Properties of Light CHAPTER 4 Light is a form of Electromagnetic Radiation Electromagnetic Radiation (EMR) Form of energy that exhibits wavelike behavior and travels at the speed of light. Together, all forms of EMR form the Electromagnetic Spectrum Speed of Light (C) = 3 x 10 8 m/s (in a vacuum) Arrangement of Electrons in Atoms Anatomy of a Wave Origin Crest Highest point of a wave Where a wave originates/ begins Wavelength (λ) Distance between 2 crests or 2 troughs Amplitude Height of a wave from origin to crest; brightness of light Components of a Wave Wavelength () lambda Units: any unit of length (m) Distance between corresponding points of a wave. Crest to Crest or Trough to Trough Trough Lowest point of a wave Components of a Wave Frequency () nu Units: Hertz (Hz) or 1/s How often a wavelength passes a given point in a specific time, usually one second. 1
Wavelength vs. Frequency Spectrums Range of wavelengths for a series of waves. Wavelength and frequency are inversely proportional As wavelength increases, frequency decreases. Mathematically: c = speed of light = 3.0 x 10 8 m/s λ = wavelength = frequency Electromagnetic Spectrum Consist of all electromagnetic radiation. Continuous Spectrum Spectrum where all wavelengths within a given range are together. Examples: Visible Light, X-Rays, U.V. Light, etc EMR Spectrum 7 Parts Longest wavelength to Shortest: Radio Microwaves Infrared Visible Light U.V. Light X-Rays Gamma-Rays What is the wavelength of EMR that has a frequency of 7.50 x 10 12 Hz? c c 8 3.0x10 m / s = 4.0 x 10-5 m 12 7.5x10 1/s Determine the frequency of light with a wavelength of 4.257 nm. Convert 4.257 nm to m 4.257 nm c = (rearrange for and then solve) ν 7.05 x 10 16 Hz 4.257 x 10 9 m 2
What is the wavelength of U.V light that has a frequency of 4.50 x 10 16 Hz? What is the wavelength of EMR that has a frequency of 6.00 x 10 14 KHz? What region of the spectrum is it found in? 6.00 x 10 17 Hz λ 6.67 x 10 9 m λ 5.00 x 10 10 m Type X rays Quantum Theory Photoelectric Effect Emission of electrons by certain metals when sufficient light shines on them Evidence that light behaves like a particle too (Einstein) Quantum Theory Quantum Finite quantity of energy that can be gained or lost by an atom. Planck s Equation: h = 6.63 x 10 34 Js E = quantum of energy E = h Energy and frequency are directly proportional Photon An individual quantum of light, caused by electrons losing quanta of energy. Quantum Theory Visible Light Emissions As electrons gain quanta of energy they release it in the form of photons. Energy States of an Atom Ground State- an atoms lowest energy level. Excited State- an atoms highest energy level. Line Spectrum - Type of spectrum produced when electrons drop from the excited to the ground states. 3
Useful Equations: C Combining these: hc E Eh What is the energy of U.V. light with a frequency of 4.50 x 10 16 Hz? E = h E = (6.626 x 10 34 J s)(4.50 x 10 16 1/s) = 2.98 x 10 17 J Determine the energy of light that has a wavelength of 450nm. 6.67 x 10 14 1/s 4.50 x 10 7 m E hν 6.626 x 10 34 Js6.67 x 10 14 1/s 4.42 x 10 19 J Problems: A. What is the energy of a photon of green light with a frequency of 5.80 x 10 14 1/s? 3.85 x 10-19 J B. What is the energy, in joules, of a quantum of radiant energy whose wavelength is 6.82 x 10 6 cm? 2.92 x 10-18 J C. Determine the wavelength of a photon that has 3.11 x 10 19 J of energy. 6.40 x 10-7 m D. Determine the frequency, in MHz, of a photon that has wavelength of 1.36 x 10 10 nm. 22.1 MHz (2.21 x 10 1 MHz) Summary Planck restricted the amount of energy that an object emits or absorbs as a quantum. (E = h ) Einstein used Planck s theory and explained the photoelectric effect. Compton light travels as tiny particles, photons. Bohr s Model The Line Spectra demonstrates that the energy levels of an electron in an atom are quantized Similar to the rungs of a ladder, nothing exist in between. (For Hydrogen (1 p + & 1 e - ) 1 st Energy Level n = 1 2 nd & so on n = 2,3,4,5,6, Only electrons dropping from a Higher Level to a Lower one emit (give off) EMR A Number of Possibilities for electron drops 4
