Lecture 6 - Atomic Structure Chem 103, Section F0F Unit II - Quantum Theory and Atomic Structure Lecture 6 • Reading in Silberberg - Chapter 7, Section 1 The Nature of Light - Chapter 7, Section 2 Atomic Spectra • Light and other forms of electromagnetic radiation - Chapter 7, Section 3 The Wave-Particle Duality of matter and Energy • Light interacting with matter • The properties of light and matter 2 Lecture 6 - Introduction Lecture 6 - Introduction We have seen how several models of nature that have been Rutherford’s model was almost immediately questioned changed or overturned: because it could not explain why the electrons in an atom did • Lavoisier’s theory of combustion overturned the phlogiston not spiral down into the nucleus model for fire. • The subatomic particles seemed to be contradicting real- • Dalton’s established the modern model that the elements world experiences. were made of indivisible atoms. - Dalton’s model was altered with the discovery of subatomic particles. • Rutherfords nuclear model of the atom overturned J. J. Thomson’s “plum pudding” model of the atom 3 4 Lecture 6 - Introduction Lecture 6 - The Nature of Light Discoveries in the early 20th century lead to a blurring in the Electromagnetic radiation is a type of energy consisting of distinctions between particulate characteristics of matter and oscillating electric (E) and magnetic (B) fields, which move wave-like characteristics of energy through space. • These discoveries lead to a powerfull model for the electronic structure of atoms. • This model allows us to predict much about the structure and properties of the atoms and of the compounds and systems they are comprise them • Forms include: - Infrared radiation - Gamma-rays - Ultraviolet radiation - Radio waves - X-rays - Microwaves 5 6 Lecture 6 - The Nature of Light Lecture 6 - The Nature of Light Electromagnetic radiation is a type of energy consisting of oscillating electric (E) and magnetic (B) fields, which move through space. • The earliest characterization of electromagnetic radiation was based c = ! " # on its wave-like properties c - Wavelength, ! (m) ! = - Frequency, " (1/s) # - Velocity, c = 2.998 x 108 m/s c # = - Amplitude ! 7 8 Lecture 6 - The Nature of Light Lecture 6 - Question Using the wave-like description of electromagnetic radiation, Today I noticed a maple tree outside of my office window had the different forms are characterized by their frequency or turned orange. It looks orange to me because it is reflecting wavelength. orange light (!=670 nm) while absorbing the other colors of visible light. What is the frequency of the light being reflected by this tree? 9 10 Lecture 6 - The Nature of Light Lecture 6 - The Nature of Light Based on classical observations, energy (waves) and matter Waves, but not particles, exhibit interference. (particles) behave differently. Refraction Diffraction 11 12 Lecture 6 - The Nature of Light Lecture 6 - The Nature of Light During the early 20th century, there were several observations Blackbody radiation that confounded the the wave-like description of “light” • When an object is heated it emits light • Blackbody radiation • As the object is heated to a higher - The colors of light emitted by an hot object temperature, the distribution of • The Photoelectric Effect wavelengths of the light emitted changes. - The behavior of electrons ejected by light from a metal • The distribution of wavelengths is not • Atomic Emission Spectra consistent with a model that allows the light energy to have any value. - The wavelengths of light emitted by excited atoms of an element 13 14 Lecture 6 - The Nature of Light Lecture 6 - The Nature of Light Max Planck proposed that this meant that The Photoelectric Effect light energy could only be emitted with • When light strikes a metal surface energies of fixed value it can eject electrons • He proposed that the light energy is emitted (or absorbed) in packets (quanta) of fixed energies, with values directly proportional to the frequency of the light being emitted (or absorbed): E = h! (The energy, E, of 1 quantum of light with frequency ".) -34 • The ejected electrons can be h = 6.6261 x 10 J•s (Planck's constant) measured as a current using a Max Planck received the Nobel Prize in Physics vacuum tube for this work in 1918 vacuum tube 15 16 Lecture 6 - The Nature of Light Lecture 6 - The Nature of Light The Photoelectric Effect The Photoelectric Effect • Albert Einstein (1879-1955) published an explanation for the photoelectric effect in 1905. - He explained that the energy of the light striking the metal plate was not dependent on the the intensity of the light, but rather, it frequency. - The light was behaving like it was made up of particles (photons) - The energy The energy of a photon is Einstein received the given by Planck’s equation, and is Nobel Prize in Physics for proportional to its frequency. this work in 1921. View Simulation E photon = h! = "Eatom 17 18 Lecture 6 - The Nature of Light Lecture 6 - Question The combined explanations for blackbody radiation (Max Today I noticed a maple tree outside of my office window had Planck) and the photoelectric effect (Albert Einstein) showed turned orange. It looks orange to me because it is reflecting that in addition to its wave-like behavior, light also had a orange light (!