Electronic Structure of Atoms Chapter 6 How are the electrons distributed in atoms? What are their relative energies? Electron Space e- e- e- Modern Atomic Theory Most of the evidence that we have about the electrons in an atom is from the light that is given off by atoms. Neon lights Fireworks Electromagnetic Radiation Electromagnetic radiation is energy in the form of light which travels through space at a velocity of ~3.0x108 m/s (the speed of light!). All electromagnetic radiation has wavelike properties. Wavelength () and Frequency () The distance between corresponding points on adjacent waves is the wavelength (). The number of waves passing a given point per unit of time is the frequency (). For waves traveling at the same velocity, the longer the wavelength, the smaller the frequency Electromagnetic Spectrum Wavelength () and Frequency () How are Wavelength and Frequency related mathematically? Wavelength () and Frequency () How are Wavelength and Frequency related mathematically? = c / (c is the speed of light) (c = 3.00 x 108 m/s) Wavelength () and Frequency () Group Work: What is the frequency of red light with a wavelength of 740 nm? = c / (c is the speed of light) (c = 3.00 x 108 m/s) Wavelength () and Frequency () Group Work: What is the frequency of red light with a wavelength of 740 nm? Frequency () = 4.05 x 1014 s-1 = c / (c is the speed of light) (c = 3.00 x 108 m/s) Visible Light The visible portion of the electromagnetic spectrum can be divided into the colors (the rainbow): Red R (longest ) Orange O Yellow Y Green G Blue B Indigo I Violet V (shortest ) Group Work Rank the following colors of light from highest frequency to lowest frequency. Yellow Red Blue Green Quantized Energy Planck - studied radiation from heated matter and proposed that atoms of a substance can have only certain energies, and therefore can emit only certain energies. The smallest unit of energy that composes a type of radiation emitted is called a quantum: Equanta = hv or E = nhv (h = 6.63x10-34 J-sec) Quantized Energy Therefore: Energy is quantized - it can have only certain allowed values. Energy can be emitted or absorbed in whole-number multiples of hv: 2 h , 3 h , 4 h , ... Photoelectric Effect Ephoton= hv = KEe- + BEe- (BE = Binding Energy of e-) Photoelectric Effect Long-wavelength radiation ejects no electrons - no matter how intense the light. As the radiation is varied to shorter wavelengths, a threshold frequency (BE) is reached where electrons are ejected from the metal surface atoms. Past the threshold frequency, the number of electrons ejected does not increase, but the KE of the electrons is greater. Increasing frequency increases the KE energy of ejected electron frequency KE electron 0 How can we increase # electrons ejected? Choose one frequency of light … (green for example) Frequency KE electron 0 Increase the intensity of light. This will increase the number of electrons ejected. This does not increase KE of electron. Intensity of Light at Constant Frequency KE electron 0 Photoelectric Effect Einstein explained the photoelectric effect using Planck’s idea of quantized energy. Einstein described each quantum of energy as a particle of light called a photon. Ephoton = hv The photons that strike the surface must have the minimum amount of energy (BE) to dislodge an electron that is attracted to the positively charged metal atom nucleus. Wave-Particle Duality Ephoton = hv = hc/ Calculate the energy (in joules) of a photon with a wavelength of 5.00x104 nm (Infrared Region) Wave-Particle Duality Ephoton = hv = hc/ 5.00x104 nm (Infrared Region) Ephoton = 3.98x10-21 J Group Work Which has the highest photon energy? Red light Blue light Yellow light Electromagnetic Spectrum Continuous Spectrum White light is composed of all wavelengths of visible light. Diffraction produces a continuous spectrum. Line Spectrum Special lights or heated elements emit only certain wavelengths of light. Diffraction results in a line spectrum, not a continuous spectrum. Hydrogen Line Spectrum Light given off by elements is