": modiecation of work by Dave Clausen) −9 frequency of this light? gives off yellow light that has a wavelength of 589 nm (1 nm = 1 10 m) frequency Solution of this light? EXAMPLE 6.1 We can Solutionrearrange the equation c = λν to solve for the frequency: Determining the Frequency and Wavelength of Radiation We can rearrange the equation c = λν to solve for the frequency: A sodium streetlight gives off yellow light that has a wavelength of 589 nm (1 nm = 1 10−9 m). What is the frequency of this light? Since c is expressed in meters per second, we must also convert 589 nm to meters. Solution We cancrearrange Since is expressed in meters the equation per c = λν second, to solve wefrequency: for the must also convert 589 nm to meters. Check Your Learning One of the frequencies used to transmit and receive cellular telephone signals in the United States is 850 MHz. Since c is What is expressed the in meters wavelength perofsecond, in meters we must these radio also convert 589 nm to meters. waves? Check Your Learning Answer: Practice Question One 0.353of mthe frequencies = 35.3 cm used to transmit and receive cellular telephone signals in the United St What is the Check Your wavelength in meters of these radio waves? Learning One of the frequencies used to transmit and receive cellular telephone signals in the United States is 850 MHz. Answer: What Accessis forthe freewavelength in meters of these radio waves? at openstax.org 0.353 m = 35.3 cm Answer: 0.353 m = 35.3 cm Atomic Spectra When a sample of any element is heated to a high enough temperature, it gives off EM radiation (it glows) The spectrum of this radiation (known as line spectra) shows intense lines at a few wavelengths, but it is mostly blank. Each element displays its own characteristic set of lines. Atomic Spectra and Planck’s Constant At the end of the 19th century, physicists didn’t understand much about this phenomenon: Why does heated matters emit light? Why only certain wavelengths? Planck’s Quantum Postulate: In 1900, Max Planck postulated that the atoms vibrate at increasing frequencies (or decreasing wavelengths), as the temperature increased. Planck had to assume that the vibrating atoms required quantized energies, that only integer multiples of a basic packet or quanta of energy. Planck equation: E = hν, where h (Planck’s constant) = 6.63 × 10−34 J · s Combined with C = λν, E = hC/λ Basic packet or quanta of energy is hν, so you can have 1 hν, 2 hν, etc., but never a fractional value of hν. Atomic Spectra and Planck’s Constant It’s complicated, but Planck’s postulate helped explain why heated matter emits EM radiation. The heat excites electrons, which causes them to increase their energy. When the electron returns to its normal energy level, it releases a photon of EM radiation. If the photon is in the visible region, we see this as light. The quantization of energy is hard to notice on our (macroscopic) scale, because h is such a small value of energy (6.63 x 10-34 J s), but it is very important on the size scale of an atom or electron. The Photoelectric Effect It had been observed that electrons could be ejected from the surface of a metal when light having a frequency greater than some threshold frequency was shone on it. This phenomenon is known as the photoelectric effect. Einstein argued that the light striking the metal surface should not be viewed as a wave, but instead as a stream of particles (later called photons) whose energy depended on their frequency, according to Planck’s formula: E = hν (or, in term of wavelength using c = νλ, E = hc/λ). The explanation of photoelectric effect created the concept of wave- particle duality. electron will increase linearly with the energy of the incoming photon. Example 6.26.2 EXAMPLE Calculating the Energy of Radiation When we see light from a neon sign, we are observing radiation from excited neon atoms. If this radiation has a 6.1 Electromagnetic Ene wavelength of 640 nm, what is the energy of the photon being emitted? 6.1 Electromagnetic Ener Solution We use the part of Planck's equation that includes the wavelength, λ, and convert units of nanometers to Solution meters so that the units of λ and c are the same. We use the part of Planck's equation that includes the wavelength, λ, and convert units of nanometers to Access for free at openstax.org meters so that the units of λ and c are the same. Check Your Learning Practice Question The microwaves in an oven are of a specimc frequency that will heat the water molecules contained in food. Check Your Learning (This is why most plastics and glass do not become hot in a microwave oven-they do not contain water The microwaves in an oven are of a specimc9frequency that will heat the water molecules contained in food. molecules.) This frequency is about 3 10 Hz. What is the energy of one photon in these microwaves? (This is why most plastics and glass do not become hot in a microwave oven-they do not contain water molecules.) 9 Answer: This frequency is about 3 10 Hz. What is the energy of one photon in these microwaves? 