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10 Modern Atomic Theory and the Periodic Table The amazing colors of fireworks result from electron transfer between energy levels of atoms. Foundations of College Chemistry, 14th Ed. Morris Hein and Susan Arena Copyright © 2014 John Wiley & Sons, Inc. All rights reserved. Learning Objectives Electromagnetic Radiation • List the 3 basic characteristics of electromagnetic radiationwavelength, frequency and speed • Calculate wavelength, frequency using the speed of light. The Bohr Atom • Explain the relationship between the line spectrum and the quantized energy levels of the electron cloud. • Describe the Lyman, Paschen and Balmer series exhibited in the hydrogen model as discovered by Bohr . • Differentiate between continuous, emission and absorption spectrums. • Describe the history of quantum theory. Modern Atomic Model-Quantum Atom Model • Describe the principal energy levels, sublevels and orbitals of an atom through quantum numbers n, l. • Explain the relationship between energy and electron position. Atomic Structure • Use quantum numbers to find elements on the periodic table. • Use the guidelines to write full, short-cut and box diagram electron configurations. • Describe orbitals of an atom with quantum numbers ml , ms . • Describe and electron using 4 quantum number. Electron Structures and the Periodic Table • Describe how the electron configurations of the atoms relate to their position and chemical reactivity. • Predict Oxidation states using electron configuration. Electromagnetic Radiation Electromagnetic Radiation: A form of energy that runs a continuum from radio to X-rays, visible light to microwaves. Each form of radiation shares common characteristics: they display wavelike properties and travel at the same speed. Basic Properties of Waves Wavelength (λ): The distance between two similar points in consecutive waves; such as from crest to crest or trough to trough. SI Units = meters, m Frequency (n or f ): The number of waves that pass a point per unit of time. SI Units = Hertz, Hz or 1/sec=(s-1) Wavelength and frequency are inversely related. Speed (v or s): how fast a wave moves through space. Parts and Properties of Waves Amplitude (Ψ ):The distance between the highest or lowest point on a wave to the resting line. SI Units = meters, m Crest:: The highest point in a wave. Trough: The lowest point in a wave. Resting line: The imaginary line that travels through the middle of the wave. Ambassador Waves transmit Energy!!! The amount of energy present is seen in the amplitude and frequency of the wave. Electromagnetic Radiation Electromagnetic Radiation Electromagnetic Spectrum: The full range of electromagnetic radiation, arranged based on wavelength. Electromagnetic radiation has both wave-like and particle properties. Radiation can behave like tiny packets (“bundles”) of energy called photons. © 2014 John Wiley & Sons, Inc. All rights reserved. Speed of Light “C” = frequency x wavelength c = lf c = 3.00 x 108 m/s 3.00 x 108 m/s = lf 1. a) Calculate the wavelength of a radio wave with a frequency of 1.1x106 Hz. f =1.1x106 Hz 3.00 x 108 m/s = l (1.1x106 Hz) 3.00 x 108 m/s = 270 m 1.1x106 Hz b) What part of the EMF does this fall into? Radio snd TV waves. How many waves will pass in a 5.0 seconds? Recall, frequency describes how many waves pass per second, thus 1.1x106Hz = 1.1x106waves per second 1.1x106 waves x 5.0 seconds = 5.5x106 waves. second 2. What is the frequency of an electromagnetic wave that has a wavelength of 2.56x10-12m? 3.00 x 108 m/s = l f 3.00 x 108 m/s = 2.56x10-12m∙f 3.00 x 108 m/s =f = 1.17x1020 Hz 2.56x10-12m What EMF wave has a wavelength of 2.56x10-12m? A gamma ray or very energetic x-ray. The Bohr Atom At high temperatures or when high voltages are applied, elements radiate (emit) colored light. When this light is passed through a prism, a set of brightly colored lines result. Line spectrum of hydrogen These line spectra indicate the light emitted has only specific wavelengths/frequencies. Each element possesses a characteristic and unique line spectrum. © 2014 John Wiley & Sons, Inc. All rights reserved. The Bohr Atom How can these experimental results be explained? From his study of the line spectrum of hydrogen, Bohr proposed a revised theory of the atom. Bohr suggested electrons exist in specific regions at defined distances from the nucleus. The electrons then move about the nucleus in circular orbits at a fixed distance from the nucleus. © 2014 John Wiley & Sons, Inc. All rights reserved. Bohr Atom Continued Bohr’s Model of the Hydrogen Atom FYI: 95% of all atoms in the universe are hydrogen. Hydrogen atoms exist in only specified energy states. Hydrogen atoms can absorb only certain amount of energy, and no others. 