09.19.2011 - chem 260/261 F11 Monday S Lecture 6 1 Lecture...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: chem 260/261 F11 Monday Septemeber 19, 2011 Lecture 6 1 Lecture 6 September 19, 2011 Chem 260/261 Today in Chemistry 260/261 •Harmonic oscillator •Describing the hydrogen atom with wave functions • quantum numbers for atomic systems • Hydrogen atom orbitals and energies Next in Chemistry 260/261 • Reading: ¡'SJ¢ £¤¥¦£¤§¨ ¡.PO¢ £¤£ • Solving the Schrödinger equation for more than one electron • Hartree orbitals • Aufbau Principle w NBOZ¦FMFDUSPO BUPNT¨ QFSJPEJD QSPQFSUJFT This simple potential model is widely used (after all we do not have many systems that can be solved exactly). unfortunately) V ( R AB ) = 1 2 k R AB ! R e ( ) 2 F = ma = -k(R-R e ) R e m 1 m 2 μ m 1 m 2 m 1 m 2 + F = ! k R AB ! R e ( ) Stiffness of the spring: k (spring constant). 1635-1703 The parabolic potential: Hooke ` s Law ! ! 2 2 μ d 2 dx 2 + ˆ V ( x ) " # $ % & ' ! ( x ) = E ! ( x ) ) ( ) ( 2 1 2 2 2 2 2 x E x kx dx d ψ ψ μ = ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ + − x = R ! R e The energy levels will be quantized because the wave function is bounded… ∫ ∞ ∞ − = 1 ) ( 2 dx x ψ Reduced mass E = n 2 h 2 8 mL ! " # $ % & 1 4 9 16 25 n=1 n=2 n=3 n=4 n=5 E = h ! n + 1 2 ! " # $ % & n=1 n=2 n=3 n=4 n=0 Harmonic Oscillator Wave functions Particle in a Box ! n x ( ) = ¡ L sin N " x L ! " # $ % & Ψ n (x) is ! a more complex formula, but behavior is similar. Energy x L 0.5 1.5 3.5 5.5 7.5 Energy x Harmonic Oscillator In both cases the lowest energy state has kinetic energy >0. This is a quantum phenomenon. No kinetic energy would mean Δx=0 and Δp=0 ç This cannot be! n=1,2,3… n=0,1,2,… ¡ = 1 2 ¢ k μ 1.6 Not\initeunlessE=hv(n+½) TheboundaryconditiondeterminesE http://phet.colorado.edu/ For the Harmonic Oscillator Simulator: http://phet.colorado.edu/en/simulation/bound-states Phase oscillation – like the oscillation of the string, but, as for a standing wave, the nodes are stationary for the energy eigenstates. n=0 P=0.843 P=0.157 Another Example of Quantum Weirdness … Tunneling E = h ! n + 1 2 ! " # $ % & 0.5 1.5 3.5 5.5 7.5 n=1 n=2 n=3 n=4 n=0 Energy x ! ( x ) 2 The probability distribution goes beyond the classical limit. In this region potential energy > total energy! (if the oscillator is classical) 16% of the time the oscillator would be measured in the l forbidden zone z Tunneling is responsible for a number of strange phenomena – but it is also useful… chem 260/261 F11 Monday Septemeber 19, 2011 Lecture 6 2 Nobel Prize 1986 Gerd Binning Heinrich Rohrer Build your own – see www.geocities.com/spm_stm/Project.html Scanning Tunneling Microsope http://eels.kuicr.kyoto-u.ac.jp/stm.en.html Perylene on graphite IBM Research: Fe on Cu surface Molecules on surfaces 48 iron atoms in a circular ring "corral" some surface state electrons and force them into "quantum" states of the circular structure. The ripples in the ring of atoms are the density distribution of a particular set of quantum states of the corral. The artists were delightedquantum states of the corral....
View Full Document

{[ snackBarMessage ]}

Page1 / 5

09.19.2011 - chem 260/261 F11 Monday S Lecture 6 1 Lecture...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online