2 10−24 J Answer: Bohr Model for Atomic Structure Rutherford had shown that the atom has a small, positively charged nucleus, and that most of the volume is essentially empty Electrons (negatively charged) are found in this “empty” space What was not known is how electrons moved in this space The obvious analogy is the solar system, with the planets moving through empty space, attracted to the sun by gravity Bohr Model for Atomic Structure Bohr assumed that the electron orbiting the nucleus would not normally emit any radiation, rather the electron emits or absorbs a photon if it moved to a different orbit. The energy absorbed or emitted would reflect differences in the orbital energies according to this equation: hc Ei and Ef are the initial and final ΔE = E f − E i = hν = orbital energies. λ When the electron is in this lowest energy orbit (n = 1), the atom is said to be in its ground state. If the atom receives energy from an outside source, it is possible for the electron to move to an orbit with a higher n value (excited state), which has a higher energy. fption allowing Planck’s for continuous of the constant atom Planck’sand values ideasEofi and Ef areofand quantization energy, the Bohr initial Einstein’s and mnding assumed mnal that the energie orbital light energie uantized: energy rgy Bohr difference Model is proportional andisfrequency. to their used, Rydberg since frequencies BohrConstant assumed and wavelengths that the electron orbiting are alw y emit any radiation (the stationary state hypothesis), but it would emit or uous values a different of energy, orbit. The Bohrorassumed energy absorbed the emitted would energies renect ofinthese differences the electron o Instead of allowing for continuous values of energy, Bohr assumed the his equation: energies of these orbitals were quantized: n this expression, k is a constant comprising fundamental constants s nd Planck’s onstant constant. and Ei and Inserting Ef are the initial and mnal the expression orbital for theThe energies, respectively. orbit energies i ference is used, since frequencies and wavelengths are always positive. Instead When thecomprising constant sesaof atom absorbs energy as a photon, fundamental constants the such electron moves as the from electron energy, Bohr assumed the energies of these electron orbitals were an orbit with a lower n to a higher n.. Inserting the expression for the orbit energies into the equation for When an electron falls from an orbit with a higher n to a lower n, the atoms emits energy as a photon. r Since DE ant comprising can only constants fundamental be discrete values, such as the photon the electron absorbed or emitted mass and charge g thecan only have expression for theaorbit wavelength with energies into a discrete the equation for ΔEvalue gives (not continuous). hich is identical to the Rydberg equation in which Rydberg Constant, When B ∞ he Rydberg constant, and compared it with the experimentally ac ∞  EXAMPLE 6.5 EXAMPLE 6.5 Calculating Example 6.5 Calculating the the Energy Energy and Wavelength and Wavelength of Electron of Electron Transitions in a Transitions in a One–electron One–electron (Bohr) (Bohr) System Calculating the Energy and Wavelength of Electron Transitions in a One–electron (Bohr) System System What Whatisisthethe energy (in joules) energy and the wavelength (in joules) (in meters) of the and the wavelength (inline in the spectrum meters) of hydrogen of the line in thethat spectrum of hydrogen that What is the energy (in joules) and the wavelength (in meters) of the line in the spectrum of represents the movement of an electron from Bohr orbit with n = 4 to the orbit with n = 6? In whathydrogen thatpart of the represents represents thethe electromagnetic movement movement spectrumofdo anwe of an electron electron from mnd this Bohr orbitfrom radiation? with nBohr orbit = 4 to the with n n orbitwith = In = 6? 4 what to the of the with n = 6? In what part of partorbit the electromagnetic spectrum electromagnetic spectrum do we mnddo we this mnd this radiation? radiation? Solution Solution Solution In this case, the electron starts out with n = 4, so n = 4. It comes to rest in the n = 6 orbit, so n = 6. The In this case, the electron starts out with n = 4, so n1 =1 4. It comes to rest in the n = 6 orbit, so n2 = 6. 2The difference in energy between the two states is given by this expression: Indifference this case, the between in energy electron the starts out two states withbynthis is given 4, so n1 = 4. It comes to rest in the n = expression: = 6 orbit, so n2 = 6. The difference in energy between the two states is given by this expression: 6 Electronic Structure and Periodic Properties of Elements This energy difference is positive, indicating a photon enters the system (is absorbed) to excite the electron This energy difference is positive, indicating a photon enters the system (is absorbed) to excite the electron from the n = 4 orbit up to the n = 6 orbit. The wavelength of a photon with this energy is found by the expression Rearrangement gives: This energy difference is positive, indicating a photon enters the system (is absorbed) to excite the electron From the illustration of the electromagnetic spectrum in Electromagnetic Energy, we can see that this wavelength is found in the infrared portion of the electromagnetic spectrum.  