=670 nm) while absorbing the other colors of particle like behavior visible light. What is the energy of a photon of orange light? Wave-like Particle-like Behaviors Behaviors Refractions Light energy can only be absorbed or emitted by Diffraction matter in discrete packets (quanta/photons) Interference 19 20 Lecture 6 - Atomic Spectra Lecture 6 - Atomic Spectra Atomic spectra • When atoms are excited they gain energy) They can then release that energy as light. - The different • A spectrum is a plot of the wavelengths (or frequencies) of wavelengths the the light that is emitted. The hydrogen of light gas in the emitted by the tube is excited excited by applying a hydrogen high voltage. atoms are dispersed with a prism. The atoms of different elements produce different atomic spectra 21 22 Lecture 6 - Atomic Spectra Lecture 6 - Atomic Spectra The “lines” in the hydrogen atomic spectrum can be fit to the Niels Bohr (1885-1962) combined the ideas of Planck and Rydberg Equation. Einstein, along with the atomic spectrum for the hydrogen atom. • He proposed that light is emitted from an atom when an electron in one energy state (initial) changes to a new, lower energy state (final). !E = Efinal " E initial • The energy of the photon emitted is equal to this change in # & where 1 1 1 7 -1 energy R R is the Rydberg constant (1.097 x 10 m ) = % 2 " 2 ( Ephoton = !E = h" n and n are positive integers with n n ! $ n n ' 1 2 2 > 1 1 2 23 24 Lecture 6 - Atomic Spectra Lecture 6 - Atomic Spectra Niels Bohr (1885-1962) combined the ideas of Planck and Combining Planck’s equation with the Rydberg equation Einstein, along with the atomic spectrum for the hydrogen gives: atom. !E = Efinal " Einitial = E • The atomic spectra indicated that the electron in a photon hydrogen atom can have only certain energy values. = h# (Planck's equation) hc = - These energy values are called stationary states. $ % 1 1 ( hcR (Rydberg equation) - An atom does not radiate light energy when in a stationary state. = ' 2 " 2 * & n1 n2 ) • An atom radiates light energy when it changes from one % 1 1 ( hcR ( E is negative for emissions) = " ' 2 " 2 * ! stationary state to another. & nfinal ninitial ) % m( % 1 ( % 1 1 ( - The difference in energies between these states is given by the = " 6.626 x 10-34 J•s 2.998 x 108 1.097 x 10-18 " ( )' s * ' m* ' n2 n2 * Rydberg equation & ) & ) & final initial ) % 1 1 ( !E = " 2.18 x 10-18 J " ( )' 2 2 * & nfinal ninitial ) 25 26 Lecture 6 - Atomic Spectra Lecture 6 - Atomic Spectra Bohr’s model of the hydrogen atom: # 1 1 & !E = " 2.18 x 10-18 J " ( )% 2 2 ( $ nfinal ninitial ' 27 28 Lecture 6 - Atomic Spectra Lecture 6 - Atomic Spectra Bohr received the 1922 Nobel Prize in Physics for this work While Bohr’s model will work with other atoms that contain just a single electron • He+, Li2+ and Be3+ Bohr’s model does not work with atoms containing more than one electron. 29 30 Lecture 6 - Question Lecture 6 - Wave-Particle Duality Use the Rydberg equation to determine the wavelength in nm The Wave-Particle Duality of Matter and Energy of light that is emitted from a hydrogen atom when an • It turns out both light energy and particles have both wave- electron drops from the n=4 to the n=2 energy level. like and particle-like behaviors. What color will this look like to your eyes? As an addendum to his 1905 paper on special relativity, Albert Einstein proposed an equivalency between energy and mass in his now famous equation: What is the energy of the photon, Ephoton, that was emitted? 2 E = mc What is the energy for a mole of these photons? What is the energy difference, "E, for the transition? (See Sample Problem 7.3) 31 32 Lecture 6 - Wave-Particle Duality Lecture 6 - Wave-Particle Duality After Planck and Einstein showed that light energy has a de Broglie combined Einstein’s equation (E = mc2) with particle-like behavior, other scientists began to ask whether Planck’s equation (E = h" = hc/!): matter might have wave-like properties. hc/! = mc2, h/! = mc, ! = h/mc • Louis de Broglie (1894-1987) reasoned that if hc mc2 For a particle that electrons have wave-like = travels at a velocity, u, properties, that this might ! less than the speed of explain why the electrons in h light Bohr’s hydrogen atom can = mc have only certain fixed ! h values.