Name ______________________
St.No. __ __ __ __ __-__ __ __ __
Date(YY/MM/DD) ______/_________/_______
Section__________
UNIT 102-11: NUCLEAR PHYSICS AND RADIOACTIVITY
The TRIUMF Cyclotron, located near the campus of UBC, which is used for
research in Nuclear Physics.
OBJECTIVES
1. To learn about nuclear structure and how to determine the binding
energy for a given nucleus.
2. To identify and understand the three major types of nuclear
radiation.
3. To explore the statistical process of radioactive decay and examine
the radioactivity of commonly occurring materials.
© 2009 by S. Johnson & N. Alberding (2013)
Page 2
Physics for Life Sciences II Activity Guide
SFU
SESSION ONE: NUCLEAR PHYSICS AND RADIATION
In the early 1930’s scientists developed a simple model of the
nucleus. According to this model. the nucleus is primarily composed
of two types of particles, protons and neutrons. A proton has a
positive charge +e = +1.6 x 10-19 C and a neutron has no electric
charge, hence its name. These two particles are referred to generally
as nucleons because they reside in the nucleus of an atom.
The number of protons in a given nucleus is known as the atomic
number, Z. The total number of nucleons is given by the atomic
mass number, A. You can specify a nucleus with just these two
numbers, so a symbol containing them has been developed in
nuclear physics:
A
ZX
where X is the chemical symbol for the element. The number of
neutrons, N, can be obtained from N = A - Z.
Experiments have shown that atomic nuclei are roughly spherical in
shape. A formula has been developed that estimates the radius of a
given nucleus depending upon its atomic mass number as follows:
r ⇡ (1.2 ⇥ 10
15
1
m)(A 3 )
From this formula you can see that the volume of a nucleus is
directly proportional to its atomic mass number, which one would
expect if nucleons act like solid balls.
✍ Problem Activity 11-1: Nuclear Sizes
Estimate the diameter of the following nuclei:
(a) 42 He
(b)
197
79 Au
© 2009 by S. Johnson & N. Alberding (2013)
Adapted from Studio Physics I: Unit 2
Unit 102-11 - Nuclear Physics and Radioactivity
Author: Sarah Johnson
Page 3
Binding Energy
The total mass of a stable nucleus is always less than the sum of the
masses of the nucleons that make up the nucleus. This mass
difference occurs because some of the mass goes into binding the
nucleus together i.e. the mass converts into the total binding
energy. This is the amount of energy that must be put into the
nucleus to break it apart. The mass difference m is defined as:
m = (mass of nucleons)
(mass of nucleus)
The binding energy can then be calculated according to special
relativity as:
Total Binding Energy =
mc2
In order to calculate the binding energy of a nucleus, you must
know the masses of the nucleons and the mass of the nucleus in
question. In nuclear physics, we specify masses in unified atomic
mass units (u). (Your textbook describes the origin of this unit.)
The masses of the nucleons in these are units as as follows:
neutron: mn = 1.008665 u
proton: mp = 1.007276 u
Another useful mass as we will see shortly is the mass of a neutral
hydrogen atom:
hydrogen: mH = 1.007825 u
✍ Problem Activity 11-2: Determining the Total Binding
Energy of Uranium
238
92 U
has an atomic mass of 238.050788 u.
(a) How many neutrons does it have? How many protons? Record
the values below.
(b) Determine the mass (in u) of the neutrons in a
© 2009 by S. Johnson and N. Alberding (2013)
238
92 U nucleus.
Adapted from Studio Physics I: Unit 2
Page 4
Physics for Life Sciences II Activity Guide
SFU
(c) Because we are using an atomic mass, we need to take into
account the electrons that are also contained in the mass along with
the nucleus. One way to account for the electrons in calculating the
mass difference is to use the mass of a Hydrogen atom instead of the
mass of a proton when calculating the mass of the nucleons. You
will then automatically include the Z electrons in the mass of the
nucleons which will then be cancelled out when you subtract off the
atomic mass (which also includes Z electrons) to determine the mass
difference.
Determine the mass (in u) of the protons and electrons in a
atom using the mass of Hydrogen, mH, given above.
238
92 U
(d) Determine the total mass of the nucleons and electrons using
your results from (b) and (c). Use this value and the atomic mass
238
given to determine the mass difference for 92 U . (Make sure that
you keep as many significant figures in your answer as you are
allowed.)
