Ch. 7 The Quantum Mechanical Atom Brady & Senese, 5th Ed.
Index 7.1. Electromagnetic radiation provides the clue to the electronic structures of atoms 7.2. Atomic line spectra are evidence that electrons in atoms have quantized energies 7.3. Electrons have properties of both particles and waves 7.4. Electron spin affects the distribution of electrons among orbitals in atoms 7.5. The ground state electron configuration is the lowest energy distribution of electrons among orbitals 7.6. Electron configurations explain the structure of the periodic table 7.7. Quantum theory predicts the shapes of atomic orbitals 7.8. Atomic properties correlate with an atom's electron configuration
Light Acts As A Wave Wavelength (λ) the distance light travels to complete one cycle Frequency (ν) the number of wave cycles in one second units are cycles per second (cps), Hertz (Hz) Hz = s -1 3
Frequency And Wavelength Are Related Note that as the frequency of the wave increases, the wavelength decreases Regardless of the frequency, light travels at the same speed, c c=λ ν the speed of light (c) = 2.99792458 10 8 m/s Learning Check: If the frequency of a radio station is 300. MHz, what is the wavelength in m? 0.999 m 4
Radiant Energy Spectrum high energy, short waves low energy, long waves 5
Photoelectric Effect (Particle Theory Of Light) Albert Einstein (1905) E=hν Shining light on a clean metal surface may eject electrons There is a threshold level needed to eject the electrons (a work function specific to the metal) Increasing intensity does not cause the effect Increasing the frequency of the light does 6
Energy And Light Waves The energy of a wave is proportional to the wave frequency, E=hν h= Planck s constant, 6.626 10-34 J s/photon Learning Check: Why is ultraviolet light (320 nm) more penetrating than a red light (700 nm)? Use energies to make your case. E 320 = 6.2 10-19 J E 700 = 3 10-19 J λ 6 x 10-9 m Red light λ 3 x 10-9 m UV light 7
Your Turn! Which is the correct energy associated with a photon of light with a wavelength of 450 nm? A. 6.7 10-4 J B. 4.2 10-19 J C. 4.2 10-28 J D. 6.7 10 5 J E. none of these 8
Problems: 73, 77, 79, 83 9
Flame Emission Elements exhibit characteristic colors when burned The characteristic spectra are also observed when elements are subject to strong electrical fields as in gas discharge tubes. Note that the light from the discharge tube is actually several different colored lines as seen on the surface of the CD 10
Atomic Emission Spectra Light emitted by excited atoms is comprised of a few narrow beams with frequencies characteristic of the element Atomic spectra are unique for each element 11
Patterns In Atomic Line Spectra For the hydrogen spectrum, a mathematical pattern was noted and reported using the Balmer-Rydberg equation n 1 and n 2 are positive integers, where n 1 <n 2 Rydberg constant, R H, is an empirical constant=109,678 cm -1 If n 1 =1, lines called Lyman series If n 1 =2, called Balmer series If n 1 = 3 called Paschen series Emitted light is quantized 12
Learning Check What is the wavelength, in m, of light observed from a transition from n=4 to n=2? 1 1 λ = 109678cm 1 2 2 1 4 2 486.272 m What is n 2 if the photon undergoes transition to n=2 and the emitted light has a wavelength of 6505Å? n=3 13
Problems: 87, 89 14
What Does Quantized Mean? energy is quantized if only certain discrete values are allowed the presence of discontinuities makes atomic emission quantized Continuous (a) and discrete (b) potential energy of a tortoise. The potential energy of the tortoise in (b) is quantized. 15
Bohr s Model Of The Atom Electrons move around the nucleus in fixed paths or orbits much like the planets move around the sun Orbit positions, labeled with the integer n, have specific potential energy The lowest energy state of an atom is called the ground state (an electron with n = 1 for a hydrogen atom) 16
Absorption And Emission Electrons that absorb energy are raised to a higher energy level A particular frequency of light is emitted when an electron falls to a lower energy level 17
Bohr Equation (1913) This equation allows the calculation of the energy, E, of any orbit b= Bohr s constant n is the orbit location 18
Bohr s Model Predicts Energy Levels Bohr s (theoretical) equation explains the experimental (empirical) Rydberg equation The combination of constants, b/hc, has a value which differs from the experimentally derived value of R H by only 0.05%! b E = E h E l = n 2 b h n 2 l 1 = b 1 with n h > n l = hc n 2 l 1 λ n 2 h or 1 λ = b hc 1 n 2 l 1 n 2 h 19
Bohr s Model Fails Theory was not able to explain the spectra of atoms with more than one electron Theory doesn t explain the collapsing atom paradox 20
