Experiment 1
This experiment consists of two parts: Identifying the different features of the NaI gamma
spectrum, and investigating the statistics of nuclear counting.
1. Identifying the features of the NaI gamma spectrum
In the introduction to this experment, we will discuss the different parts of the NaI
gamma spectrum. You will be given a printout of three different gamma spectra taken with
one of the NaI detectors in the laboratory. You are to identify all the different features of
each of the spectra. If the following features are present, be sure to indicate them on the
graphs:
a) photopeak(s)
b) Compton Region(s)
c) Compton Edge(s)
d) Backscattering peak(s)
e) Characteristic X-rays
2. Statistics of Nuclear Counting
In this part of the experiment, we will examine the statistical properties of radiation
detection. You will take 40 one minute recordings of a radioactive isotope: 137 Cs, 22 N a or
60
Co. You will repeat the measurements with the same isotope in exactly the same way. For
each one minute recording, measure the counts for three different channels: one channel near
the center of a photopeak (A), one channel near the half-maximum (B), and one channel in
a background region (C). Use the same three channels for each of your 40 recordings. The
aim of this experiment is to examine the statistical fluctations for three different values of
Nave .
We will post our values on the board, and have a classroom discussion of the results.
a) Take 40 one minute recordings with your sample at an appropriate distance from the
detector. Keep the distance the same for each recording. For each channel, we will label the
counts as A1 , A2 , ... , Ai , ... , A40 , B1 , B2 , ... , Bi , ... , B40 , and C1 , C2 , ... , Ci , ... , C40
for the three channels.
b) For each of the three channels, calculate the average number of counts, Ā, etc. of your
data:
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Ā =
B̄ =
C̄ =
Pi=40
i=1
Ai
40
Pi=40
i=1
Bi
40
Pi=40
i=1
Ci
40
c) Calculate the experimental standard deviation of the Ai ’s, etc. about their average value,
Ā for each of the three channels:
σexp (A) =
σexp (B) =
σexp (C) =
d) Calculate σth (A) =
√
Ā, σth (B) =
√
sP
i=40
i=1 (Ai
sP
39
i=40
i=1 (Bi
sP
39
i=40
i=1 (Ci
39
B̄, σth (C) =
√
− Ā)2
− B̄)2
− C̄)2
C̄. Calculate the reliability factor R
for each channel, which is defined as:
σexp
(1)
σth
Is your value for R within the expected range for each of the three channels? Discuss your
R≡
results.
In future experiments, when we measure the number of counts (N), we will use σ =
for the statistical uncertainty of our data.
√
N
Report for Experiment 1
Your lab writeup will consist of the following:
1) (3 points) Identify the isotopes of the three spectra passed out in class. For each one,
point out the different features (photopeak, compton edge, etc.).
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2. (9 points) Show the calculation (you can use excel or another speadsheet) of your average
and standard deviation for your 40 one minute recordings for each of the three channels.
Discuss your value of R for each of the three channels.
Answer the Following Questions: Maximum 8 points, two points for each correctly answered
question (part credit 1 point). That is, choose any 4 of the following 5 questions.
3. For one channel, add up the counts for all of the 40 one minute counts, and consider
the sum as the number of counts for one 40 minute recording. That is, pretend that you
took one 40 minute recording of data at a particular channel, and the number of counts you
recorded is equal to the sum of the 40 one minute counts. For this case, what is the counting
rate and the statistical uncertainty in units of counts/minute?
4. Derive the relationship σth =
used in lab to derive C̄ = pN .
√
C̄. Show all your steps. You can use the method that we
5. The half-life of an isotope is 2 minutes. If we have 1000 isotopes at time t = 0, how many
on the average do we expect to have after 2 minutes? What is the standard deviation of
this average? (Note: you might not be able to use the simple formula from Poisson statistics.)
6. You performed an experiment which entailed counting the number of particles that entered your detector. If you recorded 25,000 counts in one hour, what is the count rate and
its uncertainty in counts/min?
7. In a particular experiment you expect to get around 100 counts per hour. How long
should you collect data if you want to measure the count rate to an accuracy of 2%?
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