© 2009 by S. Johnson & N. Alberding (2013)
Adapted from Studio Physics I: Unit 2
Unit 102-11 - Nuclear Physics and Radioactivity
Author: Sarah Johnson
Page 5
(e) The last step is to determine the Total Binding Energy is to
calculate mc2 . The easiest way to do this is to use the fact that
1 u = 931.5 MeV/c2 , therefore 1 uc2 = 931.5 MeV. This will give
you a binding energy in MeV.
Radiation
Certain combinations of neutrons and protons combine to form
nuclei that are unstable. These unstable nuclei disintegrate or decay
into other nuclei and in the process emit radiation. Three distinct
types of radiation have been observed: alpha ( ↵ ), beta ( ), and
gamma (
).
Each of the three types of radiation consists of the release of a well
known particle. In the case of alpha radiation, the particle is the
nucleus of a Helium atom: 42 He. Because the alpha particle takes
protons and neutrons away from the parent nucleus during the
decay, the remaining daughter nucleus will be of a different type
from the original. In general, alpha decay can be written as:
A
ZN
!ZA
4
2
N’ +42 He
where N is the parent nucleus and N’ is the daughter. (For some
unknown reason, nuclei only have daughters, no sons. :-) )
The total energy released during an alpha decay is called the
disintegration energy, Q. It can be determined as follows:
Q = MP c 2
© 2009 by S. Johnson and N. Alberding (2013)
(MD + m↵ )c2
Adapted from Studio Physics I: Unit 2
Page 6
Physics for Life Sciences II Activity Guide
SFU
where MP is the mass of the parent, MD is the mass of the
daughter and m↵ is the mass of the alpha particle. A decay can only
occur when Q is positive. The energy released goes into kinetic
energy of the alpha particle the recoiling daughter nucleus.
✍ Problem Activity 11-3: Alpha decay of Radium
(a) 226
88 Ra is an ↵ emitter. What is the nuclear symbol for the
daughter nucleus when it undergoes alpha decay?
(b) Look up the atomic masses for 226
88 Ra , its daughter and a
Helium atom in the Appendix of your textbook. Record the values
in the space below. (If we use all atomic masses here, including for
the alpha particle, the electron masses will cancel out when
determining Q.)
(c) Now use the values you found in (b) to calculate the
disintegration energy (in MeV) when 226
88 Ra undergoes alpha
decay. (Hint: Use the same energy conversion trick you used in
Activity 11-2 to go from u to MeV.)
© 2009 by S. Johnson & N. Alberding (2013)
Adapted from Studio Physics I: Unit 2
Unit 102-11 - Nuclear Physics and Radioactivity
Author: Sarah Johnson
Page 7
A nucleus can also transmute into another type of nucleus when it
undergoes beta decay. In one type of beta decay, known as decay, the particle that is emitted is an electron. This electron does
not come from the atomic orbitals, but is emitted from the nucleus
itself when a neutron transforms into a proton:
n ! p + e + ⌫¯
It was discovered during the analysis of beta decay experiments that
in order to conserve energy and momentum a second particle must
also be emitted. In the case of - decay, the second particle is an
anti-neutrino, ⌫¯ , which is a small neutral particle composed of
anti-matter. (Anti-matter is a complicated topic which we will not
delve into here.) In general, in terms of the parent and daughter
nuclei, - decay can be written as follows:
A
ZN
!A
¯
Z+1 N’ + e + ⌫
Some nuclei instead disintegrate by another similar process known
as + decay. In this type of decay a particle known as a positron is
emitted. A positron, which is the antimatter equivalent of an
electron, has the same mass as the electron but the opposite charge.
It is generally written e+ . Another difference between + and decay is that in the former the second particle emitted is a neutrino,
rather than an anti-neutrino:
A
ZN
!A
Z
1
N’ + e+ + ⌫
An additional related process in which the nucleus absorbs one of
the orbital electrons also occurs. This process is known as electron
capture.
✍ Activity 11-4: Beta Decays
Write out the complete decay process for each of the following
nuclei. You will have to look up the identities of the daughter nuclei
in your textbook.
