Nuclear Chemistry
Kemari A. Lee
20 Mar 2024
TOTAL: 30 points
Lee Estimating Half-Life Page 2 of 13
CHM 116 POST-LAB and LAB NOTEBOOK
Nuclear Chemistry: Estimating Half Life of a “Radioactive” Element
1. Insert ONE picture of yourself in the appropriate lab attire and full PPE here (include the
Skittles® candy in your PPE picture).
**Remember to (1) show your full body so that we see you are wearing shoes; (2) wear your
PPE (safety glasses, buttoned lab coat and gloves); (3) cover your lower legs and ankles
(socks are required, even in Arizona); (4) tie back long hair in a ponytail or a bun; (5) remove
jewelry.
Note: Wearing full PPE may seem silly for tossing Skittles on a table, but we are
establishing good lab protocol. If you have not received your lab kit (which contains your
safety glasses), take the picture with what you have and include a note with your picture to
explain why you are not wearing the complete PPE.
- I do not have gloves, an apron (lab coat) or gloves on due to
not having received my lab kit yet.
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2. Enter the data that you collected during the experiment (from Tables 1 and 2 in the
procedure) HERE. Remember to adjust the number of Rounds for each Trial to how many
you completed.
Table 1 (Trial 1)
Table 2 (Trial 2)
Round
Skittles
“S” Up
(Parent
Atoms)
Skittles
“S” Down
(Daughter
Atoms)
Cumulative
Daughter
Atoms
Round
Skittles
“S” Up
(Parent
Atoms)
Skittles
“S” Down
(Daughter
Atoms)
Cumulative
Daughter
Atoms
0
55
0
0
0
55
0
0
1
17
38
38
1
20
35
35
2
7
12
50
2
6
14
49
3
6
2
52
3
3
3
52
4
4
2
54
4
0
3
55
5
2
1
55
5
6
6
7
7
8
8
9
9
10
10
3. Describe in 2 - 3 sentences, , what happens mathematically to the total number of candies
in each round (the general trend)? is this related to the concept of half-life in nuclear How
reactions (or, what is each round simulating with regards to half-life)?
4. Are your two data sets the same? exactly If not, explain (in 1 2 sentences) using your –
experimental data.
The general trend is close to being reduced in half with each round, but not exactly
in half. This experiment does accurately portray the concept of half-life while
showing a reduction close to what a half-life decay model would be. With each round
the number of candies should be 50% of what was present in the previous round.
The data shows something like that.
The data in trial one took one additional round to complete, versus trail two only took
four rounds to complete. In addition to trial two showing that the values almost
decreased in half every time.
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5. Use a graphing software to create the x-y scatter plot showing the Number of
parent nuclei remaining vs. Round # (do not connect your points). Your ONE
graph will show data points from BOTH trials of the experiment. On your graph, the
x-axis should be , and the should be Round Number y-axis Parent Atoms Remaining
(NOT the daughter atoms or cumulative daughter atoms) in that Round. In general,
scientific graphs show the independent variable on the x-axis and the dependent
variable on the y-axis. Do NOT connect your points; no trend line needed and make
sure to:
• Label the axes including the units in parentheses.
• Include a figure legend (text below the graph) explaining the data in your
graph.
• Remove any default title, legend, and gridlines.
• You should use two different symbols to represent the two data sets (i.e. a square
for Trial 1 and a circle for Trial 2)
You will not receive credit if you draw your graph by hand. Excel or Google Sheets are
good choices that you can learn how to use quickly if you don’t already have a favorite
graphing program.
See other general tips for making graphs in the How to Make a Graph in Excel document
located in the Introductory Materials for this lab.
6. Consider the trend shown in your graph in Question 5. Is it linear, exponential growth or
exponential decay? Is this trend consistent with your expectations for the kinetics of a
nuclear reaction? Briefly explain why in 2 3 sentences.–
This figure is Table 1. This graph depicts the relation how many remaining parent
atoms were produced several times. with each individual round done. Repeat steps
3-7 until all your parent atoms separate trials with 10 rounds done in each trial
The graph shown is exponential decay. This is due to the quantities of my values
rapidly decreasing.
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7. Scientists like to use data to build physical models (or mathematical models to predict how
data will look). Linear trends are easiest to work with; so we often look for ways to identify
linear trends in a data set. Nuclear reactions all follow first order kinetics meaning the rate
of a nuclear reaction is given by:
𝒓𝒂𝒕𝒆 = 𝒌[𝒓𝒂𝒅𝒊𝒐𝒂𝒄𝒕𝒊𝒗𝒆 𝒊𝒔𝒐𝒕𝒐𝒑𝒆]
in which is a first order rate constant. As shown in the kinetics portion of this course, this k
relationship can be to the following : transformed integrated rate law
𝐥𝐧[𝒓𝒂𝒅𝒊𝒐𝒂𝒄𝒕𝒊𝒗𝒆 𝒊𝒔𝒐𝒕𝒐𝒑𝒆]𝒕= −𝒌𝒕 + 𝐥𝐧[𝒓𝒂𝒅𝒊𝒐𝒂𝒄𝒕𝒊𝒗𝒆 𝒊𝒔𝒐𝒕𝒐𝒑𝒆]𝟎 Equation 1
in which is a natural logarithm, is time (represented by the Round number in your ln t
experiment), [radioactive isotope] is the concentration at time zero (the number of Skittles
0
you start with in this experiment) and [radioactive isotope] is the concentration of radioactive
t
isotope at time (number of remaining parent Skittles in this experiment). t
We need to adjust our data to create a graph which represents the above linear equation for
first order kinetics. For each round in your experiment, the natural log (ln) of the calculate
number of Parent atoms (you are NOT using the above equation to find this value; just use
the ln button on your calculator or create an equation in Excel). Enter the Round number
and number of Parent Atoms Remaining (from Tables 1 and 2 in Question #2), and
ln(Parent Atoms) in below: Table 3
Table 3: ln(Parent Atoms) vs. Round number
Trial 1
Trial 2
Round
Skittles
“S” Up
(Parent
Atoms)
ln (Parent
Atoms)
Round
Skittles
“S” Up
(Parent
Atoms)
ln (Parent
Atoms)
0
55
4.00
0
55
4.00
1
17
2.83
1
20
2.99
2
7
1.95
2
6
1.79
3
6
1.79
3
3
1.10
4
4
1.39
4
0
0
5
2
0.69
5
6
6
7
7
8
8
9
9
10
10
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8. Consider the data in Question 7 and create a new graph of your data showing a linear
relationship between Round Number (x-axis) and Natural Log of Concentration of Parent
Atoms (y-axis). You will want to exclude Rounds where # of Parent atoms is ZERO from each trial.
