Location: PAB B248
Section A: MW 1:30-4:20 PM
Section B: TTh 1:30-4:20 PM
Prerequisites: PHYS 225 and PHYS 334
Recommended: 30 credits in physics, including PHYS 231; take in parallel with PHYS 421
- Lab Notebooks and Lab Reports
- Extended Experiment and Presentation
- Class Policies
- Course Materials
The modern physics labs in the 43x series are intended to provide a bridge between the introductory labs, which are mostly "canned" in the sense that there is a fixed sequence of activities to perform and a fairly rigid analysis to carry out, and the kind of "open ended" research that you would do in a real experiment, where you don't really know what will happen or how you should interpret the results. In addition, the physics itself is more complicated than in the intro labs. As a result, most of the experiments in this course require significantly more time for data analysis and uncertainty assessment than for data taking itself.
The experiments in 432 focus mainly on the physics of individual atoms or molecules. Most are forms of spectroscopy: the basic measurements probe the relationship between the variation of a particular parameter, such as wavelength or magnetic field, and the transition energies between various electronic states of an atom or molecule. The range of electromagnetic energy treated by these experiments runs from x-rays (keV) through visible light (eV), microwaves (meV), down to radio waves (neV). Although each energy range requires different detection techniques and apparatus, there are common threads that run through many of the experiments: the physics of quantized angular momentum and its consequences, such as "selection rules" and "Zeeman energy," appear again and again.
It is expected that students will complete an experiment and turn in their lab notebook and a detailed write-up every two weeks. There will be brief lectures at the start of the first class of most weeks. By the third class of each two-week block an instructor or a TA will review students' progress to verify that they are on track to complete their experiment on time. Toward the end of the quarter, students will give brief presentations on a self-directed "extension" of one of the experiments (details below), while observing students will complete questionnaires on the presentations. There is no final exam for this course.
The currently available experiments in the 432 labs are broken into two groups. The data collection for experiments in List 1 can generally be done in one lab period, and/or the analysis is fairly straightforward. The experiments in List 2 may take more than one period and are typically richer in terms of analysis. At least three of the five required experiments must be from List 2.
Optical Spectrum of Hydrogen and Deuterium: Students measure the Balmer series emission lines of hydrogen and deuterium. Results of the measurements are used to derive a value of the Rydberg constant for each of the isotopes. The concept of reduced mass is introduced and the dependence of the Rydberg constant on this parameter is noted. A value for the H-D mass ratio is then derived from the values of the two Rydberg constants.
Moseley's Law and the X-ray Spectra of Atoms: Students measure the x-ray emission lines of multi-electron atoms using a high resolution solid state detector. They learn how the simple physics of the hydrogen atom is generalized to describe the major features of x-ray spectra for Z > 1. Students record the spectra from several samples of unknown composition, thus seeing first-hand how x-ray fluorescence can be used to determine the elemental composition of such samples. They are introduced to the physics of solid state detectors, thus acquiring insight into the remarkable resolving power of these devices.
Hanle Effect: The Hanle effect in mercury atoms is used to make a Doppler-free measurement of the lifetime of the first excited state. Light from a secondary mercury source is shone onto a primary mercury vapor cell located in a slowly varying magnetic field. This field induces a Larmor precession in the excited atoms, and as they decay to the ground state the precession results in a time-varying spatial distribution of the decay radiation. The magnitude of the decay radiation is measured as a function of magnetic field strength. The data are fit to a Lorentzian line shape, thus allowing the students to determine the lifetime as one of the fitting parameters. For many decades this method was the only Doppler-free way to measure atomic lifetimes.
Franck-Hertz Effect in Mercury and Neon: In this experiment students repeat the original measurement that demonstrates the quantization of atomic energy levels using a probe other than photons. Electrons emitted from a heated cathode are accelerated by a potential dierence as they pass through a mercury vapor. When they have gained sufficient energy, the electrons collide inelastically with mercury atoms, exciting them from the ground state. Electrons are collected at the anode, and the anode current shows minima and maxima at potential differences related to the energy difference between the ground state and the lowest lying excited states of the mercury atom. Thus, the students see striking evidence for energy quantization simply by watching the current meter. The Franck-Hertz effect is also used to investigate neon atoms where bright emission bands are visually observed in the regions where the electron have sufficient energy to excite neon atoms from the ground state.
