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WARNING!!!
This is the write up for the equipment we used before. Tomorrow we will use computercompatible counters. Procedure will change a little (not much) in terms of the collecting
data using computer interface. This will be the first time the new counters will be
used!!!!
EXPERIMENT 6
COUNTING STATISTICS
Print the report page to start your lab report
Print 2 copies of the data page
OBJECT:
To observe radioactive decay and study its statistics.
APPARATUS:
Geiger-Muller counter, radioactive gamma source.
THEORY:
The radioactive decay of atomic nuclei is a purely random process, one nuclear decay not depending upon
any other nuclear decay.
In order to study this "invisible," random decay, detectors must be used that are much more sensitive than
our own senses. The electronic output from these detectors must be related to the nuclear decay of the
atoms and must be analyzed with the aid of statistical models.
The detector to be used in this experiment is a Geiger-Muller tube, shown schematically in Fig. 1.
Figure 1. GM tube with electronics.
The GM tube is a thin conducting, electrically grounded cylinder filled with a dilute gas (10% argon, 90%
methane) with an axial wire held at a high, positive voltage. Nuclear radiation - gamma rays, high velocity
electrons, positrons, alpha particles, protons, etc., - that enter the GM rube will ionize the atoms or
molecules in the dilute gas. The free electrons created by this ionization will be accelerated in the electric
field (created by the grounded cylinder and high voltage axial wire) to high velocity and will collide with
and ionize more atoms or molecules in the gas. Eventually a large number of electrons will reach the axial
wire, constituting an easily measured electronic pulse. This pulse is shaped, amplified, and counted in the
supporting electronics.
The positive ions created in the GM tube migrate to the cylinder walls and are neutralized. Until most of
these ions are neutralized, the electric field is lower than during the initial ionization events. If another
ionizing particle enters the GM tube, the number of (secondary) electrons reaching the axial conductor
will be low, and the electronic pulse will be smaller than normal. In some cases it may be too small to be
counted by the electronics. Therefore, at high pulse counting rates, some pulses are not counted, and at
very high pulse counting rates, say 100,0100 pulses/sec, more than 20% of the pulses may not be detected.
Some nuclear radiation may not produce many initial free electrons, resulting in a small electronic pulse
that may not be counted. Therefore the GM tube is not 100% efficient in counting nuclear radiation.
When the detector is set up for counting decays of the same source during a specific time interval (let's say
30 seconds) the counts will differ from one to another, which reflects the random nature of nuclear decay.
Each nucleus has a constant probably per unit time that it will decay, but exactly when it will decay cannot
be predicted - just like the roll of the dice will eventually produce a 6 (there is always a constant probably
per roll that the dice will come up with a 6), but you cannot know exactly which roll will be the six. And
like the dice which can yield ten 6's in a row and then 40 rolls with no 6s, many atoms may decay in the
same second and very few in the very next second. Statistical models can be used to study a collection of
randomly occurring events.
In this experiment we will measure the number of decays produced by the source during 30 seconds
intervals. Each separate count represents a sample of the decay pattern of the radioactive source being
studied. This radioactive source has a long half-life time, so an average activity (decays per second)
remains constant for the lab period in which the experiment is being performed. The randomness of the
decay insures that all counts are a sample of the distribution of the decay times (and rates) of the atoms. At
very low counting rates, the theoretical distribution for random decays is the binomial distribution, and at
high counting rates, the distribution for random decays is a Gaussian, or normal distribution.
PROCEDURE
Exercise 1.
Determine the best operating voltage for your GM tube. Follow the sequence of instructions below.
1. Place a radioactive source near the GM tube.
2. Turn the GM high voltage knob to zero.
3. Turn on power to the electronics.
4. Turn the GM high voltage to about 260 volts.
5. Count for 30 seconds.
6. Increment the high voltage by 20 volts and count for 30 sec.
7. Repeat step 6 until the high voltage reaches about 1000 V or the number of counts exceeds about
10,000.
8. With reference to Figure 2, select an operating voltage from your data.
Figure 2. GM characteristic curve.
Exercise 2.
Move the source so that the observed counting rate is about 2000 counts/30 seconds. Take 50 separate 30
second counts and record your results in the Table 1 of your data page.
DATA ANALYSIS
Exercise 1.
Plot the characteristic curve of your GM tube. Explain your choice of the operating voltage.
Exercise 2.
Attach the Table to your lab report. Calculate the average count Xavg and its standard deviation  using the
formulas for Gaussian distribution. N is the total number of experiments (N=50).
Look at your data and find the maximum count Xmax , and the minimum count, Xmin. Record them. Divide
the interval
(Xmax - Xmin) into (N)1/2 = 7 parts. Look at your data again and find out how many of your counts fall into
each interval. Record your data in the Table 2. Plot L as function of X. Mark the ends of the intervals on
your graph. The graph you have made is called a histogram.
Look again at your data and fill out Table 3. Compare columns 3 and 4 in table 3. How well does the
Gaussian distribution describe your data?