Copyright©2000 by Houghton Mifflin Company. All rights reserved. 1 Atomic Structure and Periodicity Chapter 7

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 2 Overview Introduce Electromagnetic Radiation and The Nature of Matter. Discuss the atomic spectrum of hydrogen and Bohr model. Describe the quantum mechanical model of the atoms and quantum numbers. Use Aufbau principle to determine the electron configuration of elements. Highlight periodic table trends.

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 3 Matter and Energy  Matter and Energy were two distinct concepts in the 19 th century.  Matter was thought to consist of particles, and had mass and position.  Energy in the form of light was thought to be wave-like.

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 4 Physical Properties of Waves Wavelength ( ) is the distance between identical points on successive waves. Amplitude is the vertical distance from the midline of a wave to the peak or trough.

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 5 Properties of Waves Frequency ( ) is the number of waves that pass through a particular point in 1 second (Hz = 1 cycle/s). The speed (v or c) of the wave = x

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 6 Electromagnetic Radiation Electromagnetic radiation travels through space at the speed of light in a vacuum. Electromagnetic radiation is the emission and transmission of energy in the form of electromagnetic waves.

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 7 Maxwell (1873), proposed that visible light consists of electromagnetic waves. Speed of light (c) in vacuum = 3.00 x 10 8 m/s All electromagnetic radiation x c 7.1

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 8 Electromagnetic Waves Electromagnetic Waves have 3 primary characteristics: 1.Wavelength: distance between two peaks in a wave. 2.Frequency: number of waves per second that pass a given point in space. 3.Speed: speed of light is  10 8 m/s.

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 9 Wavelength and frequency can be interconverted. = c/ (neu)= frequency (s  1 ) (lamda) = wavelength (m) c = speed of light (m s  1 )

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 10 Electromagnetic Spectrum

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 11 Planck’s Constant  E = change in energy, in J h = Planck’s constant,  10  34 J s = frequency, in s  1 = wavelength, in m n = integer = 1,2,3… Transfer of energy is quantized, and can only occur in discrete units, called quanta. n n

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 12 Diffraction  X-Ray Diffraction showed also that light has particle properties.

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 13 Figure-7.5: (a) Diffraction occurs when electromagnetic radiation is scattered from a regular array of objects, such as the ions in a crystal of sodium chloride. The large spot in the center is from the main incident beam of X rays. (b) Bright spots in the diffraction pattern result from constructive interference of waves. The waves are in phase; that is, their peaks match. (c) Dark areas result from destructive interference of waves. The waves are out of phase; the peaks of one wave coincide with the troughs of another wave.

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 14 Energy and Mass Energy has mass E = mc 2 Einstein’s Equation E = energy m = mass c = speed of light

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 15 Energy and Mass Radiation in itself is quantized

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 16 Wavelength and Mass = wavelength, in m h = Planck’s constant,  10  34 J s = kg m 2 s  1 m = mass, in kg v = speed, in ms  1 de Broglie’s Equation

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 17 x = c = c/ = 3.00 x 10 8 m/s / 6.0 x 10 4 Hz = 5.0 x 10 3 m Radio wave A photon has a frequency of 6.0 x 10 4 Hz. Convert this frequency into wavelength (nm). Does this frequency fall in the visible region? = 5.0 x nm

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 18 Figure 7.6: (a) A continuous spectrum containing all wavelengths of visible light. (b) The hydrogen line spectrum contains only a few discrete wavelengths. Atomic Spectrum of Hydrogen

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 19 Atomic Spectrum of Hydrogen Continuous spectrum: Contains all the wavelengths of light. Line (discrete) spectrum: Contains only some of the wavelengths of light.

Copyright©2000 by Houghton Mifflin Company. All rights reserved e - can only have specific (quantized) energy values 2.light is emitted as e - moves from one energy level to a lower energy level Bohr’s Model of the Atom (1913) E n = -R H ( ) z2z2 n2n2 n (principal quantum number) = 1,2,3,… R H (Rydberg constant) = 2.18 x J 7.3

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 21 E = h

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 22 E photon =  E = E f - E i E f = -R H ( ) 1 n2n2 f E i = -R H ( ) 1 n2n2 i i f  E = R H ( ) 1 n2n2 1 n2n2 n f = 1 n i = 2 n f = 1 n i = 3 n f = 2 n i = 3

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 23 = h/mv = 6.63 x / (2.5 x x 15.6) = 1.7 x m = 1.7 x nm What is the de Broglie wavelength (in nm) associated with a 2.5 g Ping-Pong ball traveling at 15.6 m/s? m in kgh in J su in (m/s)

