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Chapter 7 Atomic Structure and Periodicity Topics Electromagnetic radiation The nature of matter The atomic spectrum of hydrogen The Bohr model The quantum mechanical model of the atom Quantum numbers Orbital shapes and energies Electron spin and Pauli exclusion principle Polyelectronic atoms The history of the periodic Table The aufbau principle and Periodic Table Periodic trends in atomic properties The Wave-like Electron The electron propagates through space as an energy wave. To understand the atom, one must understand the behavior of electromagnetic waves. Louis deBroglie 7.1 Electromagnetic Radiation electromagnetic radiation: form of energy that acts as a wave as it travels includes: X rays, Ultraviolet, visible light, infrared light, microwaves, and radio waves travel at a speed of 2.9979 x 108 m/s in a vacuum All forms of EMR are combined to form electromagnetic spectrum Electromagnetic Spectrum High Energy The whole range of frequencies Low Energy is called “Spectrum” Radio waves Micro waves Infrared . Ultra- Xviolet Rays Low Frequency Long Wavelength R O Y Gamma Rays High Frequency Visible Light G B Short Wavelength I V” Parts of a wave Crest Wavelength Amplitude Origin Trough Wavelength λ = Greek letter lambda distance between points on adjacent waves (consicutive peaks or troughs) Units used are in nm (109nm = 1m) Frequency = Greek letter nu number of wave cycles that passes a point in a second. 108 cycles/s= 108 s-1 =108 Hertz = 108 Hz in 1/second (Hertz = Hz) Electromagnetic radiation propagates through space as a wave moving at the speed of light. Equation: c c c = speed of light, a constant (2.998 x 108 m/s) (lambda) = wavelength, in meters (nu) = frequency, in units of hertz (hz or sec-1) 7.2 Nature of Matter Before 1900, scientists thought that matter and energy were totally different matter particles mass position energy wave massless delocalized In 1900 According to the old views, matter could absorb or emit any quantity (frequency) of energy. Max Planck found that as the cooling of hot objects couldn’t be explained by viewing energy as a wave. Max Planck studied the radiation emitted by solid bodies heated to incandescence. Max Planck postulated that energy can be gained or lost only in whole number multiples of the quantity h h =Planck’s constant= 6.626x10-34 J.s That is change in energy of a system, E is E nh n is an integer; is the frequency of EMR emitted or absorbed Nature of Matter Mack’s Planck suggested that an object emits energy in the form of small packets of energy called quanta. That is the energy is quantized Quantum- the minimum amount of energy that can be gained or lost by an atom (energy in each packet) E h Thus energy seems to have particulate properties Nature of Matter Einstein proposed that radiation itself is really a stream of particles called photons Energy of each photon is : E photon hv also showed that energy has mass E mc 2 E m 2 c hc Nature of Matter c v v c E hv h mc hc mc E hc 2 E mc shows that anything with both mass and velocity has a corresponding wavelength 2 Calculate the energy of red light vs. blue light. red light: 700 nm blue light: 400 nm red: hc E hc E blue: hc E 34 8 (6.62x1034 J s)( 3.00x108 m / s) ( 6 . 62 x 10 J s )( 3 . 00 x 10 m / s) E E 700x109 m 400x109 m E = 2.85 x 10-19 J E = 4.96 x 10-19 J What is light? Light has certain characteristics of particulate matter Light is a wave - we can measure its wavelength and it behaves as a wave If we combine E=mc2 , c=, E = 1/2 mv2 and E = h, then we can get: = h/mv (from Louis de Broglie) called de Broglie’s equation This equation allows calculation of the wavelength of a particle. Wave-Particle Duality J.J. Thomson won the Nobel prize for describing the electron as a particle. His son, George Thomson won the Nobel prize for describing the wave-like nature of the electron. The electron is a particle! The electron is an energy wave! 7.3 The Atomic Spectrum of Hydrogen Main experiments led to the information related to atom: Thompson discovery of