Light Exhibits Interference Constructive interference: waves in-phase create waves of greater amplitude ( they add) Destructive interference: waves out-of-phase create waves of lower amplitude (they cancel out) 21
Diffraction And Electrons Light exhibits interference, and it also has particle nature Electrons, known to be particles, also demonstrate interference 22
Standing vs. Traveling Waves Wind produces traveling waves on the surfaces of lakes and oceans A standing wave is produced when a guitar string is plucked: the center of the string vibrates, but the ends remain fixed 23
Standing Waves The waves created by guitar strings are those for which a half-wavelength is repeated exactly a whole number of times For a strength of length L with n, an integer, this can be written as: L = n λ 2 or rearranging λ = 2L n Wavelengths are quantized! 24
Three Models of an Electron a) Bead on a wire E=½ mv 2 b) Standing wave on a wire λ=2l/n c) Electron on a wire 25
The Electron On A Wire- Uniting The Theories Particle: the kinetic energy of the moving electron is E=½ mv 2 Standing wave, the half-wavelength must occur an integer number of times along the wire s length n(λ/2)=l de Broglie s equation provides the link between these. m=mass of particle λ = v= velocity of particle Combining these relationships: h mv 26
de Broglie Explains Quantized Energy Electron energy is quantized - it depends on the integer n Energy level spacing (and spectra) changes when electron confinement changes Lowest energy allowed is for n=1 (the energy cannot be zero, hence atom cannot collapse) 27
Wave Functions Wave that corresponds to the electron is called a wave function Wave functions for an electron are called orbitals Amplitude of the wave function at a given point can be related to the probability of finding the electron there According to quantum mechanics there are regions of the wire where the electrons will not be found, called nodes 28
Quantum Numbers Are a shorthand to describe characteristics of an electron s position and to predict its behavior n = principal quantum number. All orbitals with the same principle quantum number are in the same shell l = secondary quantum number which divides the orbitals in a shell into smaller groups called subshells m l = magnetic quantum number which divides the subshells into individual orbitals 29
Quantum Numbers: What Do They Mean? n = roughly describes a distance of the electrons from the nucleus. designated by integers: 1, 2, 3, 4, 5, 6, l = describes the shape of the orbitals. designated with numbers : 0, 1, 2, 3, 4, 5 or with letters: s, p, d, f, g, h m l =describes the spatial orientation of the orbital. designated by numbers specific to the particular orbital range from l to +l 30
How Do Quantum Numbers Relate to Each Other? Energy 0 5 s 4 s 3 s 2 s -1 0 +1-2 -1 0 +1 +2 5 p 4 d 4p 3d 3 p 2p n l 1 s m l 31
Electrons Behave Like Tiny Magnets Electrons within atoms interact with a magnet field in one of two ways: clockwise (spin up) anti-clockwise (spin down) This gives rise to the spin quantum number, m s allowed values: + 1/2 or 1/2 32
Pauli Exclusion Principle No two electrons in the same atom can have identical values for all four quantum numbers electrons can occupy the same orbital only if they have opposite spin are paired (called diamagnetic) Substances with more spin in one direction are said to contain unpaired electrons (called paramagnetic) 33
Problems: 91, 95 34
Ground State Electron Arrangements Electron configurations list the subshells that contain electrons and indicate their electron population with a superscript Orbital diagrams-represent each orbital with a circle (or box) and use arrows to indicate the spin of each electron 35
Hund s Rule Electrons fill a sublevel by occupying each orbital individually, then by pairing if needed This reduces the electrical repulsion between electrons not 36
Electron Occupancy And The Periodic Table The periodic table is divided into regions of 2, 6, 10, and 14 columns corresponding to the maximum number of electrons in s, p, d, and f sublevels 37
Sublevels and the periodic table. Each row (period) represents an energy level Each region of the chart represents a different type of sublevel 38
Where Are The Electrons? Each box represents room for an electron. Read from left to right 39
Read The Periodic Table To Determine e - Configuration Read from left to right The first e- go into the first Energy level (period 1) The first type of sublevel to fill is the 1s He has 2 e-. The e- configuration for He is: 1s 2 40
Learning Check B has 5 e- that fill the first shell next the second shell There are 2 subshells in the 2 nd shell: they fill in order of increasing energy 1s 2 2s 2 2p 1 41
