The Quantum Mechanical Atom CHAPTER 7 Chemistry: The Molecular Nature of Matter, 6 th edition By Jesperson, Brady, & Hyslop
CHAPTER 8: Quantum Mechanical Atom Learning Objectives q Light as Waves, Wavelength and Frequency q The Photoelectric Effect, Light as Particles and the Relationship between Energy and Frequency q Atomic Emission and Energy Levels q The Bohr Model and its Failures q Electron Diffraction and Electrons as Waves q Quantum Numbers, Shells, Subshells, and Orbitals q Electron Configuration, Noble Gas Configuration and Orbital Diagrams q Aufbau Principle, Hund s Rule, and Pauli Exclusion Principle, Heisenberg Uncertainty Principle q Valence vs Inner Core Electrons q Nuclear Charge vs Electron Repulsion q Periodic Trends: Atomic Radius, Ionization Energy, and Electron Affinity 2
Electromagnetic Radiation Light Energy is a Wave Electromagne,c Spectrum 3
Electromagnetic Radiation Light Energy is a Wave Waves travel through space at speed of light in vacuum c = speed of light = 2.9979 10 8 m/s Can define waves as systematic fluctuations in intensities of electrical and magnetic forces that vary regularly with time and exhibit a wide range of energy. 4
Electromagnetic Radiation Light Energy is a Wave Wavelength (λ) Distance between two successive peaks or troughs Units are in meters, centimeters, nanometers Frequency (ν) Number of waves per second that pass a given point in space Units are in Hertz (Hz = cycles/sec = 1/sec = s 1 ) Related by λ ν = c 5
Electromagnetic Radiation Light Energy is a Wave Amplitude Maximum and minimum height Intensity of wave, or brightness Varies with Kme as travels through space Nodes Points of zero amplitude Place where wave goes though axis Distance between nodes is constant 6
Electromagnetic Radiation Ex: Converting between Wavelengths and Frequency Example: The bright red color in fireworks is due to emission of light when Sr(NO 3 ) 2 is heated. If the wavelength is ~650 nm, what is the frequency of this light?! = c " = 3.00!108 m/s 650!10 "9 m ν = 4.61 10 14 s 1 = 4.6 10 14 Hz Example: WCBS broadcasts at a frequency of 880 khz. What is the wavelength of their signal?! = c! =!.""! #"$ %&'( $$"! #"! / ( = 341 m 7
Electromagnetic Radiation Electromagnetic Spectrum low energy, long waves high energy, short waves 8
Electromagnetic Radiation Electromagnetic Spectrum 9
Electromagnetic Radiation Electromagnetic Spectrum Visible light Band of wavelengths that human eyes can see 400 to 700 nm make up spectrum of colors White light is a combinakon of all these colors and can be separated into individual colors with a prism. 10
Electromagnetic Radiation Particle Theory of Light Max Planck and Albert Einstein (1905) ElectromagneKc radiakon is stream of small packets of energy Quanta of energy or photons Each photon travels with velocity = c Waves with frequency = ν Energy of photon of electromagnekc radiakon is proporkonal to its frequency Energy of photon h = Planck s constant = 6.626 10 34 J s E = h ν 11
Electromagnetic Radiation Ex: Determining Energy from Frequency Example: A microwave oven uses radiakon with a frequency of 2450 MHz (megahertz, 10 6 s 1 ) to warm up food. What is the energy of such photons in joules? E = h! E = ( 6.626!10 "34 J s) = 1.62 10 24 J ( )! 1!106 s % "1! 2450 MHz # % $ MHz & ( ' 12
Electromagnetic Radiation Photoelectric Effect If shine light on a metal surface: Below a certain frequency nothing happens Above a certain frequency electrons are ejected Increasing intensity increases # of electrons ejected Increasing frequency increases KE of electrons KE = hν BE hν = energy of light shining on surface BE = binding energy of electron h>p://hyperphysics.phy- astr.gsu.edu/hbase/mod1.html 13
Electromagnetic Radiation Photoelectric Effect Therefore Energy is Quan,zed Can occur only in discrete units of size hν 1 photon = 1 quantum of energy Energy gained or lost in whole number mulkples of hν E = nhν If n = N A, then one mole of photons gained or lost E = 6.02 10 23 hν If light is required to start reackon Must have light above certain frequency to start reackon Below minimum threshold energy, intensity is NOT important 14
Electromagnetic Radiation Ex: Energy, Frequency & Moles Example: If a mole of photons has an energy of 1.60 10 3 J/mol, what is the frequency of each photon? Assume all photons have the same frequency.! = E N A h! =!."#!!# "$ %&'()* (".#+!!# +$ %()* "! )("."+"!!# "$, %&%-) = 4.01 10 6 Hz 15
Atomic Spectra Electronic Structure of the Atom Because energy is quankzed we can study the electronic structure of an atom the frequency of light it absorbs or emits: 1. Study of light absorpkon Electron absorbs energy Moves to higher energy excited state excited state ground state +hν excited state 2. Study of light emission Electron loses photon of light Drops back down to lower energy ground state hν ground state Molecular Nature of Ma>exr, 6E 16