3. When excited hydrogen atoms lose energy, they lose only certain amount of energy, emitted as photons. 4. The different photons given off by hydrogen atoms produce the color line seen in the bright-light spectrum of hydrogen. i)The greater the energy lost by the atom, the greater the energy of the photon. 1. 2. The Bohr Atom Continued… Bohr also suggested energy absorbed or emitted by an atom is quantized (has discrete fixed units). Bohr proposed that electrons can orbit the nucleus at different distances. Each orbit is a distinct, discrete (quantized) energy level. When an atom absorbs energy, the electrons can be promoted to higher energy levels. When an atom emits energy, the electrons can decays to a lower energy level. © 2014 John Wiley & Sons, Inc. All rights reserved. The Bohr Atom Ground state: lowest energy level for an atom. Each line in the spectrum corresponds to emission of energy as an electron relaxes from a higher to lower energy level. Color of light emitted depends on the gap between the energy levels. Bohr’s theory worked very well to explain and predict the line spectrum of hydrogen…. BUT…. Bohr’s theory broke down in multi-electron systems. © 2014 John Wiley & Sons, Inc. All rights reserved. n = 4 ionization n = 3 second excited state Paschen (IR) n = 2 first excited state Balmer (Visible) n = 1 Ground state Lyman (UV) Lyman Series: Produces Ultraviolet light waves Excited electrons drop from a high energy level back to energy level 1 to produce UV light. Balmer Series: Produces visible light in the form of color Excited electrons drop from a high energy level back to energy level 2 to produce visible light. Paschen Series: Produces infrared light. Excited electrons drop from a high energy level back to energy level 3 to produce infrared light. Spectrum Facts • Electrons will remain at the lowest possible energy level that produces the most atomic stability. • More energy is required to exist farther away from the nucleus. This equates to higher potential energy. • Electrons that absorb energy can move to an energy level further away from the nucleus. • When the electrons return to the lower energy level, they give back the energy, in the form of light (color), that was absorbed. Go Packers Atomic Spectra • • • Discrete energy levels in any atom or molecule (quantum mechanics) Transitions between levels produces (or absorbs) quanta of light, also called photons. Bigger energy steps produce more powerful photons (ie..shorter wavelength, blue, UV) Emission Spectra’s show discrete colored lines. The lines correspond to photons of discrete energies that are emitted when excited atomic states in the gas make transitions back to lower levels. Background in black. A continuum spectrum is an emission spectrum where the lines over-lap with each other and we an no longer distinguish the individual emission lines. An absorption spectrum occurs when light passes through a cold, dilute gas and atoms in the gas absorb energy at specific frequencies. The absorption spectrum is the opposite of an emission spectrum. Continuous Spectrum Emission Spectrum Absorption Spectrum I believe electrons move like waves. Albert Einstein Get a grip Plank, electrons move like particles Max Plank •1901Plank found that atoms can only adsorb and emit energy in distinct quantities; (Quanta) this showed that energy displayed particle-like properties. Planck’s equation for electron energy is E = hf h = 6.6264x10-31 J-s f = frequency •1905: Einstein suggested that energy itself is quantized and can be viewed as a string of particles called photons. He established that energy has mass. Einstein described electron motion through the famous equation E = mc2 m = mass c= speed of light A photon checks into a hotel and is asked if he needs any help with his luggage. He says, "No, I'm traveling light." Ha Ha Ha!!!!!!!!!!!!!!!!!!!!!!!! Photoelectric effect •Einstein used Planck’s