P301 Lecture 12 “Bohr’s Hypotheses” Bohr formulated the following ad hoc model: 1.Atoms exist only in certain stable “stationary states” 2.The dynamic equilibrium of these stationary states is determined by the laws of classical physics, but the way the atoms interact with the electromagnetic field of light waves is not 3.The emission and absorption of EM waves by atoms takes place ONLY in conjunction with a transition between two stationary states, with the frequency of the emitted light being determined according to the Planck hypothesis: |E 1 – E 2 |= hf 4.The (orbital) angular momentum of the electron in a stationary state can only take on values given by integral multiples of Planck’s constant divided by 2  L n = nh/2  It is this last hypothesis that is the truly new (revolutionary) idea from Bohr himself, the other three are pretty much inescapable and/or had been provided by someone else already.

P301 Lecture 13 “Moseley’s Law” NOTES: Moseley started to catalogue characteristic x-ray energies (and therefore frequencies) using a technique we’ll discuss next week. He developed the above empirical relations for the frequencies, determined that atomic number, not weight, was the relevant parameter to explain the periodicity of the periodic table (e.g. he reversed the positions of Ni and Fe; K and Ar), and predicted the existence of three (and only three) previously undiscovered elements (Z=43, 61, and 75; later: Tc, Pm, and Re) “between Al and Au” KK KK LL LL LL

P301 Lecture 13 “Characteristic X-ray production” NOTES: Barkla first discovered “characteristic x- rays” in 1909, several years before Bohr, the Braggs, and Moseley did their work. The “shell” model of the atom, which arises from Bohr’s model for H, is very useful even when considering multi- electron atoms The various “shells” (K, L, M, N, etc., corresponding to increasing values for “n” in the Bohr model) are typically split into a few (or several) individual energy levels that are much more closely spaced than the separation between the shells. We will start to explore the smaller splittings later in the course.

P301 Lecture 13 “JITT question” It's electrons are easier to excite than the other two because its the only one with the spikes Tungsten Z=74 Lambda = *e-11m -› off chart Molybdenum Z=42 Lambda = *e-11m -› Bingo! Chromium Z=24 Lambda = *e-10m -› off chart [right, except at 35kV, the Ka lines of W don’t get excited; the L lines are out of the wavelength window.] Characteristic x-rays are the result of electron excitation. The electrons in Cr are bound too tightly for excitation to occur under the given conditions, and the electrons in W have less energy than those in Mo, so the peaks are absent. [reasoning is correct, but the roles of Cr and W are reversed.] It's electrons are easier to excite than the other two

P301 Lecture 13 “JITT question” What is the key similarity, and what is the key difference between the inelastic collisions discussed in the context of the Franck-Hertz experiment and those you studied in Physics I? Similarities: Momentum is conserved in both cases, but kinetic energy is not [most did not clearly answer this part of the question, those that did got it right] Differences: It's not a loss of mechanical to thermal in the atomic case, and the loss is QUANTISED in the atomic case. [11 concentrated on the quantized nature of the loss, with several others remarking on the energy-dependence of the loss, which almost amounts to the same thing]. Several of you were confused about the essential aspects of the problem: Objects only stick together in “perfectly inelastic” collisions in classical physics and the inelastic nature has little to do with relative size of the objects involved, therefore these are red herrings. ENERGY is conserved in inelastic collisions (as everywhere) it is kinetic energy that is not conserved. It's electrons are easier to excite than the other two

Franck-Hertz Experiment Fig. at right shows optical emission from Neon gas in a F-H tube. In regions where the electrons have enough energy to excite the neon atoms, the atoms emit visible light when they relax back to their ground state (from about 19eV to about 16.7 eV)

Franck-Hertz Experiment Fig. at right shows the energy levels for Hg (from the instructions for the F- H experiment in our P309 lab). In the grounds state of Mercury, there are two electrons in the 6s level, and the other levels shown are unoccupied.

How many of you recognize this?

The Structure of DNA: Rosalind Franklin and X-ray Diffraction

Bragg’s Law

d sin(  )  You get constructive interference only if: 2dsin(  ) = n This gets the right answer, but it is slightly unsatisfying (why do you consider planes of atoms rather than the atoms themselves, it doesn’t explain why some plane sets diffract and others don’t, and it doesn’t give you relative intensities of the various reflections, but it is easy to remember and it is very useful as a quick answer to give you much of the right phenomenology.