(a)
- decay of
45
20 Ca
© 2009 by S. Johnson and N. Alberding (2013)
Adapted from Studio Physics I: Unit 2
Page 8
Physics for Life Sciences II Activity Guide
(b)
+ decay of
SFU
46
24 Cr
✍ Activity 11-5: Energy Released in Beta + Decay
(a) Write down an expression for the total energy released, Q,
during a + decay in terms of the masses of parent and daughter
nuclei and the mass of the positron, me (the same as the electron
mass). Assume the mass of the neutrino is essentially zero.
(b) Most textbooks provide the atomic masses of elements which
include the mass of the nucleus and the mass of the orbital
electrons. Show that in terms of the atomic mass of the parent MP
and the atomic mass of the daughter MD that the energy released is
equal to
Q = (MP
© 2009 by S. Johnson & N. Alberding (2013)
MD
2me )c2
Adapted from Studio Physics I: Unit 2
Unit 102-11 - Nuclear Physics and Radioactivity
Author: Sarah Johnson
Page 9
Gamma radiation involves the emission of high energy photons.
These photons are emitted when a nucleus goes from a higher
energy “excited” state to a lower energy state, similar to the
emission of lower energy photons in atomic spectra, only in the case
of gamma radiation it is the nucleus that is changing states, not the
orbital electrons. One can write gamma decay as:
A
Z N*
!A
Z N+
where the asterisk denotes the excited nucleus.
One important thing to notice in all three types of decay discussed
above is that in each case the total number of nucleons = protons +
neutrons is always conserved. This is due to yet another
conservation law known as the Law of Conservation of Nucleon
Number. Protons may change into neutrons or vice versa, but the
number A must remain constant.
© 2009 by S. Johnson and N. Alberding (2013)
Adapted from Studio Physics I: Unit 2
Page 10
Physics for Life Sciences II Activity Guide
SFU
SESSION TWO: THE STATISTICS OF RADIOACTIVITY
We’re going to start this session with a radioactive counting
experiment that will continue while we do other things.
Natural Radioactivity and Statistics
Radioactivity is a statistical process in which a series of slight
disturbances of the nucleus lead to a decay. Any particular unstable
atom may remain in its unstable state for many years. However, in a
typical sample there are so many such unstable atoms that many
decays may occur in a short interval such as a second or a minute.
The exact number of decays in an interval varies from interval to
interval but the average number of decays per interval can be
predicted based on the identity of the radioactive isotopes present in
the sample.
The radiation detector we will use is a small tube containing a gas
such as helium, argon or neon that can be ionized by an incoming
particle of radiation and is called a Geiger-Müller tube. When the
gas in the Geiger-Müller tube is ionized it conducts electrical
current momentarily. When placed in a circuit the number of
radioactive particles received by the tube can be counted and can
cause an audible click and can be recorded by a computer.
Background Radiation: They came from Outer Space
There are no obvious radioactive sources in our lab. Nevertheless, a
radiation monitor will detect some radiation. What’s going on?
The radiation detected when there are no obvious sources nearby is
called “background radiation.” Some of the particles of this
radiation come from the sun, other stars and even distance galaxies.
There are also radioactive atoms inside the earth such as uranium
that decay into radon gas. The radon filters up to the earth’s surface
and emits further radiation as it decays. There are some common
elements present in the room that have isotopes which are
radioactive such as 14C, 57Fe and 40K. These radioactive isotopes of
common elements also contribute to the background radiation.
The radiation detector can be used with the Labpro computer
interface to allow automatic tracking of the background radiation
using the Logger Pro software. For example, the system can be
programmed to collect the number of counts in successive oneminute intervals for 80 minutes. The computer can then calculate
the average and standard deviation of the counts.
Previously we collected data on the background radiation in the lab.
The data can be summarized not only by the average number of
counts per minute and the standard deviation of the number of
counts per minute but also by its frequency distribution or
histogram.
© 2009 by S. Johnson & N. Alberding (2013)
Adapted from Studio Physics I: Unit 2
Unit 102-11 - Nuclear Physics and Radioactivity
Author: Sarah Johnson
Page 11
Histogram Radiation vs. Bin
Hist-Radiation (Frequency)
10
5
0
0
10
20
30
40
50
Bin (counts)
Figure 11.1 Histogram of the background radiation in the Physics Studio.
Page 2-12!
