Constants & Atomic Data. The birth of atomic physics and quantum mechanics. debroglie s Wave Equations. Energy Calculations. λ = f = h E.

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1 Constants & Atomic Data The birth of atomic physics and quantum mechanics Honors Physics Don Rhine Look inside back cover of book! Speed of Light (): c = 3.00 x 10 8 m/s Elementary Charge: e - = p + = 1.60 x C Planck s Constant: 6.63 x J-s Atomic masses... Electron: x kg Proton: x kg Neutron: x kg Energy Calculations Kinetic Energy: KE = ½mv 2 Speed of light: c = λν = λf λ (lamda) = wavelength [m] ν (nu) = f = frequency [Hz] = [s -1 ] Energy of a light quantum: E = hf New energy unit...for very small energy values 1 ev = 1.60 x [C-V] or [J] & Compton Scattering E in = E out (conservation of energy) E incoming photon = E energy e- needs to break away from atom + Are these 3 equations KE max = hf hf th identical? debroglie s Wave Equations By the way, momentum = mass * velocity p = mv h E λ = f = mv h Max Planck Develops First Quantum Model Blackbody radiation did not increase in energy as predicted by classical physics theory (ultraviolet catastrophe) In 1900 developed resonator model with quantized energy level resonator = vibrating molecule required standing waves a discrete energy levels E = hν Planck s Constant, h 6.63 x J-s Nobel Prize in 1918 E-M Spectrum Can describe photon by its λ, ν, or E! 1

2 E-M Spectrum Can describe photon by its λ, ν, or E! Heinrich Hertz shined light on surface to prove Maxwell s E-M wave equations worked Expected energy in E-M waves to hit and eject from surface of Strange result did not match classical physics no e - ejected below until certain color of light shined on surface Classical physics: low intensity of low-energy light should be enough to do the job over a long enough period of time...like heating water to boil over low flame Classical physics: high intensity of low-energy light should be enough to do the job over a shorter time...like heating water to boil faster over more low flames Result: No ejected! What happened?? Result: No ejected! What happened?? Classical physics: low intensity of high-energy light should be enough to do the job...like heating water to boil faster over more low flames Classical physics: low intensity of high-energy light should be enough to do the job...like heating water to boil faster over higher energy gas burner (MAPP gas vs. LP) Result: Electrons ejected! Why not before? Result: Electrons ejected! Even faster now! 2

3 Quantum Mechanics: must meet threshold energy level (hf t ) before emitted The further you are above the threshold, the faster the e - travels (higher kinetic energy, KE = ½ mv 2 ) Different s have different thresholds. Why? Quantum Mechanics: Different s have different thresholds. Why? a. slope of these lines = what? b. equations for these lines = what? Sample photoelectric effect calculation Suppose are being emitted from a with ν th = 5000 Angstroms. If the max observed electron speed is 10.8M kmh, what is the minimum wavelength of the incident photons? Why use the word minimum? What is the debroglie wavelength of the emitted electron? Diagram Data (& convert to appropriate units) Relevant equations Find relationship Solve Data ν th = 5000 Angstroms = 500 nm = 500 x 10-9 m 6 v = km 1000m 1hr hr 1km 3600s Mkmh = = / Equations KE = ½mv 2 c = λν = λf E = hf 1 ev = 1.60 x [C-V] or [J] KE max = hf hf th E incoming photon = E energy needed to break away from atom + = 1% of c m s Set up relationship & solve E in = E out (conservation of energy) E incoming photon = E energy e- needs to break away from atom + 3

