09.09.2011 - Chemistry 260/261 Lecture 2 September 9,...

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Unformatted text preview: Chemistry 260/261 Lecture 2 September 9, 2011 Today in Chemistry 260/261 Facing the (quantum) facts •  three experiments that began a revolution •  line spectra of the elements •  blackbody radiation (Max Planck) •  photoelectric effect (Albert Einstein) •  the wave nature of matter •  Problem Set One: Mastery Supp. + OWL due Monday by 3:00 pm Next Week in Chemistry 260/261 •  •  •  •  reading: (Mon) Chs. 5, 6 from Herbert, (Wed) 4.5 ­4.7, (Fri) 5.1 waves, wave functions, and the postulates of quantum mechanics the hydrogen atom problem set 2 due Friday, January 16 by 3:00 pm IBM Research: Fe on Cu surface What we mean by classical Classical Chemistry: Forces and Potentials 1. MATTER 1.  Force is something that causes a mass to accelerate described by the deterministic Laws of Motion Particles of matter travel in a trajectory, a path with a precise position and momentum at each instant. t0 t1 t2 t3 F = ma = m 2.  Potential is energy stored in a system due to work done on the system a.  Work is energy b.  Change in energy due to a force is: t∞ 2. FIELDS distributions of forces in space described by Field Laws a.  gravity (Isaac Newton) b.  electromagnetism (James Maxwell) !E = F • !x c.  InTinitesimal change is denoted with a d In a nutshell: According to classical mechanics, the universe consists of nothing but matter and <ields and we know the laws of both… Interactions in Chemistry -e 1 q1q2 1 ( + Ze ) ( # e ) 1 Ze = =# 4!" 0 r 4!" 0 r 4!" 0 r e1 Fx = ! dV dx r12 e2 r1B r1A The Coulomb potential describes interactions between charged particles. The MOST IMPORTANT potential energy function in chemistry. HA V =− Charles ­Augustin de Coulomb dE dx Example: hydrogen molecule (Fig. 3.8, Eq. 3.13 Oxtoby) 2 +Ze r F= dE = F • dx Interactions in Chemistry Atoms contain positive nuclei and negative electrons V (r ) = dv dx 2 =m 2 dt dt r2A r2B rAB HB e 2 ȹ 1 ȹ 1 ȹ 1 1 ȹ e 2 ȹ 1 ȹ e 2 ȹ 1 ȹ ȹ ȹ ȹ + ȹ ȹ + ȹ ȹ ȹ + ++ 4πε0 ȹ r1 A ȹ r2 B ȹ r1B r2 A ȹ 4πε0 ȹ r12 ȹ 4πε0 ȹ rAB ȹ ȹ Ⱥ Ⱥ ȹ Ⱥ ȹ Ⱥ Ⱥ e = 1.6022 × 10 ­19 Coulombs ε0= 8.85418782 × 10 ­12 m ­3 kg ­1 s4 A2 1 Interactions in Chemistry HA RAB Example: hydrogen molecule HB HA RAB Example: hydrogen molecule HB The difference in potential energy between the two atoms inTinitely separated and two atoms separated by the bond length is the bond dissociation energy (or bond energy) When the atoms are far apart the attraction between the electrons and nuclei cause the energy to drop. If the atoms get too close, the attraction to the electrons is overwhelmed by the repulsion of the two positive nuclei. The potential is greater than zero, and the slope is negative. The minimum corresponds to the bond length Since the potential energy Tirst decreased, then increased, we know that there must be a minimum somewhere in between. Three experiments that began a revolution The potential energy function, V(r) can be guessed classically. It can only be calculated and explained using quantum mechanics. 1. The Emission Spectra of Atoms are Discrete Lines Atoms absorb and emit light at a discrete set of frequencies which are characteristic of the corresponding element. (Balmer 1885) light (photons) electron IRON Interactions in Chemistry Blackbody Radiation photon wikipedia Photoelectric Effect METAL heat Two signiTicant ideas came from these experiments: 1)  Atomic energies are quantized 2)  The true nature of light and matter cannot be explained by classical physics The Wave Nature of Light , / % 2! ( B( x, t ) = B0 cos . 2!" t # ' * x + + 1 &$) 0 B T=1/ ν λ t x The Electromagnetic Spectrum λ = wavelength T = period ν = frequency oscillating magnetic and electric Tields at 90° to each other (perpendicular) , / % 2! ( E ( x, t ) = E0 cos . 2!" t # ' * x + + 1 &$) 0 wave travels at 2.9979 × 108 m s ­1 (c) ! != !1 = c" !" = c characteristics of light can also be reported ! by giving the wavenumber ! 