The histogram above shows the results of counting for 80 oneThe mean isSFU
11.06
1057 counts and standard deviation
is 3.36 counts.
minute
intervals.
Workshop
Physics Activity
Guide!
4. The horizontal axis of your graph indicates the quantities
The Frequency
Distribution
whose frequencies
you are graphing;
the vertical axis of your
graph gives the frequencies. Above each quantity on the
horizontal axis,
draw a you
rectangle
whose
height corresponds
Suppose
want
to know
more about the variation from the
to the frequency of that quantity. Repeat this step for each
average
number
of
counts?
A graphical approach is to plot a type
quantity measured.
of
graph known as a histogram or frequency distribution and study its
As an example,
consider a very simple frequency
shape.
distribution. Imagine that you have caught ten fish.
Of these ten, four are 3" long, two are 4" long, and four
anfrequency
example,distribution
consider would
a veryappear
simple
are 5" long.As
The
as follows: Imagine that you have caught ten fish.
frequency distribution.
Of these ten, four are 3"
long, two are 4" long, and four are 5" long. The frequency
distribution would appear as follows:
! Activity 2-7: FrequencyHow
Distribution
Your
to Plot afor
Frequency
Distribution
Time-of-fall Data
(a) Draw a frequency diagram (known as a histogram)
Since
a frequency
ofgrid
values shows how many times you
representing
your time-of-fall
data distribution
for the ball in the
below.
recorded each value, this distribution can be drawn by organizing
your data as follows:
(b)spreadsheet
Next, using a different
colour
1. Load your
file with
the data to be plotted into the
of pen or pencil sketch in the
computer.results of the rest of the class in
the histogram above.
2. Sort the column
How does of
thedata
shapefrom
of the the
classlowest time to the highest
frequency distribution above
time.
compare with the shape shown
Appendix C on
C-6? !
3. Count theinfrequency
ofpage
occurrence
of each quantity that was
Does the variation in the time of
recorded.fallFor
example,
if
you
recorded
a time of 0.45 seconds
data seem "normally
distributed"?
it
five different
times,How
thedoes
frequency
of 0.45 seconds is 5.
compare to your prediction in
Activity 2-6? !Explain.
© 2009 by S. Johnson and N. Alberding (2013)
Adapted from Studio Physics I: Unit 2
Page 12
Physics for Life Sciences II Activity Guide
SFU
4. The horizontal axis of your graph indicates the quantities whose
frequencies you are graphing; the vertical axis of your graph
gives the frequencies. Above each quantity on the horizontal
axis, draw a rectangle whose height corresponds to the
frequency of that quantity. Repeat this step for each quantity
measured.
5. There is a histogram tool in Excel which does a lot of the work
for. To use it you must create a column of “bins” representing
the x-axis of the histogram. Then select the data for which you
want a histogram. Select “Tools..Data Analysis..Histogram” and
follow the instructions. (There is a similar feature in Logger Pro
that is even easier to use.)
Apparatus to Measure Counts per Interval.
In the exploration of the statistics of radioactivity, we can use a
computer set up as a radiation counting system. We will need the
following equipment (one set for the whole class):
• Radiation Monitor
• a computer interface
• a computer
• radiation monitoring software (Logger Pro)
• a small sample of potasium-rich material.
Doing the Experiment
We will be doing this experiment together as a class. First we will
determine the counts/interval for 80 one-minute intervals. The
computer plots the frequency distribution histogram automatically
as it collects the data. This will allow us to obtain a frequency
distribution that can be compared to the background radiation
frequency distribution.
1. Plug the radiation monitor into the Dig/Sonic 1 input of the
Labpro,Open up the “L01001a (Counts vs Time).cmbl” setup
file in Logger Pro. Choose “Radiation Monitor” not “Student
Radiation Monitor” as the sensor input.
2. Press the Start button and see if the detector system is working.
Attach a small bag of the sample directly against the window of
the radiation monitor. The setup file collects data for 20 onesecond intervals. This can be changed by choosing
“Experiment...Data collection” from the menu. Change the
setup to take 80 one-minute intervals. The program displays a
table of counts/interval. and a graph of counts vs time.