composed of only certain ’s of light. Line Spectra Each element produces a unique line spectrum. Line Spectra Bohr Model of the Hydrogen Atom In 1913, Niels Bohr proposed the Bohr Model of the Hydrogen Atom: The electron circles the nucleus in orbits of certain radii. An electron permitted in an orbit has a specific “allowed” energy. Bohr Model of the Hydrogen Atom The allowed orbits in a H atom have energies described by the equation: En = (-RH)(1/n2) n = 1,2,3,4... RH is the Rydberg constant RH = 2.18 x 10-18 J n is the principle quantum number Bohr Model of the Hydrogen Atom En = (-RH)(1/n2) n = 1,2,3... Bohr Model of the Hydrogen Atom When the electron undergoes a transition from a higher energy level to a lower energy level, light energy is given off. The amount of energy given off is equal to the energy difference between the two levels, DE. (DE=Ef-Ei = hv=hc/). Bohr Model (Balmer Series) n=6 n=5 n=4 n=3 n=2 n=1 Bohr Model of the Hydrogen Atom (DE=Ef-Ei = hv=hc/). Bohr Model of the Hydrogen Atom Balmer Series The Balmer Series consists of the H electron transitions that produce light in the visible region. nf = 2 ni = 3, 4, 5, 6 Which is the Balmer Series? Which is the Balmer Series? Other allowed transitions are not observed by our eyes! Lyman Series nf = 1 (Ultraviolet) Paschen Series nf = 3 (Infrared) Bracket Series nf = 4 (Infrared) Balmer Series Group Work There is a 5th electron transition in the Balmer Series that does not show up in the line spectrum. Predict the wavelength and frequency of the radiation that is produced from this transition (ni =7). = 7.55x1014 s-1 = 3.97x10-7 m (397 nm) Visible Region: (7.50 x 1014 s-- 4.00 x 1014 s- ) (400 nm - 750 nm) The 5th Line in the Balmer Series is not in the Visible Region Limitations to the Bohr Model Cannot explain the spectra of multi-electron atoms. Electrons also have wavelike properties, which prohibits describing electrons as circling in orbits. Important Ideas of the Bohr Model that we use today Electrons exist only in certain discrete energy levels. Energy is involved in electron transitions between energy levels. 6.5 Quantum Mechanics and Atomic Orbitals Schrodinger’s Wave Equation incorporates both wavelike and particle-like properties of the electron. Led to quantum mechanics, a description of particle behavior on the very micro scale level. Instead of Orbits we have Probability Densities 2 = probability density 2 represents the probability of finding an electron in a certain location. Electrons reside in orbitals Orbitals and Quantum Numbers The complete solutions to the wave equation are wave functions called orbitals (not orbits), each with its own energy value. Each electron is described by a set of 4 quantum numbers: n, l, ml, and ms Orbitals and Quantum Numbers 4 Quantum Numbers: n - Principal Quantum Number (Energy, Distance) l - Azimuthal Quantum Number (Shape) ml - Magnetic Quantum Number (Direction) ms - Electron Spin Quantum Number No two electrons in the same atom can have the same 4 quantum number values. Restrictions to Quantum Numbers Possible values of quantum numbers n - (Integer values: 1, 2, 3 ...) l - (0, .... n-1) ml - (Integer values between and including -l & l) ms - (+ 1/2 or - 1/2) n (shell) l (subshell) ml (orbital) 1 0 0 2 0 0 2 1 -1, 0 +1 The Quantum number n describes the relative distance from nucleus The Quantum number l describes the orbital shape l = 0 --> s - orbital (spherical) l = 1 --> p - orbital (2 lobes) l = 2 --> d - orbitals (most have 4 lobes) l = 3 --> f - orbitals (more complicated) l = 0 l = 1 l = 2 The Quantum number ml describes the direction of orbital When l = 2 (d orbitals): ml can have values: -2, -1, 0, +1, +2 The Quantum number,ml, describes the direction of orbital When l = 2 (d orbitals): ml can have values: -2, -1, 0, +1, +2 Orbitals with the same value of n and l are in the same subshell. Group Work How many orbitals are in the subshell described? Write their symbols. 1. n = 3 and l =2 2. n = 2 and l =1 3. n = 3 and l =1 4. n = 4 and l =3 Group Work How many orbitals are in the subshell described? Write their symbols. 