2 The spectra are characteristic of different elements 400 nm … yet atoms are stable, spectral lines are observed – and the lines Wit a simple formula … 700 nm H" ν= Hg" ȹ 1 1 ȹ c = RH ȹ 2 − 2 ȹ ȹ n ȹ λ ȹ f ni Ⱥ Ne" r V(r) 2 +e r V =− -e Planck s Suggestion e ȹ 1 ȹ ȹ ȹ 4πε 0 ȹ r Ⱥ The atom should not be stable, and certainly should not give discrete lines in the spectrum Max Planck (1858 ­1947) Nobel Prize 1918 !T (" ) = Empirical formula derived by Johannes Rydberg (1854 ­1919) 8 # h" 3 c3 A puzzle! Planck s Suggestion Max Planck (1858 ­1947) Nobel Prize 1918 1 e h" kB T !T (" ) = $1 known constants c = speed of light kB = Boltzmann constant h = Titting parameter = 6.626 × 10 ­34 J s 1 h" Energy h = Titting parameter = 6.626 × 10 ­34 J s The energy of each oscillator of the black body is limited to discrete values and cannot be varied arbitrarily. E = nh! n = 0,1, 2, ... permitted energy levels 3. The Photoelectric Effect e-ee-ee- e kB T $ 1 known constants c = speed of light kB = Boltzmann constant Planck s constant QUANTIZATION $1 classicallyallowed energies Metal Surface kinetic energy of ejected electron 8 # h" 3 c3 e h = Titting parameter = 6.626 × 10 ­34 J s λ !T (" ) = 1 h" kB T The blackbody is composed of oscillators. Energy Max Planck (1858 ­1947) Nobel Prize 1918 8 # h" 3 c3 known constants c = speed of light kB = Boltzmann constant The blackbody is composed of oscillators. Planck s Suggestion ν  = frequency λ = wavelength c = speed of light RH = Rydberg Constant y = a + bx Φ frequency of light 1. No electrons are ejected, regardless of the intensity of the radiation, unless the frequency exceeds a threshold value characteristic of the metal. 2. The kinetic energy of the ejected electron varies linearly with the frequency of the incident radiation, but is independent of its intensity. 3. Even at low light intensities, electrons are ejected immediately if the frequency is above the threshold value. EK = h! " # 3 Einstein s First Paper Extended Planck s quantum hypothesis The Quantum Stone Age: Bohr s Atomic Model •  Light of frequency ν consists of quanta of energy hν (photons) E = hν = hc •  Light transfers energy and momentum only in these particle ­like photon bundles h Photons are massless particles, but still carry momentum p = In 1910, Ernest Rutherford s planetary model of the atom was widely accepted λ In 1913, Niels Bohr added a few assumptions to Rutherford s theory based on Planck s idea of quantization. λ •  An electron in the metal gains enough energy from a photon to overcome the forces that holds it in the metal. free electron $ h! " # when h! > # 1 mv 2 ax = % m 2 when h! < # &0 h! ! 1. Attraction between the proton and electron !e v r 2. Electron s motion is a circular orbit v !e r e +Ze m v2 Ze2 = r 4 !" 0 r 2 4. Angular momentum of electron is quantized and must be an integral multiple of h/2π Le = me vr = n bound electron The Quantum Stone Age: Bohr s Atomic Model 3. Forces are balanced e +Ze h n = 1,2,3... 2! Bohr s model explained atomic emission spectra!... 5. The electrons can only attain certain stable states (orbits): rn = ! 0n2h2 n2 = a0 " Ze2 me Z With certain quantized energy levels: En = hν=ΔE ! Ze4 me Z2 = !(2.18 # 10 !18 J) 2 222 8" 0 n h n RH 6. Absorption (or emission) of light corresponds to a transition between stable states excited state Atoms absorb and emit light at a discrete set of frequencies which is characteristic of the corresponding element. Energy levels of atoms are quantized. … but only that of hydrogen… Using ΔE = hν 24 != Z e me $ 1 1' &#) 2 8" 0 h 2 % nf2 ni2 ( Z2(3.29 × 1015 s-1) Bohr s model was little more than quantization grafted upon classical mechanics… still it was a step in the right direction… ground state !E = h" What kind of Physics can give rise to quantization? Standing Waves n λ 2 = L , n = 1, 2,3,K nλ = 2π r , n = 1, 2,3,K Bohr developed a theory of the atom involving electrons in orbits  ­ with a discrete number of wavelengths per orbit, if matter has wave ­like properties. 4 What kind of Physics can give rise to quantization? Circular standing wave: Bohr s hypothesis: ⇒ me vr = me v nλ nλ = 2πr , n = 1,2,3,… ⇒ r = 2π nh me vr = , n = 1,2,3,… 2π nλ nh = 2π 2π Wave Particle Duality: p= ⇒ me v = p = h λ ⇔ λ= h λ h h = p mv Bohr s theory can be justiTied. All you have to do is assume that particles behave like waves Today in Chemistry 260/261 Facing the (quantum) facts •  three experiments that began a revolution •  line spectra of the elements •  blackbody radiation (Max Planck) •  photoelectric effect (Albert Einstein) •  the wave nature of matter •  Problem Set One: Mastery Supp. + OWL due Monday by 3:00 pm Next Week in Chemistry 260/261 •  •  •  •  reading: (Mon) Chs. 5, 6 from Herbert, (Wed) 4.5 ­4.7, (Fri) 5.1 waves, wave functions, and the postulates of quantum mechanics the hydrogen atom problem set 2 due Friday, January 16 by 3:00 pm …just like Einstein s assumption that light (waves) came in discrete photons (particles). 5 ...
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This note was uploaded on 01/19/2012 for the course CHEM 260 taught by Professor Staff during the Fall '08 term at University of Michigan.

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