© 2009 by S. Johnson & N. Alberding (2013)
Adapted from Studio Physics I: Unit 2
Unit 102-11 - Nuclear Physics and Radioactivity
Author: Sarah Johnson
Page 13
We will set up the radiation monitor to repeat the 80 one-minute
counting experiment done previously, but this time we’ll put a
potassum-rich powder near the detector. NuSalt® is a commercial
product which is sometimes advised to replace table salt for the diet
of people who need to avoid sodium. It consists mainly of KCl with
some other flavour-enhancing additives. One in 9,000 atoms of K is
the 40K isotope that emits beta radiation. A 311 g NuSalt® container
has about 2.8 x 1020 atoms of 40K, of which 4927 decay per second
on average.
✍ Activity 11-6: Radiation From A Potassium-rich source
(a) First set up the NuSalt® in a little bag next to the detector
(b) Take a sample one-minute interval and compare the counts
to that of the background radiation taken earlier.
Number of background counts in a
typical one-minute interval
Number of counts in a one-minute
interval with NuSalt
You will probably not be convinced with just one such measurement
that NuSalt® has radioactivity significantly above the background
level. If the the number of counts is slightly higher, it might just be
a random fluctuation and not due to an actual increase in the
average radioactive level. (And in fact one reading might be lower
than background.) In order to clearly demonstrate the effect it is
necessary to continually repeat the measurement 80 times and
compare the histogram with that of the background.
While the NuSalt® data are being collected we’ll go ahead with
some other activities.
Radioactive Decay - Theory
As stated previously, radioactive decay is a random process. One
cannot predict exactly when a given nucleus will decay. We can
however predict roughly how many nuclei in a sample will decay
over a given time period. The number of decays N that occur in a
short time period t depends upon the length of the time period
and the total number of nuclei present N :
N=
N t
is known as the decay constant and varies depending on the type
of unstable nucleus being examined.
© 2009 by S. Johnson and N. Alberding (2013)
Adapted from Studio Physics I: Unit 2
Page 14
Physics for Life Sciences II Activity Guide
SFU
By taking the limit as the time interval approaches zero and
applying a little calculus to this equation one arrives at the
following relationship:
N = N0 e
t
which is known as the radioactive decay law. (A derivation of the
law can be found in your textbook.) Here, N0, represents the number
of nuclei present at t = 0, and N is the number at time t. As you can
see, the number of radioactive nuclei in a sample decreases
exponentially with time.
The decay constant determines how quickly a sample will decay.
Another way to specify the decay rate is by a quantity called the
half-life, T 1 ,which is defined as being the time it takes for half of a
2
sample of a given type of unstable nucleus to decay. If one
substitutes N = N0 /2 and t = T 1 into the radioactive decay law
2
equation, you arrive at an expression for the half-life:
T1 =
2
ln 2
=
0.693
In order to better understand this statistical process, in the next
activity we will simulate radioactive decay using another random
process, throwing six-sided dice. For the following activities you
will need:
• 300 six-sided dice (divided as evenly as possible
among the class groups)
✍ Activity 11-7: Theoretical Dice Decay
(a) Complete the “Theoretical Decay” table entries on the next page
by assuming that exactly 1/6 of all nuclei initially present decay
each time period. Do this by taking 1/6 of the “initial number
present” and round to the nearest whole number. Enter this number
as the “number decayed.” Note: You may do this either by using an
Excel spreadsheet or a calculator. If you use Excel, you do not have
to fill out the “Theoretical Decay” table in the activity guide.
(b) Subtract this value from the “initial number present” and record
as the “number remaining.” (The “number remaining” now becomes
the initial number for the next round.)
(c) Repeat this process until the table is complete or fewer than ten
nuclei remain undecayed.
(d) Enter your data for time and initial number present into Excel (if
you used a calculator) and make a graph of Initial Number of
Radioactive Nuclei Present vs Time. Make sure to save this
spreadsheet and graph for the next activity.
© 2009 by S. Johnson & N. Alberding (2013)
Adapted from Studio Physics I: Unit 2
Unit 102-11 - Nuclear Physics and Radioactivity
Author: Sarah Johnson
Elapsed Time
Initial Number
Present
0
300
Page 15
Number Decayed
Number
Remaining
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
© 2009 by S. Johnson and N. Alberding (2013)
Adapted from Studio Physics I: Unit 2
Page 16
Physics for Life Sciences II Activity Guide
Elapsed Time
Initial Number
Present
Number Decayed
SFU
Number
Remaining
24
25
26
27
28
29
30
(e) Describe in words what your graph looks like. Does it have the
shape you expected?