Laue Diffraction From “Techniques of X-ray Diffraction by B. D. Cullity

Test this out:

Silicon powder diffraction (Baxter lab)

Real X-ray apparatus Single crystal setup w 2-D detector Laue setup with digital “film”

“Powder” Diffraction

Bragg’s Law d sin(  )  You get constructive interference only if: 2dsin(  ) = n This gets the right answer, but it is slightly unsatisfying (why do you consider planes of atoms rather than the atoms themselves, it doesn’t explain why some plane sets diffract and others don’t, and it doesn’t give you relative intensities of the various reflections, but it is easy to remember and it is very useful as a quick answer to give you much of the right phenomenology.

P301 Lecture 13 “Characteristic X-ray production” NOTES: Barkla first discovered “characteristic x- rays” in 1909, several years before Bohr, the Braggs, and Moseley did their work. The “shell” model of the atom, which arises from Bohr’s model for H, is very useful even when considering multi- electron atoms The various “shells” (K, L, M, N, etc., corresponding to increasing values for “n” in the Bohr model) are typically split into a few (or several) individual energy levels that are much more closely spaced than the separation between the shells. We will start to explore the smaller splittings later in the course.

P301 Exam I Review Philosophy: The most important things in this course are developing an understanding and appreciation for how we know what we know about things that are very small or moving very fast. You should develop some understanding of what very small and very fast mean, but you needn’t be overly concerned with memorizing specific constants or formulae. You should be able to understand the key experimental results, their significance in shaping our current view in the world, and how their data are collected and interpreted. You should also understand and be able to use the various formulae we have derived and or presented in this class to quantify the sometimes strange phenomena involved (but recall you’ll have a formula sheet, so memorizing them is not essential).

P301 Exam I Review NO CALM QUESTION FOR MONDAY!!! Exam Mechanics: Covers material from chapters 1 through section side of 8.5x11” formula sheet is allowed. It is not to be a general note sheet 5 questions (50 points, but 9 “parts” worth 5 or 10 points each) One question has multiple parts with answers from earlier parts feeding later parts, if you have the right method on a later part but use an incorrect answer from the earlier part, you get full credit!! A mix of descriptive and computational answers. Tables from the inside front lay-out of the text will be provided. Exam will start at 11:10. Office Hours: Friday 1:30 to 3:30 Monday 8:40 to 10:30. No office hours Monday afternoon.

P301 Exam I Review Important experiments: Relativity Michelson-Morley experiment Muon lifetime observations from cosmic rays. Doppler Effect (expanding Universe, binary stars, extra-solar planets, SMOKEY, …). Synchrotron radiation (transformation of angles in relativity). Quantum Mechanics Cathode-ray tube experiments e/m of the electron X-rays: Bremsstrahlung, characteristic Photo-electric effect Franck-Hertz experiment Line spectra of gasses Compton effect Discovery of the positron (antiparticles in general) Rutherford scattering Bragg/Laue scattering Moseley’s law

P301 Exam I Review Important ideas: Relativity Speed of light is a universal constant irrespective of (initial) FoR. Lorentz transformation: time dilation/ Lorentz-Fitzgerald contraction. Relativistic mass, energy, momentum Transformation of angles Doppler Effect Space-time diagrams The invariance of interval Electricity and magnetism are intimately connected Quantum Mechanics Light is quantized (Blackbody radiation and hf=E, Compton and PE effects) Electric charge is quantized and electrons are much lighter than atoms Anti-particles exist Atoms have internal structure and dynamics (electrons, atomic spectra, X-rays, radioactivity, chemistry, Rutherford’s experiment). We can understand atoms in terms of quantize light and angular momentum (Bohr) We can explain the periodic table (sort of) Moseley

P301 Exam I Review Example descriptive questions: Identify and provide BRIEF descriptions of 4 important experimental results that came out of the study of electric currents in vacuum tubes or such tubes back-filled with dilute gas. Provide a sketch showing the essential elements of the apparatus used by Millikan to quantify individual elementary charges. Identify 3 of the crucial postulates Bohr used in constructing his model of the atom. Identify 2 experimental results that shaped Bohr’s construction of the atom. BRIEFLY describe two important results published by Einstein in Describe, BRIEFLY, the phenomenon known as the Ultra-Violet Catastrophe and how Planck’s quantum hypothesis avoids this failure of classical theory. (these last two are of the right style, but probably deal with subjects we did not cover in enough detail to be worth more than 5 points on the exam, if they would be asked at all).