Notes for Experimental Physics Experiments

Notes for Experimental Physics Experiments – 3/4/05

The following are suggestions for what you should be sure to do for each experiment.

Do not hesitate to discuss the experiments or write-ups with me and the TA’s.

Some experiments require a laptop with specific software:

Ø  Resistivity and Johnson Noise: Scope Explorer Program, pick appropriate version for OS

Ø  Radioactivity of metals: LoggerPro software (from Physics I)

Ø  Semiconductor diode characterization: LoggerPro.

Ø  Compton Scattering: Genie File Convert, MCIA-GPIB Software and Genie 2000 DOES NOT OPERATE ON WINDOWS XP/2000!!!

Ø  Atomic Spec: 3.5" floppy disk (no laptop required)

Ø  Radioactivity: LoggerPro.

Where to get the appropriate software:

LoggerPro: Physics I/II website.
Scope Explorer: This course website.
LabView: CIC Help Desk
Diode Temperature II: this course website
Genie/MCIA/File Convert: must be loaded and operated in the classroom (Hardware key!)

EXPERIMENT NOTES:

Dielectric Constant of a Gas

In this experiment, you measure the beat frequency between two oscillator circuits as you change the gas in an air gap capacitor.

·  Read chapter 8, review relevant sections of chapters 2 and 3

·  Measure the dielectric constant for CO2 (or whatever gas is in the large tank when you get it.) You are expected to measure the change in beat frequency as a function of gas pressure several times in order to compare the results of different runs. Compute the dielectric constant from the slope of the beat frequency plotted against pressure.

·  For each set of measurements, you should fit a least squares line to find the slope and compute both the uncertainty in the slope and the c2 for the fit. Discuss details of the measurement and sources of uncertainty.

·  Statistical analysis is important. Estimate uncertainty in the slope of each run. Take enough separate runs to estimate the run-to-run uncertainty. Is your measured dielectric constant consistent with literature values?

Eddy Current Measurement of Resistivity of a Metal

In this experiment, you use the current in a probe coil to detect the decaying eddy currents in a metal rod. Collect voltage versus time decay data so that you can fit log(voltage) against time over at least two decades in voltage.

·  Read chapter 10 and review relevant sections of chapters 2 and 3. The circuit should be changed to add a variable resistor in parallel with the solenoid. This damps some oscillations out of the solenoid current.

·  Use the + and – outputs on the HP current supply.

·  It is more important to do a good measurement and analysis on one sample than many not-so-good measurements on many samples. Unless there are complications, you should measure and compare the copper and aluminum cylindrical rods. You can also look at shape and size effects.

·  You will need to do either a weighted linear least squares fit or a nonlinear (exponential) fit to the data and a careful discussion of uncertainties for full credit.

·  Data can be transferred directly to a diskette using the LeCroy oscilloscope. This needs to be reformatted to make a text file.

·  Uncertainty analysis is very important for this experiment. Measure the same sample several times and compare results. Is your result consistent with the literature? If not, discuss what the sources of systematic error might be.

Johnson Noise

·  Read chapters 13 and 14 and review relevant sections of chapters 2 and 3.

·  Construction and calibration of the two-stage amplifier is very important. Make sure you have got this right before you proceed.

·  Calibrate your amplifier system as a function of frequency using a sinusoidal input from the wavefunction generator and using a voltage divider to get a small signal. Verify that the amplifier is linear at several frequencies. Show the gain as a function of frequency.

·  Measure the noise signal on the oscilloscope for at least four different resistances from 10W to 2x104W. Perform multiple measurements for any given resistance and use this information to estimate uncertainties. Napolitano suggests that you use the oscilloscope to perform analysis, but I would like for you to store the raw (voltage-time) data on diskette and analyze the data using a program so you know exactly what you are doing to the data at each step. This approach is outlined in section 14.3.1. You may need more than one 1.4 MB diskette. Note that data can now be transferred directly to your laptop, so see a TA to proceed with this part. Perform a linear regression on the rms noise signal as described in Napolitano to determine the Boltzman constant.