electron Rutherford discovery of nucleus Study of emission of light by excited hydrogen atom When H2 molecules absorb energy, some H-H bonds are broken and excited H-atoms will be produced The excited H-atoms release energy by emitting light at various wavelengths that is known as emission spectrum of H-atoms Spectroscopic analysis of the visible spectrum White light • When sunlight is dispersed by rain drops the rainbow is Produced; that is a continuous spectrum is produced. • continuous spectrum contains all colors; that is all wavelengths of the visible light The Continuous Spectrum ~ 650 nm ~ 575 nm ~ 500 nm ~ 480 nm ~ 450 nm The different colors of light correspond to different wavelengths and frequencies Spectroscopic analysis of the hydrogen spectrum… H receives a high energy spark H-H bonds Are broken and H atoms are excited Hydrogen emission spectrum is called “line spectrum” • Line spectrum • Unique to each element, like fingerprints! • Very useful for identifying elements Significance of the line spectrum of H-atom Only certain energies are allowed for the electron in the hydrogen atom That is, the energy of an electron in a hydrogen atom is quantized. Changes in energy between discrete energy levels in hydrogen will produce only certain wavelengths of emitted light. The discrete line spectrum of hydrogen shows that only certain energies are possible. The electron energy levels are quantized. If all energy levels are allowed the spectrum would be continuous 7.4 The Bohr Model Niels Bohr (Danish physicist) 1885-1962 Developed a quantum model for H atom that explained the emission line spectrum Electron moves around the nucleus only in certain allowed circular orbits, in which it has a certain amount of energy The electrons were attracted to the nucleus because of opposite charges. But electron does not fall in to the nucleus because it is moving around. The Bohr Atom He didn’t know why but only certain energies were allowed. He called these allowed energies energy levels. Putting Energy into the atom moved the electron away from the nucleus. From ground state to excited state. When it returns to ground state it gives off light of a certain energy. The Model: Summary Space around nucleus is divided into spherical (circualr) paths (orbits) each has a number called “Principal Quantum number” The electron can exist only in one of these orbitals but not in between Orbits possess fixed size and energy, therefore electron has a definite energy characteristic of its orbit En Eorbit RH Z 2 2 Energy of electron n -18 R H Rydberg constant 2.178x10 J particle En 2.178 X 10 18 23 J 6.02 X 10 particles 1kJ 1 1312kJ / mol X X X 2 2 particle 1mol 1000 J n n En 1312kJ 2 n mole An electron can pass only from one orbit to another. Absorption or emission will occur Energy of the outermost orbit is zero The Bohr Atom n=4 n=3 n=2 n=1 Bohr Model equation can be used twice to find the ∆E when an electron moves energy levels E 2.178 10 E [2.178 10 18 J( Zf 2 nf 2 E 2.178 10 18 2 Z J( 2 ) n )] [2.178 10 18 1 1 J( 2 2 ) nf ni 18 2 Zi J ( 2 )] ni Bohr Model Wavelength of photon released can be calculated by using hc E E=0 is set at an distance of ∞ away from the nucleus and becomes more negative as the electron comes closer to the nucleus E 2.178 10 18 1 J( ) 0 Example 1 1 1 Calculate the 18 E 2.178 10 J ( 2 2 ) energy required to nf ni move the hydrogen electron from n=1 1 1 18 E 2.178 10 J ( 2 2 ) 1.633 10 18 J to n=2. Find the 2 1 wavelength of radiation that had to m 34 (6.626 10 J s)( 2.9979 ) hc s be absorbed by the E 1.633 10 18 J electron. 