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Structure of the atom • What IS the structure of an atom? • What are the properties of atoms? REMEMBER: structure affects function! • Important questions: Where are the electrons? What is the energy of an electron? Chapter 3 Part 1 Dual Nature of Light λν=c E = hν Line Spectrum Bohr Model of Hydrogen Atom Chem 110 1 Light behaves as a wave! Or does it??? Several phenomena were inconsistent with the wave nature of light. Blackbody radiation Photoelectric effect Line spectrum of atoms The color of the heating element changes with temperature from black (cold) to “white” hot. Chem 110 2 Black body radiation Intensity of emitted light predicted by the wave mechanics differs from experiment. Planck shows: E= n hν n = integer ν = frequency of emitted light h = Planck s constant = 6.626 × 10−34 J-s Observed (solid lines) and predicted (classical, non-quantum model) spectra of radiating black-bodies at 5000 K (red) and 7000 K (blue). The sun has blackbody temperature of 5780 K. Energy = hν photon energy Chem 110 frequency of photon 3 Photon energy What is the energy of a green photon (wavelength equal to 523 nm)? 1. 2. 3. 4. 5. 5.74 × 10+14 J 3.80 × 10−19 J 5.23 × 10−29 J 1.90 × 10−19 J 3.80 × 10−28 J Chem 110 4 Spectroscopy: light interacting with matter λ Common use Dangerous or not??? Energy Interaction with matter gamma X-Ray ultraviolet visible infrared microwave radio Chem 110 5 Photoelectric effect: Classically, expect metal to soak up energy of light until e– binding energy (Eb) is overcome. BUT – No e– s emitted until ν = ν0 – No waiting time – Kinetic energy of e– = h(ν– ν0) = ½ mv2 where v = speed of electron emitted Ephoton = hν = Eb + ½ mv2 Chem 110 Metal atoms absorb only 1 quantum of energy: it happens all at once as if struck by a particle è photon 6 Visible (white) light contains a continuous distribution of frequencies of electromagnetic radiation. Spectrum: distribution of ν in emitted radiation Chem 110 7 Different types of light produce different spectra DEMONSTRATIONS: How can we explain all of this? Examples Laser Spectrum Type ν’s Light bulb Hg vapor Chem 110 Hg vapor spectrum 8 Observation of line spectra implies that atoms have discrete (quantized) energy levels. Excited state (E3) Excited state (E2) absorption ΔE = hν emission ΔE = hν Ground state (E 1) Chem 110 9 There are only 4 emission lines in the visible spectrum of hydrogen H2 discharge tube Chem 110 10 Each element has a unique line spectrum. (Structure affects function) Chem 110 11 To explain this phenomenon, we start with the simplest atom (hydrogen) and try to understand it. H atom has 1 proton (+) and 1 electron ( – ) . Where is the proton? Where is the electron? Bohr Model of H atom (1913) Bohr proposes that the electron is in one of several possible “orbits” around the proton. Chem 110 12 If the electron is in an “orbit”, what is it’s energy? Bohr used the line spectrum to figure out the energy differences between “orbits” and then deduced the energy of the electron in each orbit. ⎛ 1⎞ En = − RH ⎜ 2 ⎟ ⎝n ⎠ ∞ n = 6n = 5 n=4 n=3 n = 1, 2, 3, ….. principal quantum number Energy n=2 RH = Rydberg constant RH = 2.18x10–18J Chem 110 n=1 13 Energy of an Electron (Bohr Model) Energy is given off when an electron is put into orbital. Coulomb’s Law helps where E∝ Q1Q2 d Q1 = charge of electron (negative) Q2 = charge of proton (positive) d = orbit radius (distance between nucleus and electron) • Put electron into the orbital: attractive interaction Energy will be negative (means energy is given off) • Reverse the process: try to remove the electron Energy will be positive (energy is absorbed) Note: Orbit energy in Bohr Model is negative, so