Absolute Time – Radioactive Decay
Name: ________________________________________
The Geologic time scale was developed in the 18th and 19th centuries using the
principles of relative dating. Although an important advance in our understanding of
how the Earth has evolved, the scale lacked absolute dates, ages in years. With the
discovery of radioactivity in the 1900’s, geologists were presented with a tool that
could be used to place absolute ages on geologic events.
A. Radioactive Decay
To understand radioactive decay, construct a mental and physical model of how
this process works in an igneous mineral. Start out with 16 radioactive parent
isotopes in a pretend igneous mineral. Assume that once formed by cooling and
crystallization, this mineral behaves as a closed system. Thus, it neither gains nor
loses parent or daughter isotopes from outside the crystal during its existence.
1. Place a column of 16 isotopes on demonstration chart on the square labeled 0 in
the parent isotope row of the Radioactive Decay Demonstration Chart.
2. Half-life #1: At the beginning of half-life #1 (before decay), you will start with
the same number of isotopes as in half life 0. Build a second column of 16 blocks
and place it in the square for the 1st half-life (next to the original parent isotope
column).
a. During the first half-life, half of this column of parent isotopes will randomly
decay to the stable daughter element.
b. Place the decayed and now stable daughter isotopes in the 1st half-life square
in the daughter row on the decay chart.
3. Half-Life #2: At the beginning of half-life #2 (before decay), you will start with
the same number of parent and daughter isotopes as in half life #1 (after decay).
Build the parent and daughter columns and place them in the square for the 2nd
half-life.
a. Again, half of the parent isotopes will randomly decay to daughters. Reduce
the parent isotope column to its proper height by removing the newly
decayed isotopes.
b. Stack them in the daughter square of half-life #2.
4. Repeat the procedure for half-lives #3 and #4.
5. Fill out the table below up to half-life #4.
6. Half-life #5: Before proceeding to half-life #5, predict how many parent
isotopes will remain after half-life #5 has occurred.
_______________________parent isotopes
There are two half blocks (orange dot) in your isotope supply. Use these to
complete the column for half-life #5 on your radioactive decay layout chart.
Copyright © Myers and Campbell-Stone
7. Half-life #6 and up: The radioactive decay layout chart shows only five halflives because of the difficulty in handling more blocks for more half-lives. Table 1
shows additional half-live intervals. Fill out the rest of the table. After a very
long time relative to the parent isotope’s half-life, we reach infinity on the chart.
Complete the column for infinity and record the results in the table.
8. Decay curves: With your completed columns, carefully slide the parent columns
so they touch. Then slide them out of the way so you have a good view of the
daughter wall. Slide the daughter columns together so they are also touching.
a. Position your eyes just above the level of the table and note the shapes of the
parent and daughter walls. Visualize this by imagining a point at the top of
each column and imagine a smooth curving line connecting all these points.
b. Using the data from the table above, plot the two curves on the graph below.
Draw the curve for the parents as a solid line and that for the daughter as a
dashed line.
c. What type of curve, exponential or logarithmic, describes the decrease in the
parent isotopes?
___________________________
d. What type of curve, exponential or logarithmic, describes the increase in
daughter isotopes?
___________________________
Copyright © Myers and Campbell-Stone
B. Absolute Geologic Age:
Up until now we have been examining the radioactive decay moving forward in
time. However, when determining the age of a rock or geologic event we must
work backwards from the present. We can measure the present amounts of
parent and daughter in a crystal, we know the half-life of a parent isotope, and we
can use this information to calculate when the mineral formed.
a. If you haven’t already filled out the daughter/parent (Nd/Np) row on the table
on page 4, do so now. Nd is the number of daughters and Np the number of
parents.
b. Plot your results on the graph below. Connect the points you have plotted
with a smooth curving line. (Have your instructor check this curve because
the age calculations you will do depend upon this curve being accurately
drawn.)
Copyright © Myers and Campbell-Stone
c. Calculating the age of a rock: Using the Nd/Np graph above and the data
below, determine the age of the muscovite and zircon minerals.
Decay
Series
muscovite
K–
40
Ar
40
U–
Pb
Nd/Np
Half-lives
elapsed
Half-life
(yr)
3.7
1.25x109
15
0.704x109
Age (yr)
235
zircon
207
How old is the rock in which both of these minerals occur?
_____________________
Copyright © Myers and Campbell-Stone