Name
Class
Date
Skills Worksheet
Graphing Skills
Line Graphs and Radiometric Dating
Scientists use line graphs as tools to communicate data, specifically to show how
data changes over time. Line graphs make it easy to compare different sets of
data over time. For example, in radiometric dating, the absolute age of rock is
determined by comparing the relative percentages of a radioactive (parent) isotope and a stable (daughter) isotope.
Half-life is the time it takes for half of the mass of a radioactive isotope to
decay into its daughter isotope. To make a line graph of the half-life of any
radioactive isotope, plot the amount of the parent isotope against the amount
of the daughter isotope over time. Even if you do not know the time periods for
each half-life of a radioactive isotope, the relationship can still be plotted on a
line graph.
For example, suppose the original mass of a radioactive isotope is 100 kg, or
100,000 g. A table showing the half-life for this amount of radioactive isotope
would look like this:
Number of
Half-Lives
Parent
Isotope
Daughter
Isotope
Number of
Half-Lives
Parent
Isotope
Daughter
Isotope
0
100,000 g
0g
3
12,500 g
87,500 g
1
50,000 g
50,000 g
4
6,250 g
93,750 g
2
25,000 g
75,000 g
5
3,125 g
96,875 g
The data from the table can be plotted in a line graph, which would look like
this:
Amount of Isotope in Grams
120,000
100,000
80,000
Parent
60,000
Daughter
40,000
20,000
0
0
1
2
3
4
5
Number of Half Lives
PRACTICE
Use the line graph to answer the following questions.
1. How many half-lives have passed when there are three times as much daughter isotope as parent isotope?
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Earth Science
30
The Rock Record
Name
Class
Date
Graphing Skills continued
2. How many grams of the parent isotope are left in the sample after three
half-lives?
3. Why is the line graph a curve instead of a straight line?
4. If a sample contained 94,000 g of the daughter isotopes, where on the line
graph would the sample be shown?
5. The table below shows the radioactive decay of a 10 kg sample of 14 C.
Years Passed
14
Years Passed
14
0
10,000
34,200
156
5,700
5,000
28,500
312
11,400
2,500
39,900
78
17,100
1,250
45,600
39
22,800
625
51,300
20
C (g)
C (g)
Create a graph using the data above. Label the x-axis Number of Half-Lives.
Label the y-axis Number of Atoms. Plot the decay of 14C in terms of half-lives.
Each half-life for 14C is about 5,700 years.
6. About how old is a sample of bone that contains 900 14C atoms? Mark its
position on the line graph. How many half-lives have passed?
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Earth Science
31
The Rock Record
ANSWER KEY
SECTION: DETERMINING ABSOLUTE
AGE
41. Answers may vary. Sample answer:
Index fossils help geologists locate
rock layers that are likely to contain
deposits of oil and natural gas.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Math Skills
1. 1⁄2 a ⴝ 120; 2 ⴛ 1⁄2 a ⴝ 2 ⴛ 120;
a ⴝ 240
2. 1⁄2 a ⴝ 60; 2 ⴛ 1⁄2 a ⴝ 2 ⴛ 60; a ⴝ 120
3. 1⁄2 a ⴝ 105; 4 ⴛ 1⁄2 a = 4 ⴛ 105;
a ⴝ 420
4. 1⁄2 a ⴝ 25; 4 ⴛ 1⁄2 a ⴝ 4 ⴛ 25; a ⴝ 100
5. 1⁄8 a ⴝ 40; 8 ⴛ 1⁄8 a ⴝ 8 ⴛ 40; a ⴝ 320
SECTION: THE FOSSIL RECORD
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Graphing Skills
1. two
2. 12,500
3. because it shows the ratio between the
two amounts, which changes drastically with each half-life
4. between the fourth and fifth half-lives
5. The sample must be between 17,100 and
22,800 years old, and about three and
on-half half-lives have passed. The line
should be marked within this range.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
Amount of Isotope in Grams
10000
8000
6000
4000
2000
0
1
2
3
4
5
6
7
8
9
Number of Half Lives
6. Students should mark a position
between 3 and 4 on the x-axis and just
under 1000 on the y-axis. Three and a
half half-lives have passed.
Section Quizzes
SECTION: DETERMINING RELATIVE
AGE
1.
2.
3.
4.
5.
D
C
A
E
B
6.
7.
8.
9.
10.
B
E
A
D
C
A
D
B
A
B
Chapter Test A
12000
0
C
B
D
E
A
D
D
B
C
C
B
C
C
C
A
E
I
B
A
G
J
C
F
D
H
C
A
D
B
C
C
D
A
B
C
Chapter Test B
1. H
2. E
3. C
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Earth Science
59
The Rock Record