Limitations of Bohr Model Electrons have a charge, so electrons moving in circular orbits should create a magnetic field Magnetic fields are different than gravitational fields, so electrons can’t circle the nucleus, they would actually spiral into the nucleus! Most atoms have more than one electron, and the interaction between electrons could not be explained in Bohr’s model By 1920, it was clear that the Bohr model was an advance, but it could not be the correct model of the atom Bohr himself saw this, and was in the forefront of developing more accurate models Physically realistic model needed to: Retain Bohr model explanation of atomic spectra Be consistent with Planck’s quantum theory Give a description of how electrons (e-) move about the nucleus that fits the laws of physics and is mathematically stable The Quantum-Mechanical Model of an Atom In 1927, a group of theore`cal physicists found a descrip`on of electron mo`on that is stable, using quantum mechanics, a new math technique: Electrons move in unpredictable paths on spherical shells surrounding the nucleus The shells are called energy levels or quantum levels Retains Bohr explana`on of atomic spectra Electrons can move from shell to shell, not circular orbit to circular orbit Each shell outward is larger, and can hold more electrons Orbitals are areas on these spherical shells that can hold 2 electrons of opposing spins Orbitals are specified by the energy level (principal quantum number or shell number 1, 2, 3, 4…), and the sub-shell (s, p, d, f), which gives the shape of the orbital The Quantum Model of an Atom Energy levels (principal quantum number) are spherical shells Electrons move in a complex way, and their path cannot be predicted 6.3 Development of Quantum Theory 281 1s 2s 3s Orbital Shapes s – spherical shape. p – dumbbell shape (two lobes). d – four lobes. f – six lobes These shapes represent the three-dimensional regions where the electron is likely to be found. Table of orbitals and sub-shells: Energy s p d f Total Electrons level orbitals 1 1 1 2 2 1 3 4 8 3 1 3 5 9 18 4 1 3 5 7 16 32 Orbital Relative Energies Orbitals that belong to different subshells have different energies. Orbitals within the same subshell have the same energy.  The Aufbau Principle Electrons fill atomic C S orbitals from the lowest energy on up 3p 3p For equal-energy 3s 3s (degenerate) orbitals, one electron goes into each 2p 2p orbital before electrons 2s 2s get paired Up and down arrows show “spin” of electrons 1s 1s Example of atomic orbital energy diagrams: C and S  Full Electron Configuration C S Atomic orbital energy diagrams quickly become 3p 3p too large 3s 3s Therefore, it became necessary to have electron 2p 2p configuration notation 2s 2s # of e- energy level 2s1 1s 1s C: 1s2 2s2 2p2 sub-shell S: 1s2 2s2 2p6 3s2 3p4 This periodic table shows the electron configura5on for the valence subshells of atoms. By “building up” from hydrogen, this table can be used to determine the electron configura5on for atoms of most elements in the periodic table. Electron Configurations and Orbital Diagrams Orbital diagrams are pictorial representations of the electron configuration, showing the individual orbitals and the pairing arrangement of electrons.  Electron Configurations and Orbital Diagrams Hund’s rule: the lowest-energy configuration for an atom with electrons within a set of degenerate orbitals is that having the maximum number of unpaired electrons. Valence and Core Electrons The electrons occupying the orbital(s) in the outermost shell (highest value of n) are called valence electrons. The electrons occupying the inner shell orbitals are called core electrons. The core electrons represent noble gas electron configurations. Electron configurations can be expressed in an abbreviated format by writing the noble gas that matches the core electron configuration, along with the valence electrons. Abbreviated electron configurations emphasize the similarity of the configurations of elements in the same group. Group 1: Group 2: Li: [He]2s1 Be: [He]2s2 Na: [Ne]3s1 Mg: [Ne]3s2 K: [Ar]4s1 Ca: [Ar]4s2 Electron Configurations of Transition Metals Beginning with the transition metal scandium (atomic number 21), additional electrons are added successively to the 3d subshell. d subshells are filled to capacity with 10 electrons. After the 3d subshell is filled, electrons are next added to the 4p subshell. Example: Fe: [Ar] 4s2 3d6 Electron Configuration Exceptions There are some exceptions to the order of filling subshells. Examples: Cu and Cr There is stability associated with a half-filled or fully filled d subshell. An electron shifts from the 4s into the 3d subshell to achieve this stability. Cu: Expect: [Ar]4s23d9 Actual: [Ar]4s13d10 Cr Expect: [Ar]4s23d4 Actual: [Ar]4s13d5 Electron Configurations and the Periodic Table The periodic table arranges atoms so that elements with the same chemical and physical properties are in the same group. Elements in the same group have similar valence electron configurations. Valence electrons play the most important