·  Perform Fourier analysis on the noise signal to determine whether the noise is indeed “white”. Compare the noise spectrum to the gain spectrum of your amplifier.

Atomic Spectroscopy

·  Read chapters 11 and 12.

·  You will be using the Jarrell-Ash scanning spectrometer with photomultiplier detector. The spectrometer and detector are run by a LabView program. You have a lot of control over this experiment and you can do damage to the photomultiplier so review all of the material here and get a thorough introduction to the instrument before you begin..

o  You can control the current from the photomultiplier either by varying the applied high voltage or by varying the slit width on the monochromator input. Do not let the signal level exceed 5V. You should check out the system by scanning by hand and viewing the signal on the multimeter. Decrease slit width and/or voltage to keep the maximum signal below 5V. Do not increase voltage above 1000V. Remember that increasing slit width decreases wavelength resolution.

o  The “spectrometer2” version of the program can be used for long "low resolution" scans that are used for computing the Rydberg constant. You can switch to "high resolution" for the D2-H2 splitting. Later versions have computer controlled step size.

·  Find out how the spectral width of a single He line depends on slit width. Use high resolution scanning over a narrow (10-20 A) range. You will have to readjust the high voltage to keep the maximum on scale.

·  Pick a peak and slit width. Find out how the signal level depends on high voltage. (Remember, keep the voltage below 5 V output.)

·  Calibrate the monochromator by identifying spectral lines from the helium source in one long scan from 400 nm to 700 nm. Assess sources of systematic and random uncertainty. Repeat at least once and compare scans. Measure the Mercury spectrum and compare observed spectral positions with textbook positions. Note that the monochromator dial reading is not calibrated. You should keep track of where the scan started, where it ends, and how many steps were taken to get a good calibration. Note that the monochromator has significant gear backlash, so you should always start a scan with the gears moving in the direction of increased wavelength.

·  Measure the Rydberg constant by measuring and analyzing the Balmer spectrum of hydrogen between 400 nm and 700 nm.

·  Measure the mass splitting of deuterium and hydrogen for at least one line. The "Deuterium" lamp contains both hydrogen and deuterium, so you can use the H line to calibrate the shift. Make sure you have sufficient resolution to resolve H and D lines which are separated by only a few angstroms. Fit the two peaks to get the splitting as accurately as possible. Experiment with the high voltage supply and slits to get the resolution and signal maxima that you need.

·  Uncertainty analysis is very important for this experiment. How accurately can you measure the position of a single line? What is the standard deviation of data from the fit line? What is the run to run variability? What are the major sources of uncertainty? How does this uncertainty affect your ability to determine the Rydberg constant?

Faraday Effect

·  Read chapter 15 and review relevant sections of chapters 2 and 3.

·  Goal: Measure the Verdet constant for the water-filled tube.

·  Differences: You will use a RadioShack PA amplifier instead of the Bogen amp mentioned in the text. You will use the Stanford Instruments digital lockin amp instead of the PAR lockin described in the text. The solenoid is also significantly different.

·  Align the laser beam and sample so that the laser beam enters the detector with minimal scattering from the edges of the aperture.

·  Calibrate the dc signal diode voltage against polarizer angle. Identify the slope of the best angular region. The dc signal should have the form where the angle is measured with respect to the point where the signal is smallest. Test whether this is a good approximation for your data by measuring over a large enough range to include two minima.

·  Find the ac magnetic field for excitation at ~100 Hz using a pickup coil, an oscilloscope and Lenz's Law. Integrate the field along the z-axis of the solenoid. Check that the ac magnetic field at one point is linear in applied ac voltage from the amp. (Note: you may calculate the integrated Bdx from the expression, , where the constant, B0, is determined by measuring the central field and the coil geometry, and theta is the angle of a line from the axis point to the end winding, measured from the axis. Alternatively, you can measure B(x).)