9 10 nm 1.216 107 m 121.6nm 1m Calculate the energy required to remove the electron from the hydrogen atom in its ground state. Example 2 E 2.178 10 18 E 2.178 10 E 2.178 10 18 1 1 J( 2 2 ) nf ni 18 1 1 J( 2 ) 1 J (0 1) 2.178 10 18 Energy was absorbed by the electron so the value of ∆E value is positive. J Bohr Model problems: did not work for other atoms did not explain chemical behavior of atoms Heisenberg’s Uncertainty Principle According to de Broglie: Electron behaves like a wave Is it possible to specify the position of a wave at a particular instant? Energy, wavelength and amplitude can be determined But exact position is impossible to be determined The electron cannot be imagined as : moving particle In a path of the same radius (well defined orbits) Thus, location, direction and speed of motion of a particle cannot be determined Then Bohr Model had to be “Abandoned Heissenberg Uncertainty Principle “It is impossible to determine both the position and momentum of a subatomic particle (such as the electron) with arbitrarily high accuracy” The effect of this principle is to convert the laws of physics into statements about relative, instead of absolute, certainties. Heisenberg Uncertainty Principle we cannot know the exact position and momentum (motion) of the electron as more is known about position, less is known about momentum uncertainties are inversely proportional h x ( m ) 4 where ∆x: uncertainty in position ∆m : uncertainty in mometum minimum uncertainty is h/4 7.5 The Quantum Mechanical Model Exact position of electron can not be defined Exact bath of electron about nucleus can not be defined Werner Heisenberg, Louis de Broglie and Erwin Schrodinger made the approach called “Quantum Mechanics” They assumed that the electron is a standing wave The Quantum Mechanical Model Waves are associated with electrons Information about energies of electrons and their positions are obtained from studying the associated waves Description of electron is based upon “ Probability of finding a particle within a given region of space” “ but not on the exact position” Schrödinger Equation Wave equation describing electron as being a wave The amplitudes (height), , of electron wave at various points of space are calculated commonly called “wave function” provides information about the allowable energies for an electron in H atom. corresponds to a certain energy and describes a region around nucleus “Orbital” where the electron having that energy may be found Orbital: Region around the nucleus where the electron can be expected to be found The Function 2 2 describes the probability of the position of the electron at a particular point 2 Probability of finding a particle in a given region of space 2 Electric charge density at a given region of space Thus, The charge can be assumed to be spread out as a charge cloud by rapid motion of electron The cloud is denser in some regions than others The probability of finding electron in a given region in space is proportional to the density of the cloud Meaning of Wave Function the wave function itself does not have concrete meaning the square of the wave function represents the probability of finding an electron at a certain point easily represented as probability distribution where the deepness of color indicates the probability Meaning of Wave Function (a) electron density map probability of finding an electron is highest at short distances from nucleus (b) calculated probability of finding an electron at certain distances from nucleus in the 1s orbital 7.6 Quantum Numbers There are many solutions to Schroedinger’s equation for H atom Each solution is a wave function called Orbital. Each orbital can be described with quantum numbers that describe properties of the orbital Quantum numbers specify the properties of atomic orbitals and of electrons in orbitals the first three quantum numbers come from the Schrödinger equation and describe: main energy level shape orientation 4th describes state of electron Principal Quantum Number, n Main energy level occupied by electron. They are called atomic orbitals regions where there is a high probability of finding an electron. n is related to the size and energy of the orbital values are all positive integers >0 (1,2,3,…) As n increases size of orbital is larger and electron is less tightly bound to nucleus The electron spends more time further from nucleus electron has higher energy the electron’s average distance from the nucleus increases Principal Quantum Number Maximum number of electrons that can fit in an energy