- Inversion Spectrum of Ammonia: This experiment is a beautiful realization of the effects of the quantum mechanical double well potential. The ammonia molecule is pyramid shaped with the three hydrogen atoms forming the base and the nitrogen atom at the apex. The nitrogen atom sees a double-well potential with one well on either side of the plane defined by the H atoms. The wave function for the N atom can be either symmetric or anti-symmetric, the two states being split by a small energy dierence. When a RF (microwave) field is applied at this energy difference, the resulting wavefunction (a combination of the symmetric and anti-symmetric functions) shows the N atom to be tunneling back and forth from one well to the other at the frequency of the applied field. The shape of the molecule and therefore that of the double well potential is a function of the rotational state of the molecule, with the result that the tunneling is observed at many dierent frequencies depending on the particular rotational state. Students measure a number of these frequencies and fit them to a model accounting for the rotational effects. Students also observe and measure hyperfine splitting due to the quadrupole moment of the N nucleus.
Optical Pumping in Rubidium: This elegant experiment introduces the double resonance technique, whereby magnetic resonance transitions are detected by optical absorption. Circularly polarized light from a Rb lamp passes through a cell containing Rb vapor. A weak magnetic field is applied to the cell, splitting the ground state sublevels. Transition rules are invoked to explain how the population of these sublevels becomes inverted, with the result that optical transitions from the ground state to the first excited state are greatly reduced. Re-distribution among the ground state sublevels is achieved by application of a radio-frequency field, resulting in increased optical absorption in the cell. The magnitude of the magnetic field is thus measured by frequency, a parameter readily measured to high accuracy, making this double resonance technique useful as a highly sensitive magnetic field probe.
Normal and Anomalous Zeeman Effects in Mercury: Students measure the magnetic splitting of the yellow (normal) and green (anomalous) lines of mercury, and learn about the physics accounting for the two quite different spectra. A high resolution Fabry-Perot interferometer is used to measure the spectral splitting as a function of applied magnetic field. Students also learn the physics of the Fabry-Perot interferometer, thereby gaining an understanding of how this device can provide such high resolving power.
Lamb Shift in Hydrogen: According to Arthur Schawlow, "The spectrum of the hydrogen atom has proved to be the Rosetta stone of modern physics: once this pattern of lines had been deciphered much else could also be understood." In the early 20th century the spectrum of atomic hydrogen was a key factor in the development of quantum mechanics. As experimentalists made more detailed measurements, increasingly refined theoretical models kept pace with explanations of the proliferating number of features in the hydrogen spectrum. But some measurements made in the 1930's hinted at a discrepancy for which even the Dirac theory could not account. In 1947 Lamb and Retherford measured the energy difference between the lowest n = 2, S1=2 and P1=2 states, predicted to be degenerate by the Dirac theory. This measurement provided one of the first tests for the now well-established theory referred to as quantum electrodynamics (QED), which continues to provide a benchmark against which increasingly refined versions of this theory are tested even today. In this experiment, atomic hydrogen is generated in a discharge tube, and students initially observe the Doppler-broadened fine structure lines of the Balmer alpha transition at 656 nm. Then, deploying the technique of saturation spectroscopy, students record the Doppler-free spectrum, easily resolving the fine structure components of this line, and also the Lamb shift. In addition to measuring the fine structure splittings and the Lamb shift, one can use the recorded linewidths to estimate the lifetimes of the various excited states.
Pulsed NMR: In this experiment students are introduced to the modern NMR techniques underlying such applications as magnetic resonance imaging and mapping the structure of complicated organic molecules. Students learn how to put the sample in specific spin states, and then how to manipulate these spin states to accurately measure the longitudinal (spin-lattice) and transverse (spin-spin) relaxation times. In the process of mastering this "spin engineering," students learn how pulsed NMR techniques provide quantitative information about the spins and their environment that is not accessible using the simpler continuous wave NMR technique.
