Sorenson and Phelps Chapter 6; Bevington 84-86;
2. Set the pulse height analyzer for Cs-137. Measure the background count rate to a certainty of at least 3%. This means that you must obtain n counts, where n solves the algebraic equation 100% x (sqrt(n)/n) = 3%. In this case n equals 1111 counts in the window.
. 3. Arrange the source and detector to provide about 10 cts/sec. Take runs of 5, 10, 50, 100, and 200 seconds. For the report state the measured data, the calculated count rate (counts/time), the standard deviation of each measurement (sqrt(counts))/time), and the relative precision - 100% x sqrt(counts)/counts ) of each measurement. In addition, calculate these parameters for the lumped data (5 + 10 + 50 + 100 + 200 seconds). As the length of time increases, the count rates measured should "settle" on the true value with smaller and smaller uncertainty. Also as the length of time increases, the relative precision should get better (lower-valued).
. 4. For the report correct the measurements of part 3 for background and recalculate the parameters. Remember to propagate errors properly.
. Measure the counting rate as a function of distance at 3 points and correct for background. Obtain a precision of at least 3% for all points. Plot the data versus distance.
5. Measure 35 consecutive runs of about 300 counts in the Cs-137 (662 keV) energy window. Perform a Chi-squared analysis on these data as described below. Are the data consistent with a Gaussian distribution? Is the distribution too broad or too narrow?
The total report should not be longer than about 3 double spaced type written pages. (You may write it by hand).
For part 3, Plot the calculated count rate for the increasing acquisition times (part 3) and include error bars
Plot the rate vs. distance and compare to expected result. Explain differences from the expected curve. Include error bars. Calculate the efficiency as a function of distance and plot.
This part of the experiment is to distinguish if the equipment is functioning properly. If a meter is "stuck", some values might register more frequently than others and the results would not follow a Gaussian distribution but would be narrow. As pointed out by Sorenson and Phelps, the distribution might be broader than dictated by the counting statistics due to contributions from other than the random radioactive decay. The value of X2 (chi-squared) is given by:
X2 = (1/(N-1)) SUM (from i=1 to N) [Ni - Nave)]2, where N is the number of trials and Nave is the average value of all the trials. (N-1) is the number of trials with one removed to account for the use of the data to compute the mean. (N-1) represents the number of "degrees of freedom".
Compare your value of X2 with that the supplied table from Bevington's book for 34 degrees of freedom. The number you get from the table is the probability that a "real" Gaussian distribution exceeds your measured X2. In other words, if you get a P=0.99, you have a high probability that a "real" Gaussian distribution would have a higher X2. This means your X2 is too low, your distribution is too narrow - the meter's stuck! Likewise, if the P is low, there is a low probability that a "real" Gaussian distribution will produce a X2 which exceeds your X2 - you have a really broad distribution - other factors in addition to simple random radioactive decay are broadening the distribution. Comment on your findings for X2 in your report.
NOTE: A single measurement estimates the mean using the standard deviation as the uncertainty. Many measurements sample the distribution and can be used the measure the standard deviation (rather than assume it is the square root) and the mean.
(assignments will be rotated for each lab)
Laura Drubach, organizer
Mansoor Hussein, source
Richard Kuno, instrument operator
Gilbert Martinez, scribe/data
Alexander Matthies, geometry/measurement