role in chemical reactions. This describes why elements in the same group have similar chemical reactivity. Electron Configurations of Ions Ions are formed when atoms gain or lose electrons. A cation (positively charged ion) forms when one or more electrons are removed from an atom. An anion (negatively charged ion) forms when one or more electrons are added to a parent atom. (a) Na: 1s22s22p63s1. Sodium loses one electron. Na+: 1s22s22p6 (b) P: 1s22s22p63s23p3. Phosphorus gains three electrons. P3−: 1s22s22p63s23p6 (c) Al: 1s22s22p63s23p1. Aluminum loses two electrons. Al2+: 1s22s22p63s1 (d) Fe: 1s22s22p63s23p64s23d6. Iron loses two electrons and, since it is a transiMon metal, they are removed from the 4s orbital. Fe2+: 1s22s22p63s23p63d6 Periodic Variations in Element Properties Many properties of the elements vary periodically as the electronic structure of the element's changes. These properties govern the chemical behavior of elements. These periodic properties include: 1) Size (radius) of atoms and ions 2) Ionization energies 3) Electron affinities  Atomic Radius Elements get larger as you go down the periodic table (as you’d guess). Elements get smaller as you go from left-to-right across the periodic table (counter-intuitive). increasing increasing  Ionic Radius Nega`ve ions are larger than the neutral element Posi`ve ions smaller than neutral atom Isoelectronic Atoms and ions that have the same electron configuration are said to be isoelectronic. Examples of isoelectronic species: N3–, O2–, F–, Ne, Na+, Mg2+, and Al3+ (1s22s22p6) P3–, S2–, Cl–, Ar, K+, Ca2+, and Sc3+ ([Ne]3s23p6) For atoms or ions that are isoelectronic, the number of protons determines the size. The greater the nuclear charge, the smaller the radius in a series of isoelectronic ions and atoms. Ionization Energy The amount of energy required to remove the most loosely bound electron from a gaseous atom in its ground state is called its first ionization energy (IE1). X(g) ⟶ X+(g) + e− IE1 The energy required to remove the second most loosely bound electron is called the second ionization energy (IE2). X+(g) ⟶ X2+(g) + e− IE2 The energy required to remove the third electron is the third ionization energy, and so on. Energy is always required to remove electrons from atoms or ions, so ionization processes are endothermic and IE values are always positive. As size (atomic radius) increases, the ionization energy decreases. First ionization energies: Decrease down a group Increase across a period There are some deviations from this trend. The first ionization energy of the elements in the first six periods are plotted against their atomic number. Deviations in Ionization Energy Trend Deviation: Beryllium (Be) has a higher IE1 than boron (B). The electron removed during the ionization of Be ([He]2s2) is an s electron. The electron removed during the ionization of B ([He]2s22p1) is a p electron. This means that an s electron is harder to remove from an atom than a p electron in the same shell. Deviations in Ionization Energy Trend Deviation: Oxygen (O) has a lower IE1 than nitrogen (N). Removing one electron from O will eliminate the electron–electron repulsion caused by pairing the electrons in the 2p orbital. This means that removing an electron from O is more energetically favorable than removing an electron from N. Successive Ionization Energies Removing an electron from a cation is more difficult than removing an electron from a neutral atom because of the greater electrostatic attraction to the cation. Likewise, removing an electron from a cation with a higher positive charge is more difficult than removing an electron from an ion with a lower charge. Thus, successive ionization energies for an element always increase. At some point, there is always a large increase in successive ionization energies for an element. This large increase corresponds to the removal of core electrons, which are harder to remove than the valence electrons. Example: Sc and Ga both have three valence electrons. The large increase in ionization energy occurs after the third ionization.  Table 6.3 Successive Ionization Energies for Selected Elements (kj/mol) Element IE1 IE2 IE3 IE4 IE5 IE6 IE7 K 418.8 3051.8 4419.6 5876.9 7975.5 9590.6 11343 Ca 589.8 1145.4 4912.4 6490.6 8153.0 10495.7 12272.9 Sc 633.1 1235.0 2388.7 7090.6 8842.9 10679.0 13315.0 Ga 578.8 1979.4 2964.6 6180 8298.7 10873.9 13594.8 Ge 762.2 1537.5 3302.1 4410.6 9021.4 not available not available As 944.5 1793.6 2735.5 4836.8 6042.9 12311.5 not available Electron Affinity The electron affinity (EA) is the energy change for the process of adding an electron to a gaseous atom to form an anion. X(g) + e− ⟶ X−(g) EA1 This process can be either endothermic or exothermic, depending on the element. For some elements energy is released when the gaseous atom accepts an electron (negative EA). For other elements energy is required for the gaseous atom to accept an electron (positive EA). Higher electron affinity means, higher negative EA value or easier to accept an electron. This version of the periodic table displays the electron affinity values (in kJ/mol) for selected elements.