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Mary J. Bojan FA 2010 1 Structure of the Atom – Part I (continued) • 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? Dual Nature of Light λν=c E = hν Line Spectrum Bohr Model of Hydrogen AtomMary J. Bojan FA 2010 2 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)Mary J. Bojan 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 Classically, expect metal to “soak” up energy of light until e– binding energy (Eb) is overcome. Metal atoms absorb only 1 quantum of energy: it happens all at once as if struck by a particle → photon 3 FA 2010Mary J. Bojan FA 2010 When light of wavelength = 420nm is focused on a metal surface, electrons are ejected with a speed of 7.50 x10-5 m/s. What is the binding energy of the electron in the metal? 4Mary J. Bojan FA 2010 5 Line Spectra of Atoms Spectrum Type ν’s Examples Monochromatic Continuous Discrete (or line) DEMONSTRATIONS: How can we explain all of this? Spectroscopy: study of light interacting with matter Spectrum: distribution of ν in emitted radiationMary J. Bojan Line spectra Hydrogen Neon 6 FA 2010Mary J. Bojan Observation of line spectra implies that atoms have discrete (quantized) energy levels. 7 FA 2010Mary J. Bojan n = 1, 2, 3, ….. principal quantum number RH = Rydberg constant = 2.18x10-18J 8 FA 2010Mary J. Bojan FA 2010 9 Energy of an Electron (Bohr Model) • 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) Energy is given off when an electron is put into orbital. Coulomb’s Law helps where Q1 = charge of electron (negative) Q2 = charge of proton (positive) d = orbit radius (distance between nucleus and electron) Note: Orbit energy in Bohr Model is negative, so it must correspond to energy needed to put electron into the orbit.Mary J. Bojan where ni and nf are integers. This predicts the H-atom spectrum EXACTLY! Note: nf > ni ΔE is + (absorbs photon) nf < ni ΔE is - (emits photon) Atoms absorb or emit light when e− changes its orbit ΔE = Ef – Ei = hν Line spectrum is due to electronic transitions 10 FA 2010Mary J. Bojan FA 2010 11 Problem Solving: Bohr Model 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 → n = 6 2. n=6 → n = 3 3. n=3 → n = 6 4. n=1 → n = 4 5. n=6 → n = 1Mary J. Bojan FA 2010 12 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) Bohr model explained some experimental evidence for hydrogen atom, but it failed for other atoms. Enter the Quantum World…Mary J. Bojan FA 2010 13 Electron microscope Used to image some of the tiniest objects. Electrons diffract when interacting with matter. Image of HIV budding from T-cellMary J. Bojan At what velocity must a neutron, which weighs 1.67 × 10-24 g, be moving in order for it to exhibit a wavelength of 400 pm? A. 9.92 × 102 m/s B. 9.92 × 10-1 m/s C. 9.92 × 101 m/s D. 9.92 × 104 m/s E. 9.92 × 103 m/s 14 FA 2010Mary J. Bojan FA 2010 15 Heisenberg Uncertainty Principle • 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 • It is not appropriate to imagine e– moving in nice little orbits around the nucleus • Contradicts Bohr’s planetary model of the hydrogen atom It is NOT possible to simultaneously know the position & velocity (momentum, mv) of a particle with complete certainty Can we say anything about where the e– are?Mary J. Bojan FA 2010 16 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)Mary J. Bojan Tells us WHERE the electron is Tells us the ENERGY of the electron FA 2010 An orbital • specifies the probability of finding an electron in a given region of space, (i.e. orbitals have shapes) • specifies the energy of the electron • is characterized by quantum numbers (3 of them!) 17Mary J. Bojan FA 2010 18 Classical waves • Only certain stable modes are allowed • Modes characterized by an integer ⇔ number of nodes (1 for each dimension) • Equal (degenerate) νs appear in 2–, 3–D due to symmetry.Mary J. Bojan 3-D expect 3 quantum numbers n,  and m 1. Principal quantum # (n) 19 FA 2010Mary J. Bojan 20 FA 2010Mary J. Bojan Quantum Numbers 2. Azimuthal quantum # () Use symbols rather than numbers for   = 0 1 2 3 21 FA 2010Mary J. Bojan 3. Magnetic quantum number (m) 22 22 FA 2010Mary J. Bojan FA 2010 23 Summary Orbitals: • Allowed energy states for electrons in atom. • Describes spatial distribution of electrons in these energy states. Orbital number shape name of orbitals? ___________________________________________________________________________________ s 1 spherical p 3 dumbell d 5 clover leaf f 7 ?!?!? Quantum


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PSU CHEM 110 - Structure of the Atom

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