4 Einstein s Next New Idea Photoelectric effect implies light is also quantized into packets of energy called photons Each photon has energy E = hf Awarded Nobel Prize in 1921 for this quantum mechanics breakthrough What other key ideas did Einstein propose (before and after this breakthrough)? Arthur Compton (1923), Nobel Prize 1927 Photon = wave or particle? If particle, can use photons to collide with, and should have billiard ball-like collisions Some energy should transfer to e -, and photon should lose some as it bounces off Use x-rays on block of carbon atoms in crystal lattice structure It worked scattered photon had lower energy By product: x-ray crystallography common technique still used today! Compton Effect Models of the Hydrogen Atom Theoretical models evolved as experimental observations provided more insight, especially the strange quantum phenomena... Ancient Atom Billiard Ball (John Dalton 1803) Plum Pudding J.J. Thomson Solar System Ernest Rutherford Quantized Energy Level Niels Bohr Particle Wave Model - debroglie Electron Cloud Model - Schrödinger PhET Simulation & Virtual Lab Exercise Ancient Idea of Atom 400 BC Leucippus & Democritus Atom = Smallest Indivisible Quantity Billiard Ball Model John Dalton ( ) Early chemist explored structure of molecules Around 1800 Dalton proposed all chemical compounds comprised of atoms that cannot be altered or destroyed Discovery of Electrons & Plum Pudding Model J.J. Thomson ( ) Electric field could bend beam from cathode ray Correctly assumed beam was composed of negatively charged particles that must be part of an atom, corpuscles (e - ) First to propose atom comprised of smaller parts Atoms neutrally charges, so assumed there must be a sea of + charges around corpuscles Thomson also predicted charge:mass ratio of e - Nobel Prize in 1906 Millikan s famous 1909 oil drop experiment measured charge (and therefore mass) of e - (1923 Nobel Prize) Crooke s Tube Cathode Ray Tube 4

5 Rutherford s Scattering Experiment Mostly empty space w/ + core solar system model Ernest Rutherford, : Directed + charged alpha particles He 2+ at thin gold leaf foil (couple hundred atoms in thickness) J.J. Thomson s model predicted α particles pass through Particles were scattered! Rutherford assumed that positively charges grouped together in a nucleus caused scattering Proposed planetary model but not stable in classical physics electron orbits would lose energy and decay Proposed existence of neutron as well (proven in 1932 by Chadwick) Nobel Prize in 1913 Quantized Model of the Hydrogen Atom Niels Bohr ( ) Incorporated Planck s & Einstein s ideas Developed quantized energy model Explained (some) spectral emissions Nobel Prize 1922 Matter Waves debroglie model uses wave-particle duality Louis debroglie ( ) 1924: All moving particles behave like matter and waves simultaneously 1927 experimental evidence: (particles) moving through slits formed diffraction patterns (like waves) debroglie Wavelength & frequency: h E λ = f = m v h Matter waves explained Bohr model standing waves fit electron orbits Nobel Prize 1929 Heisenberg Uncertainty Principle Werner Heisenberg ( ) 1927: it is fundamentally impossible to make simultaneous measurements of a particle s position and momentum (mass x velocity) with infinite accuracy Result: can t pin down location of electron as assumed in Bohr & debroglie atomic models Look at debroglie s equation: h λ = m v debroglie: If you know wavelength, then you know the exact momentum (p = mv) Heisenberg said that is impossible! Nobel Prize 1932 Electron Cloud Model Erwin Schrödinger ( ) Built on debroglie and Heisenberg s ideas...developed more complex wavefunction equation (ψ) model Predicted behavior of e - in space and time think of it as predicting where and when an e - based on probability* If you map out these likely locations over time, you would see a cloud of possible locations around the nucleus* ψ 2 is proportional to the probability of finding the e - at a particular location at a particular time* The most likely location (highest probability) corresponds to the Bohr/deBroglie orbits Nobel Prize 1933 *Another scientist, Max Born ( ), is credited with developing the statistical interpretation of Schrödinger s equations. He won a Nobel Prize in The birth of quantum mechanics These were just a few of the scientists who help develop an initial understanding of a new field of physics...quantum mechanics Our understanding of the sub-atomic structure of the atom continues to evolve through both theory and experimentation Many practical applications followed (e.g., modern electronics, lasers, nuclear power) 5