Department of Physics, Middlebury College

1992-93

Modern Physics Laboratory



V. The Geiger-Müller Tube and Poisson Statistics



Discussion

The Geiger-Müller detector is a gas-filled, cylindrical chamber in which a pair of electrodes collect electron-ion pairs produced by penetrating radiations that ionize atoms or molecules of the chamber gas, as shown in Fig. 1. The electrical pulse generated by the electron-ion pairs can be amplified and sent to an electronic counter or scaler where the radiation event is registered.

Positive high voltage is applied to a wire along the central axis of the chamber and the conducting walls of the tube are connected to ground potential. The chamber is filled with a special low pressure gas mixture and is sealed to prevent contamination of the chamber gas by the atmosphere. A thin piece of mica at one end of the chamber provides a window for penetrating radiations. Radiations that pass through the end-window ionize atoms of the gas mixture and the resulting electron-ion pairs experience forces due to the electric field between the central anode wire and the conducting wall. Electrons drift to the anode wire and ions drift to the wall, creating a small voltage pulse that can be transmitted to an appropriate amplifier.

Alpha and beta particles are charged and interact readily with atoms in the gas mixture; however, if their energies are too low, they can be stopped in the window material and no ionization events result. Gamma radiation is uncharged and therefore interacts only weakly with the chamber gas atoms. Gamma rays are detected only indirectly, when they strike electrons in the chamber wall and the electrons recoil into the cylindrical chamber causing ionization of the chamber gas. A typical Geiger-Müller tube detects only 1-10% of the incident radiation from a source placed near the end-window of the tube.

Procedure

(1) Obtain a Model E-2 Nuclear Scaler, accompanying manual1, and a radioactive source set containing 60Co, 90Sr, and 210Po sources.

(2) Determine the Geiger-Müller tube response curve for the E-2 Nuclear Scaler. Using the 60Co source, measure the count rate in counts per minute (cpm) while varying the GM tube voltage from 200 to 700 V in 50 V steps. See p. 16 of Ref. 1 for a typical response curve. Plot your curve and designate clearly the operating voltage (center of the plateau region) to be used in the rest of the experiment. Be sure to use appropriate error bars when plotting your data.

(3) For each of the three radioactive sources, make 25 one minute measurements of the source counting rate in cpm. Place sources in the second highest slot of the sample tray holder of the E-2 Nuclear Scaler unit. From these measurements, compute the mean, m, and the standard deviation, , of the counting rates measured for each of the three sources.

(4) For each of the three sources, make a histogram of the 25 individual counting rate measurements. Be sure to choose an appropriate scale and "bin" size so that your histogram has some reasonable width, as in Fig. 2.

Analysis

(1) For each of the three sources, use the mean counting rate µ deduced from your data to evaluate the Poisson probability function2

P(n)

=

µn

e,

__

n!

where n is an integer number of counts and P(n) is the probability of measuring that number of counts. It is understood that n and µ refer to the number of counts measured in the same time interval, i.e. one minute for your measurements. Multiply P(n) by 25 and by a factor appropriate to the bin size, to obtain a distribution that can be plotted directly on the appropriate histogram. You will almost certainly find the use of a programmable calculator or a computer helpful in making your calculations. When completed, your three histograms should look similar to the one in Fig. 2.

The numerical evaluation of P(n) involves some subtleties that you may wish to discuss with the instructor. You are encouraged to consult Ref. 3 to get some ideas.

(2) Discuss the agreement of your data with the predictions of Poisson statistics.

References
1. Model E-2 Nuclear Scaler, manual (The Nucleus, Oak Ridge, TN).
2. H.D. Young, Statistical Treatment of Experimental Data (McGraw-Hill, New York, 1962), p. 59.
3. F. Reif, Fundamentals of Statistical and Thermal Physics (McGraw-Hill, New York, 1965), pp. 610-614.

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