The Quantum Mechanical Atom CHAPTER 7 Chemistry: The Molecular Nature of Matter, 6th edition By Jesperson, Brady, & Hyslop

CHAPTER 8: Quantum Mechanical Atom Learning Objectives Light as Waves, Wavelength and Frequency The Photoelectric Effect, Light as Particles and the Relationship between Energy and Frequency Atomic Emission and Energy Levels The Bohr Model and its Failures Electron Diffraction and Electrons as Waves Quantum Numbers, Shells, Subshells, and Orbitals Electron Configuration, Noble Gas Configuration and Orbital Diagrams Aufbau Principle, Hund’s Rule, and Pauli Exclusion Principle, Heisenberg Uncertainty Principle Valence vs Inner Core Electrons Nuclear Charge vs Electron Repulsion Periodic Trends: Atomic Radius, Ionization Energy, and Electron Affinity

Electromagnetic Radiation Light Energy is a Wave Electromagnetic Spectrum Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

Electromagnetic Radiation Light Energy is a Wave Waves travel through space at speed of light in vacuum c = speed of light = 2.9979 × 108 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. Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

Electromagnetic Radiation Light Energy is a Wave Wavelength () Distance between two successive peaks or troughs Units are in meters, centimeters, nanometers Frequency () 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    = c Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

Electromagnetic Radiation Light Energy is a Wave Amplitude Maximum and minimum height Intensity of wave, or brightness Varies with time as travels through space Nodes Points of zero amplitude Place where wave goes though axis Distance between nodes is constant Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

Electromagnetic Radiation Ex: Converting between Wavelengths and Frequency Example: The bright red color in fireworks is due to emission of light when Sr(NO3)2 is heated. If the wavelength is ~650 nm, what is the frequency of this light?  = 4.61 × 1014 s–1 = 4.6 × 1014 Hz Example: WCBS broadcasts at a frequency of 880 kHz. What is the wavelength of their signal? = 341 m Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

Electromagnetic Radiation Electromagnetic Spectrum low energy, long waves high energy, short waves Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

Electromagnetic Radiation Electromagnetic Spectrum Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

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 combination of all these colors and can be separated into individual colors with a prism. Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

Electromagnetic Radiation Particle Theory of Light Max Planck and Albert Einstein (1905) Electromagnetic radiation is stream of small packets of energy Quanta of energy or photons Each photon travels with velocity = c Waves with frequency =  Energy of photon of electromagnetic radiation is proportional to its frequency Energy of photon E = h  h = Planck’s constant = 6.626 × 10–34 J s Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

Electromagnetic Radiation Ex: Determining Energy from Frequency Example: A microwave oven uses radiation with a frequency of 2450 MHz (megahertz, 106 s–1) to warm up food. What is the energy of such photons in joules? = 1.62 × 10–24 J Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

If shine light on a metal surface: 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 = h – BE h = energy of light shining on surface BE = binding energy of electron Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E http://hyperphysics.phy-astr.gsu.edu/hbase/mod1.html

Therefore Energy is Quantized Electromagnetic Radiation Photoelectric Effect Therefore Energy is Quantized Can occur only in discrete units of size h 1 photon = 1 quantum of energy Energy gained or lost in whole number multiples of h E = nh If n = NA, then one mole of photons gained or lost E = 6.02 × 1023 h If light is required to start reaction Must have light above certain frequency to start reaction Below minimum threshold energy, intensity is NOT important Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

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. = 4.01 × 106 Hz Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

Electronic Structure of the Atom Atomic Spectra Electronic Structure of the Atom Because energy is quantized we can study the electronic structure of an atom the frequency of light it absorbs or emits: 1. Study of light absorption Electron absorbs energy Moves to higher energy “excited state” 2. Study of light emission Electron loses photon of light Drops back down to lower energy “ground state” Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Mattexr, 6E

A continuous spectrum of light is an unbroken spectrum of all colors Atomic Spectra Spectrum of Light A continuous 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 emitted by an atom is a discontinuous (or line) spectrum of light A discontinuous spectrum has only a few discrete lines Each element has a unique emission spectrum Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Mattexr, 6E

Atomic Spectra Spectrum of Light Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Mattexr, 6E

Electronic Structure of the Atom Atomic Spectra Electronic Structure of the Atom Hydrogen is the simplest atomic spectra with only one electron Emission: (Hydrogen, Mercury, Neon) Absorption: (Hydrogen) Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Mattexr, 6E http://facstaff.cbu.edu/~jvarrian/252/emspex.html

RH = 109,678 cm–1 = Rydberg constant  = wavelength of light emitted Atomic Spectra Rydberg Equation RH = 109,678 cm–1 = Rydberg constant  = wavelength of light emitted n1 and n2 = whole numbers (integers) from 1 to  where n2 > n1 If n1 = 1, then n2 = 2, 3, 4, … Can be used to calculate all spectral lines of hydrogen The values for n correspond to allowed energy levels for atom Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Mattexr, 6E

 = 410.3 nm Violet line in spectrum Atomic Spectra Ex: Rydberg Equation Example: Consider the Balmer series where n1 = 2 Calculate  (in nm) for the transition from n2 = 6 down to n1 = 2. = 24,373 cm–1  = 410.3 nm Violet line in spectrum Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Mattexr, 6E

n2 = 3 Atomic Spectra Ex: Rydberg Equation Example: A photon undergoes a transition from nhigher down to n = 2 and the emitted light has a wavelength of 650.5 nm? n2 = 3 Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Mattexr, 6E

Understanding Atomic Structure 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 emitted Electron restricted to certain fixed energy levels in atoms Atomic line spectra tells us Energy of electron is quantized and is the simple extension of Planck's Theory Therefore any theory of atomic structure must account for Atomic spectra Quantization of energy levels in atom Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Mattexr, 6E

What do we mean by “Quantized” “Quantum” What do we mean by “Quantized” Energy is quantized if only certain discrete values are allowed Presence of discontinuities makes atomic emission quantized Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

Quantization of energy in hydrogen atom Bohr Model Bohr Model of an Atom First theoretical model of atom to successfully account for Rydberg equation Quantization 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 Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

Energy Level Diagram for a Hydrogen Atom Bohr Model Energy Level Diagram for a Hydrogen Atom Absorption 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 Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

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 = h 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 E between levels E = Eh – El h = higher l = lower Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

Theory could not explain spectra of multi-electron atoms Bohr Model Bohr’s Model Fails Theory could not explain spectra of multi-electron atoms Theory doesn’t explain collapsing atom paradox If electron doesn’t move, atom collapses Positive nucleus should easily capture electron Vibrating charge should radiate and lose energy Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

Ex: Bohr’s Model of Energy Levels 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, energy is emitted energy is absorbed no change in energy occurs light is emitted none of these Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

Problem Set A Which electromagnetic radiation has a higher energy? Radio waves or microwaves? UV light or X rays? How does thermal imaging work? (Use what you have learned about the electromagnetic spectrum to briefly explain). Blue, red, and green lasers have wavelengths of 445 nm, 635 nm, and 532 nm respectively what are their frequencies, and what is the energy in Joules of a photon from each laser? In Neon there is a line with the frequency of 4.546 x1014 Hz. What is its wavelength and color of the line? And what is the energy of each of its photons? What is the wavelength of light (in nm) that is emitted 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 emitted? 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?