equation to explain the photoelectric effect •Electrons are ejected from the surface of a metal when light shines on the metal. •For each metal, a minimum frequency of light is needed to release electrons. • Red light has too low a frequency to cause ejection of electrons from sodium while faint violet light releases electrons easily. Einstein proposed that light consists of quanta of Energy that behave like tiny particles of light. He called these energy quanta photons. Einstein suggests every photon carries an amount of energy described by Planck’s equation: E = hn deBroglie (Mid-1920’s) found a way to please them both: the “Wave-particle duality of Nature” Einstein E= mc2 Planck and hf = E mc2 = hf mc2 = h c l Since both equations equal energy, deBroglie set them equal to each other. Recall, c = lf Thus, f = c/ l Substitute… The final equation l = hc = h Solve equation for l simplify predicts the wavelength mc2 mc of a particle at a given l = h Let c = velocity mass and velocity. Thus mv combining both men’s ideas. Ultimately, this suggests electrons act both like waves and particles. Both matter and radiation possess a remarkable duality of character, as they sometimes exhibit the properties of waves, at other times those of particles. Now it is obvious that a thing cannot be a form of wave motion and composed of particles at the same time - the two concepts are too different. (Werner Heisenberg, on Quantum Theory, 1930) The famous Heisenberg uncertainty principle was first proposed by Werner Heisenberg in 1927. According to this principle, it is impossible to simultaneously measure the position and momentum of a particle (exactly). Indeed, a good knowledge of the particle's position implies a poor knowledge of its momentum, and vice versa. Note that the uncertainty principle is a direct consequence of representing particles as waves. In the mid-1920s, Erwin Schrodinger, building on the dual nature of matter, began focusing on the wave-like properties of the electron by visualizing them like standing waves. Schrodinger treatment of the electron as a wave enabled him to develop a mathematical and graphical model that described electron behavior. His mathematical model gave us the position and shape of electron orbitals. He suggests that 90% of the time, electrons with a designated amount of energy existed in a specific orbital. Basically, he figured out the shapes for s, p, d and f orbitals. Max Born verified Schrodinger’s probability. Arthur Compton (1892-1962) demonstrated that a photon could collide with an electron. Incident Photon Motion of Electron after collision (Random energy) Motion of photon After collision The Darkroom Mystery You have a friend who is taking a photography class at school. She is learning to be a good photographer as well as how to process her film. So she regularly uses a darkroom for developing her picture. The darkroom is equipped with a dim red light so that your friend can see enough to handle the film and the developing solution. One day when the red bulb burned out, your friend replaced it with a dim yellow bulb that she found. She and several other students were later dismayed when they ruined their film while using the darkroom. When your friend told you of this disaster, you immediately understood what had happened. Explain what happened to your friend’s film. Arthur Compton verified energy has mass, as Einstein suggested. He demonstrated that a photon could collide with an electron. In 1925 Wolfgang Pauli enunciated his exclusion principle - "under no circumstances whatsoever may two electrons have precisely the same set of quantum numbers" The Dual Particle/Wave Nature of Matter Quantum mechanics deal in electron probabilities; orbits from Bohr theory are replaced by orbitals. Orbitals: regions of space with a high probability of finding an electron. An orbital for a hydrogen atom. © 2014 John Wiley & Sons, Inc. All rights reserved. Modern Atomic Model Quantum Theory Electron Cloud ( Home of the electrons.) · Region, surrounding the nucleus, made up of mostly empty space. · Can be described as the atoms volume. · A region where 90% of the time you will find electrons is called an orbital. Electrons · Only moveable part of the atom. · Housed in specific regions corresponding to energy requirements; orbitals. · Electrons are described using