level: 2n2 Angular Momentum Quantum Number: l It indicates the shape of the orbital The number of possible shapes (or l values) for an energy level is equal to n The possible values of l are 0 and all positive integers less than or equal to n-1 l has integer values from 0 to n-1 l = 0 is called s l = 1 is called p l =2 is called d l =3 is called f l =4 is called g Magnetic Quantum Number, ml ml indicates the orientation of the orbital in space relative to the other orbitals in the atom ml has integer values from + including 0 l-l each orbital holds maximum of 2 electrons total number of orbitals is equal to n2 for an energy level number of possible ml values for a certain subshell is equal to 2l + 1 Quantum Numbers for the first four levels of orbitals in the hydrogen atom 7.7 Orbital shapes and Energies s orbitals: 1: s spherical l value of 0 Representations of the Hydrogen 1s, 2s, and 3s Orbitals A. The Electron Probability Distribution B. The surface contains 90% of the total electron probability p-orbitals - + + - + - p orbitals: 3 2px, 2py, 2pz dumbbellshaped l value = 1 No 1p orbitals 1st occur at n=2 for n>2, shape is same but size increases d- orbitals -+ + d orbitals: 5: 3dxz, 3dyz, 3dxy, 3dx2-y2, dz2 mostly cloverleaf l value of 2 1st occur at n=3; no d-orbitals for n=1 or n=2 for n>3, same shape but larger size f-orbitals f orbitals: 7 types various shapes l value of 3 begin in n=4 Other shapes can exist in energy levels as long as they follow the rules g (l =4) starts in 5 with 9 orbitals h (l =5) starts in 6 with 11 orbitals, etc but no known elements have electrons in them at ground state Remember that all orbitals of the same n has the same energy; they are called “degenerate” 7.8 Electron spin and the Pauli Principle Spin Quantum Number: ms Electron has a magnetic moment with two possible orientations when the atom is placed in an external magnetic field The electron could have two spin states only 2 possible directions ms can have two possible values: +½ and -½ paired electrons must have opposite spins Pauli Exclusion Principle: In a given atom, no two electrons can have the same set of four quantum numbers (n, l, ml , ms ) An orbital can hold only two electrons and they must have opposite spins. 7.9 Polyelectronic Atoms Three energy contributions must be considered in the description of polyelectronic atom: Kinetic energy of electrons - as the electrons move around the nucleus Potential energy - from attraction between electrons and nucleus Potential energy of repulsion between two electrons Electron Correlation Problem can’t find the exact location of electrons can’t find the specific repulsions between electrons so we must treat each electron as if it has an average amount of attraction to nucleus and repulsion to other electrons Electron Shielding occurs when an electron is not attracted to the nucleus because of electrons in lower energy levels repelling it. Penetration Effect all orbitals in the same energy level do NOT have the same amount of energy ( are not degenerate) same as the case in H-atom Ens < Enp < End < Enf the amount of energy in each sublevel is determined by its average distance from the nucleus For example, in He atom, 2p orbital has its maximum probability closer to the nucleus than 2s orbital, thus we would predict 2p would have less energy than 2s. However, 2s electron spends more time closer to nucleus and usually has less energy. That is 2s electron penetrates to the nucleus more than an electron in a 2p orbital 7.10 The history of the Periodic Table Developed independently by German Julius Lothar Meyer and Russian Dmitri Mendeleev (1870’s). They didn’t know much about atom. Elements were arranged in columns by similar properties. Properties of missing elements were predicted. Mendeleev's Early Periodic Table, Published in 1872 7.11 The aufbau Principle and Periodic Table Electron Arrangement in Atoms The way electrons are arranged in various orbitals around the nuclei of atoms. Aufbau is a German word means “Building up” Aufbau principle - electrons enter the lowest