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 24 E photon = 2.18 x J x (1/25 - 1/9) E photon =  E = x J = 6.63 x (Js) x 3.00 x 10 8 (m/s)/1.55 x J = 1280 nm Calculate the wavelength (in nm) of a photon emitted by a hydrogen atom when its electron drops from the n = 5 state to the n = 3 state. E photon = h x c /  = h x c / E photon i f  E = R H ( ) 1 n2n2 1 n2n2 E photon = Ignore the (-) sign for and

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 25 The Bohr Model Ground State: The lowest possible energy state for an atom (n = 1). Ionization: n f =  => 1/n f 2 = 0 => E=0 for free electron. Any bound electron has a negative value to this reference state.

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 26 E = h = hc P = mv To be well memorized E = mc 2 i f  E = R H ( ) 1 n2n2 1 n2n2 E photon =

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 27 Schrödinger Wave Equation In 1926 Schrödinger wrote an equation that described both the particle and wave nature of the e - Wave function (  ) describes: 1. energy of e - with a given  2. probability of finding e - in a volume of space Schrödinger's equation can only be solved exactly for the hydrogen atom. Must approximate its solution for multi-electron systems.

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 28 Quantum Mechanics Based on the wave properties of the atom  = wave function = mathematical operator E = total energy of the atom A specific wave function is often called an orbital.

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 29 Schrödinger Wave Equation  fn(n, l, m l, m s ) principal quantum number n n = 1, 2, 3, 4, …. n=1n=2 n=3 distance of e - from the nucleus

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 30 Probability Distribution  SQUARE of the wave function:   4 probability of finding an electron at a given position Radial probability distribution is the probability distribution in each spherical shell.

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 31 e - density (1s orbital) falls off rapidly as distance from nucleus increases Where 90% of the e - density is found for the 1s orbital

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 32 Figure 7.12: (a) Cross section of the hydrogen 1s orbital probability distribution divided into successive thin spherical shells. (b) The radial probability distribution.

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 33 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.

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 34 Quantum Numbers (QN) 1.Principal QN (n = 1, 2, 3,...) - related to size and energy of the orbital. 2.Angular Momentum QN (l = 0 to n  1) - relates to shape of the orbital. 3.Magnetic QN (m l = l to  l) - relates to orientation of the orbital in space relative to other orbitals. 4.Electron Spin QN (m s = + 1 / 2,  1 / 2 ) - relates to the spin states of the electrons.

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 35  = fn(n, l, m l, m s ) angular momentum quantum number l for a given value of n, l = 0, 1, 2, 3, … n-1 n = 1, l = 0 n = 2, l = 0 or 1 n = 3, l = 0, 1, or 2 Shape of the “volume” of space that the e - occupies l = 0 s orbital l = 1 p orbital l = 2 d orbital l = 3 f orbital Schrödinger Wave Equation

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 36 m l -lto +l

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 37 Each orbital can take a maximum of two electrons and a minimum of Zero electrons. Zero electrons does not mean that the orbital does not exist.

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 38 Degenerate

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 39 Pauli Exclusion Principle In a given atom, no two electrons can have the same set of four quantum numbers (n, l, m l, m s ). Therefore, an orbital can hold only two electrons, and they must have opposite spins.

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 40 Figure 7.13: Two representations of the hydrogen 1s, 2s, and 3s orbitals.

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 41 Figure 7.14: Representation of the 2p orbitals. (a) The electron probability distributed for a 2p orbital. (b) The boundary surface representations of all three 2p orbitals.

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 42 m l = -1 m l = 0m l = 1 2p Degenerate Orbitals

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 43 Figure 7.16: Representation of the 3d orbitals.

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 44 m l = -2m l = -1m l = 0m l = 1m l = 2 3d

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 45 How many 2p orbitals are there in an atom? 2p n=2 l = 1 If l = 1, then m l = -1, 0, or +1 3 orbitals How many electrons can be placed in the 3d subshell? 3d n=3 l = 2 If l = 2, then m l = -2, -1, 0, +1, or +2 5 orbitals which can hold a total of 10 e -

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 46 Figure 7.20: A comparison of the radial probability distributions of the 2s and 2p orbitals. Probability to be in the nucleus Zero probability to be in the nucleus P orbital is more diffuse

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 47 Figure 7.21: (a) The radial probability distribution for an electron in a 3s orbital. (b) The radial probability distribution for the 3s, 3p, and 3d orbitals.