four-quantum numbers. n, l, ml , ms n l n = Principal quantum number ml ms Describes the energy level of the electron which often corresponds to the row number n = 1, 2, 3, 4, etc.. Maximum number of electrons in a principal quantum number is 2n2 o when n = 2; 2 (2)2 = 8, when n = 4; 2(4)2= 32 Each energy level is divided into sublevels. o The sublevels have different energy requirements. The number of sublevels in each principal energy level corresponds to the principal quantum number. o Example. When n = 2, that means there are 2 sublevels in this principal energy level. Energy Levels of Electrons Bohr’s idea of quantized energy levels does have parallels in quantum mechanics. For example, quantum mechanics predicts discrete, quantized principal energy levels for electrons in an atom. Principal energy level (n): provides a general idea of the distance of an electron from the nucleus (as n increases, so does the distance from the nucleus) n can be a positive integer (1,2,3, etc.) © 2014 John Wiley & Sons, Inc. All rights reserved. l= Sublevel Shape There are four sublevel shapes and they are described by the letters s, p, d, and f. Each of the sublevels are composed of orbitals. Orbitals are areas that can hold a maximum of 2 electrons. o s = sharp (composed of 1 orbital) Quantum number = 0 o p = principal (composed of 3 orbitals) Quantum number = 1 o d = diffuse (composed of 5 orbitals) Quantum number = 2 o f = fundamental (composed of 7 orbitals) Quantum number = 3 1s < 2s < 3s < 4s < 5s < 6s < 7s P-sublevel looks like dumbells The p-sublevel continues to get further away from The nucleus as “n” increases. Principal quantum level n =3 Contains three sublevels/orbitals (3s, 3p and 3d orbitals) The 5 3d orbitals have unique shapes relative to s and p orbitals. 10 total electrons can occupy the 5 d orbitals of a subshell. © 2014 John Wiley & Sons, Inc. All rights reserved. Principal quantum level n =4 Contains four sublevels/orbitals -(4s, 4p, 4d and 4f ) The 7 - 4f orbitals have unique shapes relative to s and p orbitals. 14 total electrons can occupy the 7 f orbitals. As the electron cloud build, the region fills with the uniquely shaped orbitals. Electron Configurations are AWESOME!!!! Electron configurations: •Show the number of electrons in the atom •Show which principal quantum levels are involved •Show which sublevels are involved •More information can be gleaned from the electron configuration and thus…there is more information to come. 1s22s22p63s23p63d104s24p64d104f145s25p65d16s2 Luteium The Aufbau principle is really a thought process in which we think about building up an atom from the one that precedes it in atomic number, by adding a proton and neutrons to the nucleus and one electron to the appropriate atomic orbital. Recall… The number of sublevels , s,p,d,f, in each principal energy level, 1, 2, 3…7, corresponds to the principal quantum number. This holds true through energy level 4. When n =1 •Energy level 5 only uses 4 sublevels, •Energy level 6 only uses 3 sublevels •Energy level 7 only uses 2 sublevels. 6 2 3 4 5 7 1s 2s 2p 3s 3p 4s 4p 5s 5p 6s 6p 7s 7p 3d 4d 4f 5d 5f 6d We simply do not have enough elements to require more than 4 sublevels at this time. Electrons enter the lowest energy sublevels first. The energy requirements of some sublevels may surprise you. Let’s take a look. Notice that sublevel 4s is filled before sublevel 3d. That is due to the lower energy requirement for 4s when compared to 3d. 1s 2s 3s 4s 5s 6s 7s 2p 3p 4p 5p 6p 7p 3d 4d 5d 6d 4f 5f As you followed the arrows you saw the pathway for entering the lowest energy levels first. The s and p sublevels have row numbers and principal quantum numbers that correspond. The row numbers and principal quantum numbers of the d and f sublevels do not correspond. Electron Filling Sublevel Filling Diagram © 2014 John Wiley & Sons, Inc. All rights reserved. Three types of electron configurations: Lutetium Full Configuration: 1s22s22p63s23p63d104s24p64d104f145s25p65d16s2 Short-cut configuration: [Xe] 4f145d16s2 Box Diagram Configuration Yikes… you need to show every electron arrow! So let’s NOT do lutetium!! Sodium : Full: Box : 1s22s22p63s1 The box diagram uses the full configuration and it represents each electron with an arrow. Short-cut: 1s2 [Ne] 3s1 2s2 2p6 3s1 ml = Magnetic orientation This letter