1. n = 3 and l =2 (Five 3d orbitals) 2. n = 2 and l =1 (Three 2p orbitals) 3. n = 3 and l =1 (Three 3p orbitals) 4. n = 4 and l =3 (Seven 4f orbitals) Spin Quantum Number, ms Two electrons can have the same set of the three quantum numbers, n, l, and ml , if they have different values of ms. A way to represent two electrons with opposite spin in the same orbital 2 Electrons in the Same Orbital n l ml ms 1 0 0 +1/2 1 0 0 -1/2 2 Electrons in the Same Orbital n l ml ms 1 0 0 +1/2 1 0 0 -1/2 2 1 -1 +1/2 2 1 -1 -1/2 Group Work Write the symbol and draw a possible shape of the orbital occupied by the electron with the following set of quantum numbers: n l ml ms 3 2 0 +1/2 Orbital Energies What are the relative energies of the subshells and orbitals? Hydrogen Atom Orbital Energies Multi-Electron Atom Orbital Energies 1s 2s 2p 3s 3p 3d Relative Energies of Orbitals Electron Configurations Ground State: Electrons are filled so that they are arranged in the most stable arrangement. Excited State: Any arrangement other than the ground state. Filling Electrons into Orbital Diagrams Rules Aufbau principle Electrons fill into the lowest energy orbitals first. Pauli exclusion principle Only two electrons can occupy each orbital, and they must have opposite spin. Hund’s rule Electrons fill singly into different orbitals of the same sublevel before pairing up. Electron Configurations Electron configurations are short-hand notations that show the number of electrons in each subshell. 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 Electron Configurations H 1s1 He 1s2 Li 1s22s1 Be 1s22s2 B 1s22s22p1 C 1s22s22p2 F 1s22s22p5 Ne 1s22s22p6 Electron Configurations Ne 1s2 2s2 2p6 Kr 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 Electron Configurations Write the electron configuration for Na and compare it to Li. Write the electron configuration for Cl and compare it to F. The sublevel that fills last can be identified from the periodic table What is the Electron Configuration for Sulfur? 4f 5f What is the Electron Configuration for Iron and Selenium? 5f 4f Abbreviated Electron Configurations The complete electron configuration for Se is: 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p4 The abbreviated electron configuration is: [Ar] 4s2 3d10 4p4 What is the Complete and Abbreviated Electron Configuration for Silicon? 5f 4f Si The f-Block Elements What is the Abbreviated Electron Configuration for Lead (Pb)? 5f 4f Pb Exceptions Exceptions to the normal filling order are a result of the special stability of the filled and half-filled d-subshell. Cu 1s2 2s2 2p6 3s2 3p6 4s1 3d10 Cr 1s2 2s2 2p6 3s2 3p6 4s1 3d5 Valence Electrons Valence electrons are the electrons in the outer-most shell. H (1) 1s1 He (2) 1s2 Li (1) 1s2 2s1 Be (2) 1s2 2s2 B (3) 1s2 2s2 2p1 C (4) 1s2 2s2 2p2 F (7) 1s2 2s2 2p5 Ne (8) 1s2 2s2 2p6 Valence Electrons Valence electrons are the electrons in the outer-most shell. How many valence electrons in Br? 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p5 H (1) 1s1 He (2) 1s2 Li (1) 1s2 2s1 Be (2) 1s2 2s2 B (3) 1s2 2s2 2p1 C (4) 1s2 2s2 2p2 F (7) 1s2 2s2 2p5 Ne (8) 1s2 2s2 2p6 Valence Electrons Valence electrons are the electrons in the outer-most shell. How many valence electrons in Br? 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p5 H (1) 1s1 He (2) 1s2 Li (1) 1s2 2s1 Be (2) 1s2 2s2 B (3) 1s2 2s2 2p1 C (4) 1s2 2s2 2p2 F (7) 1s2 2s2 2p5 Ne (8) 1s2 2s2 2p6 Group Work Determine the number of valence electrons for each element. Cl Se Pb Cs C Electron Configurations for Ions Common ions form by gaining or losing valence electrons in order to have the same number of electrons as the closest noble gas. Mg 1s2 2s2 2p6 3s2 Mg2+ 1s2 2s2 2p6 = [Ne] Neon’s electron configuration Electron Configurations for Ions When transition metals form cations, the valence s electrons are lost before the d electrons. Fe [Ar] 4s2 3d6 Fe2+ [Ar]4s0 3d6 = [Ar]3d6 Fe3+ [Ar]4s0 3d5 = [Ar]3d5 Electron Configurations for Ions What is the abbreviated electron configuration for Ti and Ti2+?