Hydrogen s Line Spectrum Several Series of lines are observed Electron Drops to the n = 1 Level Lyman Series (U.V. Range) Electron Drops to the n = 2 Level Balmer Series (Visible Range) Electron Drops to the n = 3 Level Paschen Series (Infrared Range) The Lines become more closely spaced as the levels increase The Bohr model explained spectral lines but not how atoms bonded. Ultimately Displaced Louis de Brogile (French Graduate Student) If light behaves as waves & particles, can particles of matter behave as waves? Derived an Equation h mv Predicts that all matter exhibits wavelike motions. h Planck s Con. m mass v - velocity Large Objects have Small Wavelengths 200 g Baseball @ 30 m/s = 10-32 cm Undetectable Uncertainty of Light Heisenberg s Uncertainty Principle It is impossible to know exactly both the position & the momentum of a particle at the same time. Position then Momentum Small Objects have Large(er) Wavelengths 9.11 x 10-28 g @ 30 m/s = 10-3 cm Very Detectable w/ proper instruments New Ballgame Classical Mechanics vs. Quantum Mechanics 5
Classical Vs Quantum Mechanics 1. Classical adequately describes the motions of bodies much larger than the atoms of which they are composed. It appears that such a body loses energy in any amount. 2. Quantum describes the motions of subatomic particles and atoms as waves. These particles gain or lose energy in packages called quanta. Quantum Mechanical Model Modern description of the electrons derived from the mathematical solution to the Schrodinger equation. Erwin Schrodinger - used wave mechanics to show the electrons about the nucleus emit vibration frequencies that were constant. Quantum Numbers - specify the properties of atomic orbital and their electrons. Principal Quantum Number (n) Main energy level surrounding the nucleus. Tells the approximate size of each orbital. Primary distance from the nucleus. Has possible values of n =1 to n=7 n=1 is the closest to the nucleus n=7 is the farthest from the nucleus. Orbital Quantum Number (l) AKA: Angular Momentum Quantum Number Tells the shape/type of the orbitals. Referred to as sublevels or subshells. Values correspond to specific orbital shapes: l=0 s shape spherical l =1 p shape peanut shaped l=2 d shape daisy shaped l=3 f shape variety of shapes Orbital Shapes s orbital d orbital p orbital f orbital Magnetic Quantum Number (m l ) Orientation of an orbital about the nucleus. Tells the number of orbitals within that sublevel Possible values of l to +l l = 0 (s) m l = 0 1 orbital l = 1 (p) m l = -1, 0, 1 3 orbitals l = 2 (d) m l = -2, -1, 0, 1, 2 5 orbitals l = 3 (f) m l = -3, -2, -1, 0, 1, 2, 3 7 orbitals 6
p orbital, 3 orientations. s orbital, 1 orientation. p x orbital p y orbital p z orbital p xyz orbital d orbital, 5 orientations. f orbital, 7 orientations. Spin Quantum Number (m s ) Indicates two possible states on an electron in an orbital. Since electrons are all negative, they spin in opposing directions in order to occupy the same orbital Value is either +½ or ½ Quantum Number Rag: Quantum Numbers Magnetism Caused by the motion of electrons about the nuclei of atoms. Diamagnetism substance is weakly repelled by a magnetic force. Paramagnetism substance is weakly attracted by a magnetic force. Ferromagnetism Strong attraction by a magnetic force. 7
Assigning Quantum Numbers You can identify the four quantum numbers of any electron in your atom: 3p -1 0 +1 n = 3 (principal energy level) l = 1 ( p type orbital) m l = -1 (first orbital) m s = + ½ ( up arrow) Try: 2s Quantum Numbers Principal Sublevels Orbitals Energy Level N=1 1s 1s N=2 2s, 2p 2s(one) + 2p(three) N=3 3s, 3p, 3d 3s(one) + 3p(three) + 3d (five) N=4 4s, 4p, 4d, 4f 4s(one) + 4p(three) + 4d (five) + 4f(seven) Quantum Numbers Principal Q.N. # Orbitals per Main level (n 2 ) # Electrons per main level (2n 2 ) 1 1 2 2 4 8 3 9 18 4 16 32 Quantum Numbers Orbital Max # electrons s 2 p 6 d 10 f 14 Rules for Electron Arrangement Aufbau Principle Electrons occupy the lowest energy level that will receive it. Pauli Exclusion Principle In order to occupy the same orbital, electrons must have opposing spins No two electrons can have the same set of 4 quantum numbers (n,l,m l,m s ) Hund s Rule Orbitals of equal energy each receive one electron (all of equivalent spin) before any receive two. Bus Seat Rule Order of Energy Levels Necessary to follow the Aufbau Principle This is the energy order, not geographical order! Number - principal quantum number; the main energy level Letter orbital quantum number; the shape Useful Diagram: 1s 2s 3s 4s 5s 6s 7s 2p 3p 4p 5p 6p 7p 3d 4d 5d 6d 7d 4f 5f 6f 7f 8