In the next activity we will simulate radioactive decay by throwing
300 dice 30 times. In order to make this easier, we will share the
work by dividing up the dice between the groups. All the groups
will have to combine their data after they have finished rolling their
set of dice. You cannot proceed with the analysis until all groups are
finished.
✍ Activity 11-8: Experimental Dice Decay
(a) Enter the number of dice in your set in the first row of initial
number present. Toss your set of the dice and remove each one
showing the number one. The number you remove will be the
“number decayed.” Enter this number into the table below.
(b) Subtract the “number decayed” from the “initial number
present” to obtain the “number remaining.” Enter this into the table.
(c) Toss the remaining dice and again remove all those that “decay.”
(d) Repeat this process until the chart is complete or no dice remain.
© 2009 by S. Johnson & N. Alberding (2013)
Adapted from Studio Physics I: Unit 2
Unit 102-11 - Nuclear Physics and Radioactivity
Author: Sarah Johnson
Elapsed Time
Initial Number
Present
Page 17
Number Decayed
Number
Remaining
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
© 2009 by S. Johnson and N. Alberding (2013)
Adapted from Studio Physics I: Unit 2
Page 18
Physics for Life Sciences II Activity Guide
Elapsed Time
Initial Number
Present
SFU
Number Decayed
Number
Remaining
23
24
25
26
27
28
29
30
(e) Now combine your data with all of the other groups by adding
together the “Initial Number Present” for each time from each
group. The number in the t = 0 row should equal 300. Put this data
into the table below.
Elapsed Time
Initial Number
Present
0
300
1
2
3
4
5
6
7
8
9
10
11
© 2009 by S. Johnson & N. Alberding (2013)
Adapted from Studio Physics I: Unit 2
Unit 102-11 - Nuclear Physics and Radioactivity
Author: Sarah Johnson
Page 19
Elapsed Time
Initial Number
Present
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
(f) Enter your experimental data for initial number present into a
new column in your saved spreadsheet next to the theoretical
data for the same quantity. Add this data to your theoretical graph
of Initial Number of Radioactive Nuclei Present vs Time so that
you now have two decay curves. Submit your spreadsheet with
graph to WebCT.
© 2009 by S. Johnson and N. Alberding (2013)
Adapted from Studio Physics I: Unit 2
Page 20
Physics for Life Sciences II Activity Guide
SFU
(g) How do your two decay curves compare? Would you say that
they agree with each other?
(h) Use the graph to estimate the amount of time necessary for your
experimental number to go from:
300 to 150 _______
250 to 125 _______
200 to 100 _______
150 to 75 _______
100 to 50 _______
(i) Based on your answers above, what is the approximate half-life
of your “radioactive” sample?
Now let’s return to the radioactive counting experiment on NuSalt®
that we started at the beginning of the session.
The histogram of the number of counts in 80 one-minute intervals
will be displayed and distributed to the class.
✍ Activity 11-9: Finale: The Radioactivity of NuSalt®: Is it
significantly above the background level?
(a) Write down the mean and standard deviation of the NuSalt®
data collected in class.
© 2009 by S. Johnson & N. Alberding (2013)
Adapted from Studio Physics I: Unit 2
Unit 102-11 - Nuclear Physics and Radioactivity
Author: Sarah Johnson
Page 21
(b) In order to compare this data with the background data we must
calculate a quantity known as the standard deviation of the mean,
SDM , which is the standard deviation divided by the square-root
of the number of samples. Calculate this quantity for the NuSalt®
data.
(c) Calculate
activity guide.
SDM
for the background data given earlier in this
(d) Now write the mean and the standard deviation of the mean in
the following format: Mean ± SDM in the spaces below.
NuSalt® data: ____________ ± ____________
Background: ____________ ± ____________
(e) Scientists say that the signal is significantly above background
(with 68% confidence level) if the signal and the background data
do not come within one SDM of each other. The 95% confidence
level occurs when the signal and background do not come within
two SDM of each other. Is the NuSalt® data signal here
significantly above background? How sure are you? What is your
approximate confidence level?
© 2009 by S. Johnson and N. Alberding (2013)
Adapted from Studio Physics I: Unit 2