describes the orbital’s magnetic orientation about the x, y, and z axes. ml tells us how the electron cloud surrounding the nucleus is directed in space. ml is described numerically using 0, 1, 2, 3, 4 and so on. o The + sign indicates a positive direction, the – sign indicates a negative direction. o ml for the s orbital= 0 o ml for the p orbitals= 0, 1 (-1, 0, 1) o ml for the d orbitals= 0, 1, 2 (-2, -1, 0, 1, 2) o ml for the f orbitals= 0, 1,2,3, (-3, -2,-1, 0, 1, 2, 3) -3 -2 -1 0 1 2 3 How many electrons can fit in an orbital? Pauli Exclusion Principle: an atomic orbital can hold two electrons, which must have opposite spins. Electron spin is represented by arrows ( or ) ms = Electron Spin (±½) This quantum number describes the direction of the electron’s spin. The 2 electrons in each orbital will spin in opposite directions to reduce repulsion. Each electron can be described by assigning the 4 quantum numbers 3d7 n 3 l 2 s=0, p=1 d=2, f=3 Recall there are 5d orbitals -2 ml -1 -1 ms -½ 0 1 Electrons enter 1 at a time. ±2, ±1, 0Numbers > 5 are -½ Numbers < 5 are +½ 2 Level n 1 2 3 4 5 6 7 Total number of electrons in level, 2n2 2(1)2 = 2 2(2)2 = 8 2(3)2 = 18 2(4)2 = 32 2(5)2 = 50 2(6)2 = 72 2(7)2 =98 Number of sublevels, n 1: s 2: s, p 3: s, p, d 4: s, p, d, f 5: s, p, d, f, ? 6: s, p, d, f, ?, ? 7: s, p, d, f, ?, ?, ? Sublevel Orbitals, n2 (1)2= 1 (2)2= 4 (3)2= 9 (4)2= 16 (5)2= 25 (6)2= 36 (7)2= 49 Energy Levels of Electrons Practice What is the maximum number of electrons that can occupy the n = 3 sublevel? a. 8 b. 2 c. 18 d. 10 The n = 3 sublevel has 3 types of orbitals: s (1), p (3), and d (5). Two electrons can occupy each orbital. (9 x 2 = 18) © 2014 John Wiley & Sons, Inc. All rights reserved. Atomic Structure of the First 18 Elements Valence Electrons: electrons located in the highest energy (outermost) orbitals of an atom. Oxygen Example Electron configuration 1s22s22p4 Outermost valence electrons are in the n =2 subshell; oxygen has 6 total valence electrons. The column number (1A-7A) in the periodic table gives the valence electrons of an element. Valence electrons participate in bonding to form molecular compounds (see Chapter 11). © 2014 John Wiley & Sons, Inc. All rights reserved. Predicting Oxidation State • We can predict the oxidation state of elements by looking at all the valence electrons relative to stability. • Transition and inner transition metals can have more than one oxidation state because now that some electrons are housed in the “d or f” orbitals. • There are different ways to enhance stability. Rules for Stability: Most stable: all sublevels are full 2nd most stable: all sublevels are full or half-full 3rd most stable: d or f sublevels enlist promotion of 1 or 2 electrons from the s-orbital to create a half-full d or f sublevel. Least stable-desirable: one sublevel is neither full or half-full o d and f sublevels can have oxidation states result using promotion (columns 6 and 11) or one or more oxidation states resulting from giving away different numbers of electrons. Learn by doing! Predicting Oxidation States of Copper 1 electron from 4s2 can be promoted to 3d10 1s22s22p63s23p64s23d9 1s22s22p63s23p64s13d10 Written numerically, it is easy to see what electron will be given away during chemical reactions. 1s22s22p63s23p63d10 4s1 = Cu+1 If no promotion occurs, what electrons will be given away? Resulting in 1s22s22p63s23p63d9 = Cu+2 Using the short-Cut form is even easier [Ar] 4s23d9 [Ar] 4s23d9 [Ar] 4s13d10 = Cu+1 = Cu+2 [Ar] 3d9 4s2 Electron Filling Practice The electron configuration [Ar] 4s1 is the ground state electron configuration of: a. K b. P c. Fluorine The element contains 1 valence electron in the fourth period (due to n = 4). d. Na © 2014 John Wiley & Sons, Inc. All rights reserved. Electron Filling Practice The electron configuration [Ne] 3s23p1, is the ground state electron configuration of: a. Na b. Al c. Ar The element contains 3 valence electrons in the third period (due to n = 3). d. S © 2014 John Wiley & Sons, Inc. All rights reserved. Chemical Periodicity Groups of elements show similar chemical properties because of similarities in their valence electrons. Group number equals the total number of outermost valence electrons. Example Group 7 – contains the ns2np5 valence configuration © 2014 John Wiley & Sons, Inc. All rights reserved.