it must correspond to energy needed to put electron into the orbit. Chem 110 14 Recall the Goal • What IS the structure of an atom? • What are the properties of atoms? REMEMBER: structure affects function! • Important questions: Where are the electrons? What is the energy of an electron? Chem 110 15 Review Quantized Energy • Energy comes in discrete packets, or “quanta” • Energy of a quantum ε is ε = hν ν = frequency of light h = Planck’s constant = 6.63 × 10−34 J·s • Total energy in light beam is nhν (n = 1, 2, 3, …) Dual Nature of Light Wave λν = c Particle E = hν Experimental support: • black-body radiation (Planck, 1900) • photoelectric effect (Einstein, 1905) • line spectra of hydrogen (Bohr, 1913) Chem 110 16 Bohr Model of H atom (1913) Line spectrum is due to electronic transitions Atoms absorb or emit light when e− changes its orbit ΔE = Ef – Ei = hν ⎛1 1⎞ hν = ΔE = RH ⎜⎜ 2 − 2 ⎟⎟ ⎝ ni nf ⎠ where ni and nf are integers. This predicts the H-atom spectrum EXACTLY! Note: nf > ni nf < ni ΔE is + ΔE is – (absorbs photon) (emits photon) Chem 110 17 Energy levels in Bohr Model ∞ n = 6n = 5 n=4 n=3 Energy n=2 Chem 110 n=1 18 Be able to use the Bohr Model to solve problems describing electronic transitions in the Hydrogen atom. If ni = 2 and nf = 1, is energy emitted or absorbed? 1 . emitted 2 . absorbed Of the following transitions in an H-atom, which one results in the emission of the highest energy photon? 1. n=1 è n = 6 2. n=6 è n = 3 3. n=3 è n = 6 4. n=1 è n = 4 5. n=6 è n = 1 Chem 110 19 The Bohr model explained some experimental evidence for hydrogen atom, but it failed for other atoms. From Orbits to Orbitals : DeBroglie (1924): if light has dual wave/particle behavior, perhaps matter does also. Wavelength of matter waves: λ = h/mv · Electron waves discovered in 1927 (Davidson and Garmer) (Basis for electron microscope) · For a baseball and bacteria, λ is too small to observe, but for electrons λ is of atomic size producing profound effects. Electrons in atoms behave as "standing" waves. (Schrödinger equation, 1926) Enter the Quantum World… Chem 110 20 There is experimental evidence for the wave behavior of electrons X-Ray diffraction electron diffraction Chem 110 21 Electron microscope provides experimental evidence that particles have wave properties. Electrons diffract when interacting with matter. Used to image some of the tiniest objects. Image of HIV budding from T-cell Chem 110 22 Heisenberg Uncertainty Principle It is NOT possible to simultaneously know the position & velocity (momentum, mv) of a particle with complete certainty • Derives from wavelike nature of matter This really becomes important when dealing with subatomic matter • All electrons have a velocity, therefore, you cannot specify their exact location • Contradicts Bohr’s planetary model of the hydrogen atom In other words: It is not appropriate to imagine e– moving in nice little orbits around the nucleus Can we say anything about where the e– are? Chem 110 23 Solutions of Schrödinger equation are wavefunctions (Ψ) H Ψ= E Ψ Ψ(x,y,z) = wavefunction (no physical significance) Ψ2(x,y,z) = probability of finding one electron in a region of space, also called electron density Think of electrons as clouds of electron density. Orbitals = Ψ2(x,y,z) Chem 110 24 Prepare for recitation tomorrow BRING • Chem 110 Student packet • textbook • Calculator • Completed homework (pp. 26-27) – Explain your reasoning! – Use Problem Solving Guidelines in the student packet (p 16, sample problems on pp 17-19) You will be working on the recitation worksheet found on page 28-29. (Don’t do it ahead of time…) • First RQ will be at the beginning of recitation tomorrow • First Quiz on Angel tomorrow Chem 110 25