* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download correctly
Quantum state wikipedia , lookup
Probability amplitude wikipedia , lookup
Interpretations of quantum mechanics wikipedia , lookup
Relativistic quantum mechanics wikipedia , lookup
EPR paradox wikipedia , lookup
Molecular Hamiltonian wikipedia , lookup
Copenhagen interpretation wikipedia , lookup
History of quantum field theory wikipedia , lookup
Renormalization group wikipedia , lookup
Canonical quantization wikipedia , lookup
X-ray fluorescence wikipedia , lookup
Renormalization wikipedia , lookup
Quantum electrodynamics wikipedia , lookup
Bohr–Einstein debates wikipedia , lookup
X-ray photoelectron spectroscopy wikipedia , lookup
Hidden variable theory wikipedia , lookup
Double-slit experiment wikipedia , lookup
Particle in a box wikipedia , lookup
Tight binding wikipedia , lookup
Atomic orbital wikipedia , lookup
Electron scattering wikipedia , lookup
Electron configuration wikipedia , lookup
Matter wave wikipedia , lookup
Hydrogen atom wikipedia , lookup
Theoretical and experimental justification for the Schrödinger equation wikipedia , lookup
Introduction to Modern Physics A (mainly) historical perspective on - atomic physics - nuclear physics - particle physics Theories of Blackbody Radiation Classical disaster ! Quantum solution Planck’s “Quantum Theory” I , T 5 hckT e 1 The “oscillators” in the walls can only have certain energies – NOT continuous! The Photoelectric Effect Light = tiny particles! Wave theory: takes too long to get enough energy to eject electrons Particle theory: energy is concentrated in packets -> efficiently ejects electrons! The Photoelectric Effect Energy of molecular oscillator, E = nhf Emission: energy nhf -> (n-1)hf Light emitted in packet of energy E = hf Einstein’s prediction: hf = KE + W (work function) c = f Frequency Speed of light 3 x 108 meter/second or 30cm (1 foot) per nanosecond Wavelength (meter) #vibrations/ second hf = KE + W (work function) The Photoelectric Effect Photon Theory Wave Theory Increase light intensity -> Increase light intensity -> more electrons with more KE more photons -> more electrons Frequency of light does not affect electron KE X X but max-KE unchanged ! Max-KE = hf - W If f < f(minimum) , where hf(minimum) = W, Then NO electrons are emitted! How many photons from a lightbulb? 100W lightbulb, wavelength = 500nm Energy/sec = 100 Joules E = nhf -> n= n = E/hf = E/hc 100J x 500 x 10-9 6.63 x 10-34 J.s x 3 x 108 m/s = 2.5 x 1020 !! So matter contains electrons and light can be emitted in “chunks”… so what does this tell us about atoms?? Possible models of the atom Which one is correct? The Rutherford Experiment Electric potential V(r) ~ 1/r Distance of closest approach ~ size of nucleus At closest point KE -> PE, and PE = charge x potential KE = PE = 1/40 x 2Ze2/R R = 2Ze2/ (40 x KE) = 2 x 9 x 109 x 1.6 x 10-19 x Z 1.2 x 10-12 J = 3.8 x 10-16 Z meters = 3.0 x 10-14 m for Z=79 (Gold) The “correct” model of the atom …but beware of simple images! Atomic “signatures” Rarefied gas Only discrete lines! 1 1 R 2 2 2 n 1 1 1 R 2 2 2 n 1 An empirical formula! n = 3,4,… The Origin of Line Spectra Newton’s 2nd Law and Uniform Circular Motion F = ma Acceleration = v2/r Towards center of circle! How do we get “discrete energies”? Angular momentum L = mvr Radius r Linear momentum = mv Bohr’s “quantum” condition – motivated by the Balmer formula h L mvrn n 2 n 1,2,3,... Electron “waves” and the Bohr condition De Broglie(1923): = h/mv Only waves with a whole number of wavelengths persist n = 2r Same!! h L mvrn n 2 Quantized orbits! Electrostatic force: Electron/Nucleus COULOMBS LAW Combine Coulomb’s Law with the Bohr condition: Newton’s 2nd Law Circular motion 1 ( Ze)e mv 2 2 40 rn rn F ma 2 v a r h L mvrn n 2 nh v 2mrn n h 0 n rn r1 2 mZe Z 2 2 2 h 0 (6.626 x10 )(8.85 x10 ) r1 2 31 19 me (3.14)(9.11x10 )(1.602 x10 ) 34 2 0.529 x10 10 m (for Z = 1, hydrogen) 12 Calculate the total energy for the electron: Total Energy = Kinetic + Potential Energy Electrostatic potential Electrostatic potential energy 1 Q 1 Ze V 40 r 40 r 1 Ze U eV 40 r 2 Total energy 1 2 1 Ze 2 En mv 2 40 rn Substitute Z 2e 4 m 1 Z 2 En 2 2 2 2 E1 8 0 h n n 4 me E1 2.17 x10 18 Joules 13.6eV 2 8 0 h 13.6eV En 2 n So the energy is quantized ! … now we can combine this with hf Eu El hf hc 1 Z e m 1 1 En E ' 2 3 2 hc 8 0 h c n' n 1 2 4 …and this correctly predicts the line spectrum for hydrogen, …and it gets the Rydberg constant R right! …however, it does not work for more complex atoms… Experimental results Quantum Mechanics – or how the atomic world really works (apparently!) Take the wave description of matter for real: De Broglie(1923): = h/mv Describe e.g. an electron by a “wavefunction” (x), then this obeys: h d U ( x) ( x) E ( x) 2 2m dx 2 2 Schroedinger’s famous equation Now imagine we confine an electron in a “box” with infinitely hard/high walls: Waves must end at the walls so: and the energy levels for these states are: Discrete energies! The probabilities for the electron to be at various places inside the box are: vs. Classical Mechanics Uniform probability! Applying the same quantum mechanical approach to the hydrogen atom: Probability “cloud” Bohr radius The “n = 2” state of hydrogen: Atomic orbitals Weird stuff!! Weird stuff!! Ghosts!!?? Conclusions - Classical mechanics/electromagnetism does not describe atomic behavior - The Bohr model with a “quantum condition” does better…but only for hydrogen - Quantum mechanics gives a full description and agrees with experiment - …but QM is weird!!