Draw a trend line (OR straight line of best fit) through each set of data points. (Include
the equations of both trend lines and the R values in the figure legend below the
2
graph. These will be provided by Excel).
• Label the axes including the units in parentheses.
• Include a figure legend (text below the graph) explaining the data in your
graph.
• Remove any default title, legend, and gridlines.
• You should use two different symbols to represent the two data sets (i.e. a square
for Trial 1 and a circle for Trial 2)
See other general tips for making graphs in the How to Make a Graph in Excel
document located in the Introductory Materials for this lab.
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9. Consider the trend lines in Question 8 and answer the following questions.
a. equations for your trend linesWhat are the for Trial 1 and Trial 2? (graphing
program will provide this)
b. In regard to the integrated rate law (see Equation 1 in Question 7) for a nuclear
reaction, what do the slopes of the trendlines in your graph represent?
c. In regard to the integrated rate law (see Equation 1 in Question 7) for a nuclear
reaction, what does the y-intercept represent?
10. Consider the following data for an experiment similar to the one you conducted with Skittles.
Round
Skittles “S” Up
(Parent Atoms)
Skittles
“S” Down (Daughter Atoms)
0
100
0
1
55
45
2
24
31
3
12
12
4
5
7
5
3
2
6
1
2
7
0
1
a. How many Rounds (cycles of decay) does it take for 100 Skittles to “decay”
according to the above data for this experiment?
Trial 1: y= -0.993x + 3.9629
Trial 2: y= -0.6019x + 3.6143
The slope represents the rate constant for decay, k. The integrated rate law for a
nuclear reaction, can be represented as lnN = x t + lnN . It is an equation of
0
straight line of type y = mx + b.
The y-intercept indicates the ln (# of parent atoms) in round number = 0
Y-intercept = b = lnN0
N is the initial number of radioactive nuclei, N is the number of radioactive
0
nuclei present at time t and is the decay constant.
# of cycles for 100 Skittles: 7
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b. Now consider repeating the same experiment, but instead starting with a sample
of twice the size (200 Skittles). How many cycles of decay would you predict it
would take for your entire sample to decay completely? Explain your answer in
2 3 sentences. –
11. Putting it all together! Radioisotopes are often used in diagnostic imaging for detecting
disease. The isotope Cu (copper-64), which has a half-life of 12.7 hours, is used to study
64
diseases affecting copper metabolism such as Wilson’s disease. What percentage of the
original activity in the sample remains after 38.0 hours? Show your work, include units,
and pay attention to significant figures.
Hint: Remember that this process follows first order kinetics and
that half-life is given by: 𝒌 = 𝟎.𝟔𝟗𝟑
𝒕𝟏𝟐
⁄
# of cycles for 200 Skittles: 8
Explain: It would take one additional cycle of decay for the entire sample to
decay completely compared to the 100 Skittles sample. This is because the
half-life decay process is independent of the initial quantity. Each cycle
reduces the number of remaining Skittles by approximately half.
K=In (2) / t1/2 = 0.693 / 12.7 hours = 0.0545h
-1
Equation : A / A * 100 = (e ) * 100
t o -kt
= (e ) * 100
-0.0545x38.0
= 0.126 * 100
= 12.6 %
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116 Online Lab Notebook Entry ( 5 Points)
Experiment Title: Nuclear Chemistry
Date of Experiment: 20 Mar 2024
Student Name: Kemari A. Lee
Purpose/Goal of Experiment:
The purpose of this experiment was to estimate the half-life of a radioactive isotope.
Since we could not do an actual decay, we used skittles. Students will gain a concept of
decaying radioactive particles in the half-life completion.
Planned Observations:
- Observe the mathematical patterns of this experiments and the equation of a
half-life.
- The trend of skittles decaying.
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Qualitative/ Quantitative Observations:
- Above are the data tables from Trials 1 and 2.
- This figure is Table 1. This graph depicts the relation how many remaining parent
atoms were produced several times. with each individual round done. Repeat steps
3-7 until all your parent atoms separate trials with 10 rounds done in each trial.
Data for Table 3
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This graph shows the relationship between the natural log concentration of parent
atoms and the round number. In addition to both trial 1 and 2 equation of the line
and R values.
2
Data/Calculations:
K=In (2) / t1/2 = 0.693 / 12.7 hours = 0.0545h-1
Equation : At / Ao * 100 = (e-kt) * 100
= (e-0.0545x38.0) * 100
= 0.126 * 100
= 12.6 %
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Conclusion:
From this experiment I have concluded that I was able to observe the mathematical
patterns of this experiments and the equation of a half-life. With seeing the trend of skittles
decaying through the interpretation of excel graphs based off my given date. After
accomplishing this lab I was able to determine the first order of kinetics and the half-life
given by an equation and isotope copper-64.
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