Noble Gas Core Notation For Mn Find the last noble gas that is filled before Mn Next fill the sublevels that follow. 2 5 [Ar] 4s 3d 42
Creating An Orbital Diagram Examine the electron configuration for the atom. For each sublevel, determine the correct number of orbitals there is one box for each value of m l (2l+1 boxes) Note the number of electrons in each sublevel Distribute the electrons into the orbital, first individually, then pairing (Hund s rule) Each arrow represents an e - Make sure that the paired electrons have opposite spin directions (Pauli exclusion principle) 43
Orbital Diagram & e-configurations - N E POT 5s 4s 3s 5p 4p 3p 3d 2s 1s 2p Each arrow represents an electron 1s 2 2s 2 2p 3 44
Orbital Diagram & e- configurations - V E POT 4s 3s 3p 3d 2s 1s 2p Each arrow represents an electron 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 3 45
Learning Check: Write electron configurations and orbital diagrams for Na E POT 5s 4s 3s 5p 4p 3p 3d 2s 2p Na 1s2 2s2 2p6 3s1 1s 46
Problems: 105,119, 121 47
Electronic Classification Core e - : complete the previously filled noble gas Valence e - : are in the highest energy level outside the noble gas core. Involved in bonding. Pseudo-valence e- : are outside the noble gas core in lower energy levels contribute to shielding occasionally take part in bonding 48
Representative Elements For the representative elements (A groups): the electrons with the highest n value or valence shell are normally the only electrons important for chemical properties the valence electrons consist of electrons in just the s and p subshells A valence configuration shows only valence electrons for bromine: Br 4s 2 4p 5 49
Exceptions to the electronic configurations Following the rules for Cr, Cu, Ag, and Au using noble gas notation we expect the following: Element Expected Experimental Cr Cu Ag Au [Ar] 3d 4 4s 2 [Ar] 3d 9 4s 2 [Kr] 4d 9 5s 2 [Xe] 5d 9 6s 2 [Ar] 3d 5 4s 1 [Ar] 3d 10 4s 1 [Kr] 4d 10 5s 1 [Xe] 5d 10 6s 1 50
Uncertainty Principle: Erwin Schrödinger: wave is most significant character of electrons Werner Heisenberg: We cannot know exactly both the position and speed of an electron. All acts of measurement interact with electrons. 51
Orbitals Represent Uncertain Positions Plot shows that electron density varies from place to place Electron density variations define the shape, size, and orientation of orbitals 52
s Orbitals And Nodes Orbitals get larger as the principle quantum number n increases Nodes, or regions of zero electron density, appear beginning with the 2s orbital. 53
p Orbitals Possess a nodal plane that separates the lobes of high probability Dot-density diagrams of the cross section of the probability distribution of a single (a) 2p and (b) 3p orbital showing the nodal plane and the size difference 54
There Are Three Different Orbitals In Each p Subshell The directions of maximum electron density lie along lines that are mutually perpendicular. Orbitals are labeled as p x, p y, and p z 55
d Orbital Shape and Orientations Shape and orientation of d orbitals are more complicated than for p orbitals. f orbitals are even more complex than the d orbitals 56
Shielding And Effective Nuclear Charge Shielding: occurs when core electrons block the valence electrons from experiencing the full attraction of the nucleus Effective nuclear charge (Z* eff ): the amount of positive charge felt by outer electrons in atoms other than hydrogen Z* eff =Z-shielding electrons is lower than the atomic number because of shielding 57
Trends In Atomic and Ionic Radii (pm) 58
Ion vs. Atom Radii Positive ions are always smaller than the atoms from which they are formed due to decreased shielding effects Negative ions always larger than the atoms from which they are formed due to increased electron repulsion 59
Ionization energy (IE) IE is the energy required to remove an electron from an isolated, gaseous atom X(g) X + (g) + e Successive ionizations are possible until no electrons remain Trends in IE are the opposite of the trends in atomic size 60
Trends in IE 61
Successive IE 62
Irregularities in I.E. 63
Electron Affinity (EA) Is the potential energy change associated with the addition of an electron to a gaseous atom or ion in its ground state X + (g) + e X(g) Addition of one electron to a neutral atom is exothermic for nearly all atoms Addition of subsequent electrons always requires energy 64
Successive EA Consider the addition of electrons to oxygen: Change O(g) + e O (g) O(g) + 2e O 2 (g) O (g) + e O 2 (g) Ea (kj/mol) -141 +844 +703 65
Trends in Electron Affinity In general, electron affinity: increases (as an exothermic value) from left to right in a period increases (as an exothermic value) bottom to top in a group 66
Problems: 123, 125, 127, 131, 135 67