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UNIT 5 – Models of Atomic Theory Student Objectives You Have A TEACHER NOTES 2011 UNIT 5 | 1 UNIT 5 – Models of Atomic Theory Student Objectives You have a team of enthusiastic teachers longing to help you be able to… 1. Perform calculations involving the speed of light (c), the wavelength (λ), and the frequency (f) of electromagnetic radiation (emr) 2. Perform calculations involving the energy, the wavelength (λ), and the frequency (f) of electromagnetic radiation. 3. Place forms of electromagnetic radiation in correct energy order on an electromagnetic spectrum. 4. Compare the energy, frequency, and wavelength of electromagnetic radiation. 5. Label an energy level diagram, indicating both excitation and relaxation 6. Describe the four quantum numbers used to define the region of space that has a 90% probability of finding an electron with a given energy. 7. Explain the information provided by each of the quantum numbers. 8. Distinguish between an energy level, sublevel, and an orbital. 9. List the allowable quantum numbers for each energy level. 10. Draw an orbital diagram using the Aufbau principle, Hund’s rule, and the Pauli Exclusion Principle. 11. Write the electron configuration for an atom. LIGHT AND ELECTRON CONFIGURATION Much of what we know about the atom has been learned through experiments with light; thus, you need to know some fundamental concepts of light in order to understand the structure of the atom, especially the placement of the electrons. I. Light A. Characteristics of Light 1. Has "Dual" nature (or split personality) 2. There are times in which it behaves like a WAVE and other times when it behaves like a PARTICLE (called a photon) B. Light as a WAVE: You must be able to describe its wavelength, frequency, and velocity (speed) 1. Speed of light in a vacuum is the most accurately known constant, c, in the universe. c = 3.0 x 108 meters/sec OR 3.0 x 1017 nm/sec (assuming a vacuum) CHEMISTRY TEACHER NOTES 2011 UNIT 5 | 2 2. Wavelength is represented by the Greek letter, lambda ( ). It is the length between corresponding parts of adjacent crests and can be expressed in ANY units of length you choose (feet, inches, meters, kilometers, etc) 3. Frequency is represented by the Greek letter, nu () or the letter f. It is the number of wave crests which pass a given point in 1 second. Its units are:cycles / second, sec-1,or Hertz (Hz). II. Electromagnetic Spectrum: A. Visible Light: considered to have a wavelength of between 700 nm and 400 nm. The longest wavelength in visible is red (about 700 nm) and the shortest visible wavelength is violet (about 400 nm). The only thing that makes one color of light different from another is its wavelength and frequency; the velocity is always the same (the speed of light!). B. Continuous Spectrum: Has all the energies of visible light. The colors of visible light in order from longest wavelength to shortest spell out: ROY G BIV. C. Entire Range of light energy: Includes ALL energies of light. Become very familiar with the electromagnetic spectrum!!! Example 5-1: Label the following electromagnetic spectrum from low energy on the left hand side to high energy on the right hand side. AM/FM& TV MICRO- INFRA- VISIBLE ULTRA- X-RAYS GAMMA (RADIO) WAVES RED (IR) VIOLET RADIATION (UV) Long Short 700 nm R O Y G B I V 400 nm Low f High f Low E I better memorize High E this by the next quiz… argh! RED MARTIANS INVADE ROYGBIV USING X-RAY GIZMOS CHEMISTRY TEACHER NOTES 2011 UNIT 5 | 3 III. Light as a WAVE: c = f where c = speed of light (3.0 x 108 m/sec OR 3.0 x 1017 nm/sec) Note: BE CAREFUL OF THE UNITS YOU USE!!! If speed of light is in meters, then wavelength must be in meters. Example 5-2: Does a longer or a shorter wavelength have the HIGHER frequency? Shorter wavelength Example 5-3: Are wavelength and frequency directly or inversely related? Inverse Example 5-4: If the wavelength is known to be 550 nm, what is its frequency? 3.0x1017 f 5.45x1014s 1 550 Example 5-5: If the frequency of light is known to be 9.45 x 1014 s-1, is the light visible? HINT: Calculate the wavelength in nm. 3.0x1017 14 317nm 9.45x10 NO, it is not visible Example 5-6: If the wavelength of light is 7.23 x 10-5 cm, is it visible? NO, it is not visible 2 5 1x10 m 1nm 2 7.23x10 cm 7.23x10 nm 9 1cm 1x10 m CHEMISTRY TEACHER NOTES 2011 UNIT 5 | 4 IV. Light as Particles: When light behaves as a particle, it is called a PHOTON. We are interested in how much energy they have. The unit of energy we will use is the Joule, J, and the equation which allows us to calculate the energy of one photon is: hc E hf OR E where h= Planck's Constant = 6.63 x 10─34J•sec photon photon Example 5-7: What is the energy of a photon of light whose frequency is 7.85 x 1015 Hz? Is this visible? E 6.63x10347.83x1015 5.19x1019J/photon 3.0x1017 38.2 nm NOT Visible 7.85x1015 Example 5-8: If a light has a wavelength of 550 nm, what is the energy of one photon of this light? 