energy first. • Orbitals of different energies overlap • Electron Configurations • Electron configuration describes the distribution of electrons among the various orbitals in the atom The spdf notation uses numbers to designate a principal shell and the letters to identify a subshell; a superscript number indicates the number of electrons in a designated subshell Orbital Diagram An orbital diagram uses boxes to represent orbitals within subshells and arrows to represent electrons: Each box has arrows representing electron spins; opposing spins are paired together EOS Rules for Electron Configurations Electrons occupy the lowest available energy orbitals Pauli exclusion principle – no two electrons in the same atom may have the same four quantum numbers •Orbitals hold a maximum of two electrons with opposed spins Rules for Electron Configurations For orbitals of identical energy, electrons enter empty orbitals whenever possible – Hund’s rule When electrons occupy orbitals of equal energy, they don’t pair up until they have to. Electrons in half-filled orbitals have parallel spins EOS Rules for Electron Configurations Capacities of shells (n) and subshells (l) EOS Rules for Electron Configurations Subshell filling order : Each subshell must be filled before moving to the next level Electron Configurations Let’s write the electron configuration for Phosphorus We need to account for all 15 electrons in phosphorus Increasing energy 7s 6s 5s 7p 6p 6d 5d 5p 4d 4p 3d 4s 3p 3s 2s 1s 5f 4f 15P The first two electrons go into the 2p 1s orbital Notice the opposite direction of the spins only 13 more to go Increasing energy 7s 6s 5s 7p 6p 6d 5d 5p 4d 4p 5f 4f 3d 4s 3p 3s 2p The next electrons go into the 2s orbital only 11 more 2s 1s Increasing energy 7s 6s 5s 7p 6p 5p 4p 4s 6d 5d 4d 5f 4f 3d 3p 3s 2p 2s • The next electrons go into the 2p orbital • only 5 more 1s Increasing energy 7s 6s 5s 7p 6p 5p 4p 4s 6d 5d 4d 5f 4f 3d 3p 3s 2p 2s 1s • The next electrons go into the 3s orbital • only 3 more Increasing energy 7s 6s 5s 4s 3s 2s 1s 7p 6p 5p 4p 6d 5d 4d 5f 4f 3d 3p • The last three electrons go into the 3p orbitals. 2p They each go into separate orbitas (Hund’s) • 3 unpaired electrons • = 1s22s22p63s23p3 The Aufbau Principle A hypothetical building up of an atom from the one that precedes it in atomic number (Z = 1) H 1s1 (Z = 3) Li 1s22s1 [He]2s1 (Z = 2) He 1s2 Abbreviated electron configuration (Z = 3) Li 1s22s1 EOS The Aufbau Principle [He]2p2 [He]2p3 [He]2p4 [He]2p5 [He]2p6 EOS Orbital Diagram for A Nitrogen Atom 7N 1s 2s 2p 3s Orbital Diagram for A Fluorine Atom 9F 1s 2s 2p 3s Orbital Diagram for A Magnesium Atom 12Mg 1s 2s 2p 3s 8O 1s 2s 2p 3s Write the orbital diagram for the electrons in an iron atom 26Fe 1s 2s 2p 3s 3d 3p Orbitals fill in an order Lowest energy to higher energy. Adding electrons can change the energy of the orbital. Full orbitals are the absolute best situation. However, half filled orbitals have a lower energy, and are next best • Makes them more stable. • Changes the filling order Write the electron configurations for these elements: Titanium - 22 electrons 1s22s22p63s23p64s23d2 Vanadium - 23 electrons 1s22s22p63s23p64s23d3 Chromium - 24 electrons 1s22s22p63s23p64s23d4 (expected) But this is not what happens!! Chromium is actually: 1s22s22p63s23p64s13d5 Why? This gives us two half filled orbitals (the others are all still full) Half full is slightly lower in energy. The same principal applies to copper. Copper’s electron configuration Copper has 29 electrons so we expect: 1s22s22p63s23p64s23d9 But the actual configuration is: 1s22s22p63s23p64s13d10 This change gives one more filled orbital and one that is half filled. Remember these exceptions: d4, d9 Irregular configurations of Cr and Cu Chromium steals a 4s electron to make its 3d sublevel HALF FULL Copper steals a 4s electron to FILL its 3d sublevel Electron Configurations of Ions Cations: lose e– to attain a complete valence shell Example: (Z = 11) Na (Z = 11) Na+ Details of the Periodic Table Elements in the same column have the same electron