Transmission 0.7 Beta
BackgroundThe transmission of beta particles (electrons and positrons) emittedby a source through material shows a quite different behavior than that of monoenergetic electrons. The electron energy spectrum of most betasources, e.g.
Thesource, is continuous with an intensity maximum at about 0.7 MeV and a maximumelectron energy of 2.2 MeV. High energy electrons loose energy inmaterials through (a) inelastic collisions with the atoms of the materialionizing its atoms and (b) through radiation of electromagnetic radiation(Bremsstrahlung). Calculating the transmission rate for electrons isvery complicated making it necessary to measure it as a function ofmaterial thickness. This is important if one needs to design shieldingfor highly active material.Often it is found that the experimental result can be described by asimple exponential function. ExperimentUse a source, a Geiger-Mueller (GM) tube and thecorresponding electronics. Connect the coaxial cable of the GM tube tothe input of the counter and set the time interval to 60 seconds.(THEEND WINDOW IS VERY FRAGILE. DO NOT TOUCH IT.) As absorber material youwill use index cards.
Determine the detector plateau. The GM tube together withthe counting electronics starts to work only above a certainminimal voltage which needs to be determined experimentally. To dothis set the counting time to 10 seconds amd mount the source asclose to the detector as possible (do not damage the thin entrance window!).
If you use a small detector(about a diameter of 1”) start with a voltage of 320 V. If youhave a bigger detector you need to start at about 450 - 500 V. Ifthe system does not show any counts, increase the voltage by 20 Vand try again. Once you onbain counts record the number of countsobtained for this voltage, increase the voltage by 20 Vand record the number of counts again. Repeat this process until at some point thenumber of counts do basically not change anymore. You have now reacheda counting plateau. Plot the counts as a function of detectorvoltage.
Select as an operating voltage a value where the counts donot vary anymore. (Typical values for the small detector are 420 Vand for the large detectors 740V).
Place the source in such a way that it is as close as possible tothe detector but that you can insert all index cards without havingto move the detector. Determine the background rate by counting about 200 events withouta source. Note the time it took to reach that many counts. (What isthe uncertainty in the background rate?). Put the source back and without any cards, count until you have about 200 counts and recordthe time. Place 10 index cards between the source and the detector.
Transmission 0.7 Beta 5
Transmission 07 Audi A3
And countagain until you have about 100 - 200 counts and record the time. Continue to add index cards until you measure only backgroundevents.
Beta 1.0
In this case all your electrons have been absorbed. Take more data in between to get a set of about 10 measurements,covering the range of index cards up to your maximum. Analysis. For each data point, subtract the expected number of backgroundevents from the measured events and calculate the final rate and its error. When calculating thefinal rate make sure you include the contribution from the background using error propagation. Plot the natural logarithm of the rate (and its correspondingerror) as a function the number of index cards. You should see a straight line, indicating that the expression inis indeed a reasonable description.
From the slope determine and(indluding their errors) andcheck that these values are consisyent with your measurement.