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 48 Energy of orbitals in a single electron atom Energy only depends on principal quantum number n E n = -R H ( ) 1 n2n2 n=1 n=2 n=3

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 49 Energy of orbitals in a multi-electron atom Energy depends on n and l n=1 l = 0 n=2 l = 0 n=2 l = 1 n=3 l = 0 n=3 l = 1 n=3 l = 2

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 50 “Fill up” electrons in lowest energy orbitals (Aufbau principle) H 1 electron H 1s 1 He 2 electrons He 1s 2 Li 3 electrons Li 1s 2 2s 1 Be 4 electrons Be 1s 2 2s 2 B 5 electrons B 1s 2 2s 2 2p 1 C 6 electrons ??

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 51 Figure 7.25: The electron configurations in the type of orbital occupied last for the first 18 elements.

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 52 C 6 electrons The most stable arrangement of electrons in subshells is the one with the greatest number of parallel spins (Hund’s rule). C 1s 2 2s 2 2p 2 N 7 electrons N 1s 2 2s 2 2p 3 O 8 electrons O 1s 2 2s 2 2p 4 F 9 electrons F 1s 2 2s 2 2p 5 Ne 10 electrons Ne 1s 2 2s 2 2p 6

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 53 Order of orbitals (filling) in multi-electron atom 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 54 Figure 7.26: Electron configurations for potassium through krypton.

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 55 Figure 7.27: The orbitals being filled for elements in various parts of the periodic table.

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 56 What is the electron configuration of Mg? Mg 12 electrons 1s < 2s < 2p < 3s < 3p < 4s 1s 2 2s 2 2p 6 3s = 12 electrons 7.7 Abbreviated as [Ne]3s 2 [Ne] 1s 2 2s 2 2p 6 What are the possible quantum numbers for the last (outermost) electron in Cl? Cl 17 electrons1s < 2s < 2p < 3s < 3p < 4s 1s 2 2s 2 2p 6 3s 2 3p = 17 electrons Last electron added to 3p orbital n = 3l = 1m l = -1, 0, or +1m s = ½ or -½

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 57 Valence Electrons The electrons in the outermost principle quantum level of an atom. Inner electrons are called core electrons.

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 58 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)

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 59 Figure 7.36: Special names for groups in the periodic table.

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 60 Ionization Energy The quantity of energy required to remove an electron from the gaseous atom or ion. This is an Endothermic Process: Energy is absorbed & Sign will be +ve

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 61 I 1 + X (g) X + (g) + e - I 2 + X + (g) X 2 + (g) + e - I 3 + X 2+ (g) X 3 + (g) + e - I 1 first ionization energy I 2 second ionization energy I 3 third ionization energy I1 < I2 < I3I1 < I2 < I3

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 62

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 63

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 64 Figure 7.31: The values of first ionization energy for the elements in the first six periods.

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 65 Exceptions Be 1s 2 2s 2 B 1s 2 2s 2 2p 1 Shielded Electron N 1s 2 2s 2 sp 3 O 1s 2 2s 2 2p 4 Repulsion to doubly electrons

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 66 Periodic Trends First ionization energy: increases from left to right across a period; decreases going down a group.

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 67 General Trend in First Ionization Energies Increasing First Ionization Energy

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 68 Electron Affinity The energy change associated with the addition of an electron to a gaseous atom. X(g) + e   X  (g) This is an Exothermic Process: Energy is Released & Sign will be -ve

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 69 X (g) + e - X - (g) F (g) + e - X - (g) O (g) + e - O - (g)  H = -328 kJ/mol EA = +328 kJ/mol  H = -141 kJ/mol EA = +141 kJ/mol

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 70 Figure 7.33: The electron affinity values for atoms among the first 20 elements that form stable, isolated X - ions.

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 71

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 72 Exceptions C - (g) can be formed easily while N - (g) cannot be formed easily: C - 1s 2 2s 2 p 3 N - 1s 2 2s 2 2p 4 O - (g) can be formed because the larger positive nucleus overcome pairing repulsions. Extra repulsion

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 73 Periodic Trends Atomic Radii: decrease going from left to right across a period; increase going down a group.

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 74 Figure 7.35: Atomic radii (in picometers) for selected atoms.

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 75 Information Contained in the Periodic Table 1.Each group member has the same valence electron configuration (these electrons primarily determine an atom’s chemistry). 2.The electron configuration of any representative element. 3.Certain groups have special names (alkali metals, halogens, etc). 4.Metals and nonmetals are characterized by their chemical and physical properties.

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 76 Paramagnetic unpaired electrons 2p Diamagnetic all electrons paired 2p