34 17 6.63x10 3.0x10 19 Ephoton 3.62x10 J/photon 550 Example 5-9: If one photon of light is known to have energy of 3.33 x 10─19 J, is it visible? hc 6.63x10343.0x1017 -19 597nmYES E photon 3.33x10 CHEMISTRY TEACHER NOTES 2011 UNIT 5 | 5 V. Bohr Atom Don’t Forget!! Bohr said that electrons are in energy levels!!! But he also proposed the planetary model. Silly ole Bohr. A. electrons possess certain fixed amounts of energy B. electron cloud made up of energy levels which are like the rungs of a ladder BUT they are not EQUALLY SPACED C. amount of energy possessed by an electron determines its energy level D. levels farther from nucleus represent higher energy E. in order to move from one energy level to another, electrons must gain or lose an exact amount of energy known as a Quantum. **The ground state is where the electron normally hangs out. The excited state is where the electron has more energy than it normally has (meaning it has gained some quanta of energy!) n= ___5 n= ___4 n= ___3 n= ___2 n= ___1 e- ____gains energy e- ____loses EMR (energy) Process___________Excitation, light Process___________Relaxation, light absorption emission GROUND STATE: GroundAll electrons State:__________________________ in lowest energy available EXCITED STATE: When an electron temporarily moves to a higher energy level CHEMISTRY TEACHER NOTES 2011 UNIT 5 | 6 VI. Emission Spectra v. Absorption Spectra Niels Bohr studied the emission spectrum of hydrogen to determine that electrons are on different energy levels. Every element has a unique emission/absorption spectrum. This is one way to identify an element. Emission Spectra: the light emitted as electrons fall to lower energy levels Electrons emit photons of a specific energy. If the wavelength is in the visible range, we see bands of light against a black background. Absorption Spectra: the light absorbed by electrons as they move to higher energy levels Electrons absorb photons of a specific energy. If the wavelength is in the visible range, we see black bands in the rainbow. VII. Schrodinger Model: Quantum Mechanical Model (1926) A. AGREES with Bohr about quantized energy levels B. DIFFERS: does not define an EXACT path called an orbit. The math describes a region in space with a high PROBABILITY of finding an electron. Unfortunately, we still call this an ORBITAL. ELECTRON LOCATION: The location of the electron is described by 4 quantum numbers: n, l, ml, and ms. Think of these as being the “address” for an electron’s probable location! (State, city, street, house number… each gets more and more specific.) n= ENERGYLEVEL (Principle Quantum Number) The higher the value of n… the further away from the nucleus the electrons are, and the higher the energy level The maximum number of electrons in any energy level: #e- = 2n2 Nucle us (where n=energy level) n = 1 n = 2 n = 3 Example 5-10: Fill in the chart below. n = 4 Energy n = 1 n = 2 n = 3 n = 4 n = 5 n = 6 n = 7 Level (n) Maximum 2 8 18 32 50 72 98 number of electrons CHEMISTRY TEACHER NOTES 2011 UNIT 5 | 7 l = SUBLEVELS (Second Quantum Number) Each energy level is divided into SUBLEVELS Sublevels are regions in space with a specific SHAPE. Sublevels are labeled by the letters s,p,d,f,g,h… (The only ones we are going to work with and that you need to know are s, p, d, and f.) Electrons in the sublevels have a specific amount of energy. Energy of electrons in the sublevels: s < p < d < f. (s-electrons have the least energy; f- electrons have the most energy.) Each energy level (n) has one more sublevel than the previous energy level. Here is a trick for remembering the order of the sublevels: Silly People Do Flips! Example 5-11: Fill in the chart below. Energy Level (n) Sublevels Present 1 s 2 s, p 3 s, p, d 4 s, p, d, f mℓ = ORBITALS (Magnetic Quantum Number) Each sublevel contains ORBITALS which are regions of high PROBABILITY for finding electrons… the mℓ indicates the ORIENTATION of those orbitals! Each orbital can hold only TWO electrons The surface of the orbital is drawn to represent area where any particular electron can be found 90% of the time.
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