For each experiment you perform, you will turn in your lab notebook and a formal lab report. Lab notebooks are turned in to your TA by 4 pm on Friday at the end of each 2-week lab block. The notebook must include:
- In-class notes, i.e. a journal of your progress on the experiment
- A well-annotated hand drawing of the apparatus
- All raw data, including uncertainties
- A preliminary analysis of the results, including discussion of uncertainty propagation
- Answers to any exercises assigned in the lab manual
For details please see the Lab Notebooks page.
The reports should be submitted online on Canvas as PDFs and are due by 5 pm on Friday at the end of each 2-week lab block. Each report must include
- A formal description of the experiment and its relevance or importance
- A discussion of the key observables, how they are measured, and their uncertainties
- A summary of the data taken
- Details of the analysis performed, including uncertainty propagation. Any spreadsheets or computer code or the like used in the analysis, including all inputs, should be attached as additional files to the lab report submission in Canvas
- A listing of the experimental results, including a discussion of the dominant uncertainties, and comparison to values available in the literature, when available
More details can be found on the Lab Reports page.
Late work will not be accepted, it will be assigned a grade of zero. There are only two exceptions to this policy:
- The work is late because of illness, family emergency, etc., that causes you to be unable to do any school work.
- You contact the instructor more than 24 hours prior to the due date and request an extension.
The idea of the "extended" experiment is to get you to dig deeper into an experiment you found interesting and explore it more intensely. For example, you might study additional samples, investigate a different parameter space, carry out a computer simulation to compare against your measurement, track down a systematic error and see if you can correct for it or eliminate it, or use the apparatus to make a wholly new kind of measurement.
Ideas for extending each experiment will be posted on the class website. You are also welcome (and encouraged!) to come up with your own ideas. When thinking of possibilities, you will need to consider their feasibility. For example, you cannot completely reconfigure a setup while it is still being used by others for regular experiments, neither should you depend on the purchase of special material or equipment, since this may take too much time (or money). You may very well need to do some outside reading or research for your special experiment, even if you follow some of the suggested options. Ask the instructor or TAs about books or papers to read, and do your own literature searches on the web and in the library.
Each group will give a presentation to the class on their extension. Each student will also be required to complete at least 2 questionnaires on their classmates' presentations. Extra credit will be awarded for filling out additional questionnaires. For more details, please see the Experiment Extensions page.
Click here for Class Policies: Rules, Requirements, and Grading
The primary course reading materials are those that appear on the experiment pages linked above. These will not be handed out in class. You are expected to print out your own copies of the experiment instructions or otherwise have them available with you during the labs.
Recommended texts (copies are on reserve in the Physics/Astronomy Reading Room):
- Experiments in Modern Physics, Adrian C. Melissinos (Academic Press, San Diego, CA, 1966)
- The Art of Experimental Physics, Daryl W. Preston and Eric R. Dietz (John Wiley & Sons, New York, 1991)
- Atomic Physics, C. J. Foot (Oxford University Press, Oxford, 2005)
Additional reading material in three-ring binders may be borrowed from the lab as needed. The binders contain some relevant journal articles, older versions of experiment instructions, and copies of textbook material.
The following links point to articles that give information on experimental uncertainty and error analysis, and how to calculate and present uncertainty in lab reports:
- Notes on data analysis and experimental uncertainty (elementary treatment with many useful hints, by David Pengra and L. T. Dillman).
- Quickie Statistics Summary (from Physics 331).
- LSQFit.xls: an Excel spreadsheet that will calculate a fit line using full weighting of uncertainties; also calculates reduced χ2. From the Methods of Experimental Physics course at the University of Minnesota (written by Kurt Wick).
- Examples of error propagation (from the University of Chicago).
- Error Analysis and Signal Averaging notes from Prof. Bob Van Dyck
You will also need two cardboard expansion report covers, green or tan engineering paper, and insertable notebook dividers to build your lab notebook. Please see details on the Lab Notebooks page.
Click here for the Scope Exercise.
The syllabus page shows a table-oriented view of the course schedule, and the basics of course grading. You can add any other comments, notes, or thoughts you have about the course structure, course policies or anything else.
To add some comments, click the "Edit" link at the top.