Atomic Spectra Spectrum of Light A con,nuous spectrum of light is an unbroken spectrum of all colors i.e., visible light through a prism; sunlight; incandescent light bulb; or a very hot metal rod An atomic spectrum or the light emi>ed by an atom is a discon,nuous (or line) spectrum of light A disconknuous spectrum has only a few discrete lines Each element has a unique emission spectrum Molecular Nature of Ma>exr, 6E 17
Atomic Spectra Spectrum of Light Molecular Nature of Ma>exr, 6E 18
Atomic Spectra Electronic Structure of the Atom Hydrogen is the simplest atomic spectra with only one electron Emission: (Hydrogen, Mercury, Neon) AbsorpKon: (Hydrogen) Molecular Nature of Ma>exr, 6E h>p://facstaff.cbu.edu/~jvarrian/252/emspex.html 19
Atomic Spectra Rydberg Equation 1 1 n1 1 λ = R H 2 n 2 2 R H = 109,678 cm 1 = Rydberg constant λ = wavelength of light emitted n 1 and n 2 = whole numbers (integers) from 1 to where n 2 > n 1 If n 1 = 1, then n 2 = 2, 3, 4, Can be used to calculate all spectral lines of hydrogen The values for n correspond to allowed energy levels for atom Molecular Nature of Ma>exr, 6E 20
Atomic Spectra Ex: Rydberg Equation Example: Consider the Balmer series where n 1 = 2 Calculate λ (in nm) for the transikon from n 2 = 6 down to n 1 = 2. 1! = R " 1 H $ 2! 1 # 2 6 2 % ' = 109,678 " 1 cm!1 & 4! 1 % $ ' # 36 & = 24,373 cm 1! = 1 = 4.1029 "10!5 cm " 1 m 24,372.9 cm!1 100 cm " 1 nm 1 "10!9 m λ = 410.3 nm Violet line in spectrum Molecular Nature of Ma>exr, 6E 21
Atomic Spectra Ex: Rydberg Equation Example: A photon undergoes a transikon from n higher down to n = 2 and the emi>ed light has a wavelength of 650.5 nm?! = 650.5 nm! 1!10"7 cm 1 nm = 650.5!10"7 cm 1 650.5! 10 "7 cm = 109,678 cm"1 ( 1 2 " 1 2 1 7.13455 = ( 1 4! 1 n 2 ( ) 2 ) n 2 ( ) 2 ) 1 = 1 ( ) 2 4! 1 7.13455 = 0.110 n 2 ( n ) 2 2 = 1 0.110 = 9.10 Molecular Nature of Ma>exr, 6E n 2 = 3 22
Atomic Spectra Understanding Atomic Structure Atomic line spectra tells us when excited atom loses energy Only fixed amounts of energy can be lost Only certain energy photons are emi>ed Electron restricted to certain fixed energy levels in atoms Atomic line spectra tells us Energy of electron is quan,zed and is the simple extension of Planck's Theory Therefore any theory of atomic structure must account for Atomic spectra QuanKzaKon of energy levels in atom Molecular Nature of Ma>exr, 6E 23
Quantum What do we mean by Quantized Energy is quankzed if only certain discrete values are allowed Presence of disconknuikes makes atomic emission quankzed 24
Bohr Model Bohr Model of an Atom First theorekcal model of atom to successfully account for Rydberg equakon QuanKzaKon of energy in hydrogen atom Correctly explained atomic line spectra Proposed that electrons moved around nucleus like planets move around sun Move in fixed paths or orbits Each orbit has fixed energy 25
Bohr Model Energy Level Diagram for a Hydrogen Atom AbsorpKon of photon Electron raised to higher energy level Emission of photon Electron falls to lower energy level Energy levels are quantized Every time an electron drops from one energy level to a lower energy level Same frequency photon is emitted Yields line spectra E =! b n 2 =! R H hc n 2 26
Bohr Model Bohr model of the Hydrogen Atom n = 1 First Bohr orbit Most stable energy state equals the ground state which is the lowest energy state Electron remains in lowest energy state unless disturbed How to change the energy of the atom? Add energy in the form of light: E = hν Electron raised to higher n orbit n = 2, 3, 4, Higher n orbits = excited states = less stable So electron quickly drops to lower energy orbit and emits photon of energy equal to ΔE between levels ΔE = E h E l h = higher l = lower 27
Bohr Model Bohr s Model Fails Theory could not explain spectra of mulk- electron atoms Theory doesn t explain collapsing atom paradox If electron doesn t move, atom collapses PosiKve nucleus should easily capture electron VibraKng charge should radiate and lose energy 28
Bohr Model Ex: Bohr s Model of Energy Levels Example: In Bohr's atomic theory, when an electron moves from one energy level to another energy level more distant from the nucleus, A. energy is emi>ed B. energy is absorbed C. no change in energy occurs D. light is emi>ed E. none of these 29
Problem Set A 1. Which electromagnekc radiakon has a higher energy? Radio waves or microwaves? UV light or X rays? 2. How does thermal imaging work? (Use what you have learned about the electromagnekc spectrum to briefly explain). 3. Blue, red, and green lasers have wavelengths of 445 nm, 635 nm, and 532 nm respeckvely what are their frequencies, and what is the energy in Joules of a photon from each laser? 4. In Neon there is a line with the frequency of 4.546 x10 14 Hz. What is its wavelength and color of the line? And what is the energy of each of its photons? 5. What is the wavelength of light (in nm) that is emi>ed when an excited electron in the hydrogen atom falls from n = 5 to n = 3? Would you expect to be able to see the light emi>ed? 6. How many grams of water could have its temperature raised by 7 C by a mole of photons that have a wavelength of 450 nm?