configuration. Elements in columns have similar properties. Noble gases have filled energy levels. Transition metals are filling the d orbitals Valence electrons- the electrons in the outermost energy levels (not d). Core electrons- the inner electrons. C 1s2 2s2 2p2 Valence Electrons and Core Electrons Valence electrons are those with the highest principal quantum number The electrons in the outermost energy levels (not d). Sulfur has six valence electrons Valence Electrons and Core Electrons Electrons in inner shells are called core electrons Sulfur has 10 core electrons EOS Periodic Relationships We can deduce the general form of electron configurations directly from the periodic table The Periodic Table More exceptions 2 1 Lanthanum La: [Xe] 6s 5d 2 1 1 Cerium Ce: [Xe] 6s 4f 5d Promethium Pr: [Xe] 6s2 4f3 5d0 2 7 1 Gadolinium Gd: [Xe] 6s 4f 5d 2 14 1 Lutetium Pr: [Xe] 6s 4f 5d We’ll just pretend that all except Cu and Cr follow the rules. Main Group (Representative) and Transition Elements Elements in which the orbitals being filled in the aufbau process are either s or p orbitals of the outermost shell are called main group (Representative) elements “A” group designation on the periodic table The first 20 elements are all main group elements Transition Elements In transition elements, the sublevel (shell) being filled in the aufbau process is in an inner principal shell (d or f) d-Block transition elements: Electrons enter the d-sublevels. f-Block transition elements: d sublevels are completely filled. Electrons enter f-sublevels Lanthanides: electrons fill 4f subleve Actinides: electrons fill 5f sublevels The Periodic Table Periodic Relationships 7.12 Periodic Trends in Atomic Properties Ionization Energy Ionization energy the energy required to remove an electron completely form a ground state atom in the gaseous phase A (g) + energy A+ (g) + e Highest energy electron removed first. First ionization energy (I1) is that required to remove the first electron. Second ionization energy (I2) - the second electron, etc. Successive ionization Energies for Mg • • • I1 = 735 kJ/mole I2 = 1445 kJ/mole I3 = 7730 kJ/mole The effective nuclear charge increases as electrons are removed It takes much more energy to remove a core electron than a valence electron because there is less shielding. Successive ionization Energies Continual removal of electrons increases ionization energy greatly B B+ + e– I = 801 kJ mol–1 B+ B+2 + e– I = 2427 kJ mol–1 B+2 B+3 + e– I = 3660 kJ mol–1 B+3 B+4 + e– I = 25,025 kJ mol–1 B+4 B+5 + e– I = 32,822 kJ mol–1 Core electron Ionization Energy First ionization energies across Periods and Groups The Values of First Ionization Energy for the Elements in the First Six Periods For B electrons in 2s provide some shielding From nucleus charge E for O < E for N due to extra electron repulsion in the doubly occupied O 2p orbitals Ionization Energy Ionization Energy Electron Affinity Electron Affinity – the energy change when an electron is added to a gaseous neutral atom A + e- A- + energy Cl(g) + e- Cl-(g) E = -349 kJ/mol • Electron affinities are expressed as negative because the process is exothermic Electron affinity values Electron Affinity Electron Affinity Across Period: releases more energy so number increases (gets more negative) because electrons added in the same energy level do not shield electrons from nuclear charge Down Group: releases less energy so number decreases (gets less negative) because the electrons being added are farther away from the attracting protons Atomic Radii Size of orbitals can not be specified exactly, neither can the size of atom Atomic Radii – half the distance between the nuclei of identical atoms that are bonded together Atomic Radii Across Period: atoms get smaller because of the increased number of protons attracting the electrons the electrons added in the same energy level do not shield electrons from nuclear charge Down Group: atoms get larger increases because the energy levels being added to the atom Atomic Radii Properties Summary of Periodic Trends