·  Observe the voltage oscillation of the diode voltage on the oscilloscope for ~10V peak to peak voltage across the power resistors.

·  Test whether the ac diode signal voltage is proportional to field amplitude by varying the drive amplitude and measuring the signal using the lockin amp.

·  Note that the formula given by Napolitano for the Faraday rotation (eq. 15.10) is approximate. The angular rotation is proportional to the integral of field times Verdet constant as a function of position along the beam path,

The magnetic field B(x) can be measured using a small coil and the relation
. It is safe to assume V(x) is a constant of the material.

·  Uncertainty analysis is very important for this experiment. Most of it is uncertainty propagation through several stages. First, measuring the slope of the dc signal vs polarization curve. Second, accounting for variations in the dc laser output signal. Second, finding the integrated field. Third, measuring the magnitude of the ac signal.

Radioactivity

You have already done the counting portion of this lab. Now you should proceed to the decay and attenuation portions. Use the geiger monitor and use tongs to handle materials.

·  Read chapters 17 and 18. Chapter 18 describes the parts of this experiment.

·  Calculate the approximate radiation dose you receive by sitting ½ meter from the source for 8 hours.

·  Data can now be collected directly to your laptop using the LOGGERPRO software.

·  Perform measurements of attenuation and distance effects on count rate using the Cs137 source. (pp. 346-7) (There is no need to do the counting statistics experiments, you've done them already.) The signal should drop off as
where r is the distance to the front face of the detector and r0 is a distance to correct for the fact that the Geiger tube active area extends beyond the front face.

·  Measure and fit the decay of the Ba source produced by elution from a Cs cell. (p. 353). Keep track of which sources you have done, they are no good for several hours after they are used. Measure at least 3 elutions and compare results.

·  Fitting is very important for this experiment. You should carefully determine background so that it can be subtracted. The uncertainty in counts at a position is just the square root of the actual measurement, so the variance that you use in chi-squared fitting should be taken to be equal to the measured signal count. (I expect to see nonlinear least squares fitting with variable weights.) Multiple runs will allow you to estimate uncertainty in a different way than from just curve fit results on one sample.

Positron Annihilation

·  Read chapters 17 and 19, review section 3.5.

·  Learn about the detection system by measuring the spectrum of single channel amplifier output pulses as described in section 19.2.1. Do both detectors and show graphs of the results. You should attempt to set the gain so as to get the main annihilation gamma ray peak at about 3 V. Check the effect of detector distance. At the peak, plot singles rate as a function of energy window width. Choose an appropriate window width and show it on your singles scan. Run the singles scan over a range such that you can see both peaks (511 keV and ~1275 keV) and resolve the Compton escape edge of the 511 keV peak as well.

·  Set the energy windows to the 511 keV peak. Measure distance dependence of count rate and fit to where I0 and r0 are fitting parameters and r' is the distance from the front of the detector to the source. Count long enough to good statistics.

·  Observe the coincidence signal when the SCA’s are set on the 511 keV peak and with the detectors close (a few cm) to the source. Determine how it depends on coincidence module settings. Plot your coincidence rate against delay window width time.

·  Observe the angular dependence of the coincidence signal. How important is the spatial extent of the detector?

·  Repeat the coincidence experiment for both detectors set on the 1.275 MeV peak of the sodium source.

·  If we have the source, observe the coincidence effect for the Co source as discussed in section 19.3.

Compton Effect

·  Read chapters 17 and 20.

·  Data is now collected directly to your laptop using GENIE software. See your TA for instructions. There have been problems with Windows XP systems.

·  Calibrate the energy scale of the detector using a straight line fit to the peak of known sources. (Determine the peak position for each source by fitting each peak to a Gaussian function.) Estimate the uncertainty in each peak position by varying the peak position in your fit and determining the limits at which chi-squared increases by 20% above its minimum value. Is channel number linear in gamma ray energy?