Orbital Notation (Diagrams) Orbital Notation Each orbital represented by a line Each electron is represented by an Arrow: + ½ ( ) -½ ( ) REMEMBER: s sublevels contain 1 orbital p sublevels contain 3 orbitals d sublevels contain 5 orbitals f sublevels contain 7 orbitals Examples: H (1 e -1 ) He (2 e -1 ) 1s 1s Orbital Notation (Diagrams) Write the orbital notation for the following elements: Al Zn P Cl 1s 2s 3s 4s 5s 6s 7s 2p 3p 4p 5p 6p 7p 3d 4d 5d 6d 7d 4f 5f 6f 7f Al Zn P Cl Solutions 1s 2s 2p 3s3p 1s 2s 2p 3s 3p 4s 3d 1s 2s 2p 3s 3p 1s 2s 2p 3s 3p Warm Up Write an orbital diagram for Nickel: 1s 2s 2p 3s 3p 4s 3d Identify the quantum numbers for this electron: 3d _ n = 3 l = 2 m l = 0 m s = +1/2 Electron-Configuration Notation Shorthand notation for Orbital Diagrams Eliminates the lines & arrows Superscripts are used to illustrate the number of electrons in the sublevel Same order of sublevels Examples H (1 e -1 ) - 1s 1 He (2 e -1 ) - 1s 2 Li (3 e -1 ) - 1s 2 2s 1 Electron-Configuration Notation Write the electron-configuration for the following: Br Pb Cs Kr Electron Configuration Polka: 9
Solutions Br : 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 5 Pb : 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 6 5s 2 4d 10 5p 6 6s 2 4f 14 5d 10 6p 2 Cs : 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 6 5s 2 4d 10 5p 6 6s 1 Kr : 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 6 Identifying Unpaired Electrons Paired electrons when 2 electrons are within the same orbital. 1s Unpaired electrons when a single electron is within an orbital. 1s Identifying Unpaired Electrons Noble Gas Configuration Na : 1s 2 2s 2 2p 6 3s 1 1 unpaired electron O : 1s 2 2s 2 2p 4 2 unpaired electrons B : 1s 2 2s 2 2p 1 1 unpaired electron 3s 2s 2p 2s 2p Shortest method of writing the electron configurations. Use the last noble gas to occur prior to the element that is being configured. Start at the next sublevel, where n equals the period in which the element being configured can be found. Example: Zr Noble gas would be Kr and start configuration at 5s. [Kr] 5s 2 4d 2 Writing in noble gas configuration Write the noble gas configuration for the following: V Rb I Hg U W Answers V [Ar] 4s 2 3d 3 Rb [Kr] 5s 1 I [Kr] 5s 2 4d 10 5p 5 Hg- [Xe] 6s 2 4f 14 5d 10 U - [Rn] 7s 2 5f 4 W- [Xe] 6s 1 4f 14 5d 5 10
Exceptions to the Aufbau Principle All elements prefer a more stable configuration of electrons. Copper According to Aufbau Principle: 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 9 4s is full, 3d is partially full Fully filled and ½ filled orbitals are more stable than orbitals that are only partially filled According to Nature: 1s 2 2s 2 2p 6 3s 2 3p 6 4s 1 3d 10 4s is ½ full, 3d is full Elements that are 1 shy of a full or ½ filled d orbital configuration will have electrons transfer from the s to the d to reach this stable state. Chromium According to Aufbau Principle: 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 4 4s is full, 3d is partially full Notable configurations: Copper and Chromium According to Nature: 1s 2 2s 2 2p 6 3s 2 3p 6 4s 1 3d 5 4s is ½ full, 3d is ½ full Bottom Line: Full>Half Full>Partially Full Lewis Dot Notation Describes the number of valence electrons in an atom as dots around the symbol. Valence electron - refers to electrons found in the highest occupied energy level electron within an atom. 5 1 4 6 X 8 2 3 7 Lewis Dot Notation Draw the electron-configuration and electron-dot notation for Nitrogen. 1s 2 2s 2 2p 3 The highest energy level is 2. There are 5 valence electrons in Nitrogen. N Lewis Dot Notation Write the noble gas-configuration and electron dot notation for the following. Al As I Sr Lewis Dot Notation Al Al : [Ne] 3s 2 3p 1 As : [Ar] 4s 2 3d 10 4p 3 I : [Kr] 5s 2 4d 10 5p 5 Sr : [Kr] 5s 2 Sr I As 11