Laboratory Manual for Introductory Geology 4e

TABLE 12.1 Geologically important radioactive isotopes used for radiometric dating
Parent isotope
Daughter decay
product
Half-life (years)
Useful dating
range (years)
Datable materials
Samarium-147 Neodymium-143 106 billion .10,000,000 Garnets, micas
Rubidium-87 Strontium-87 48.8 billion .10,000,000
Uranium-238 Lead-206 4.5 billion .10,000,000
Uranium-235 Lead-207 713 million .10,000,000
Potassium-40 Argon-40 1.3 billion .10,000
Potassium-bearing minerals (mica,
feldspar, hornblende)
Uranium-bearing minerals (zircon,
apatite, uraninite)
Uranium-bearing minerals (zircon,
apatite, uraninite)
Potassium-bearing minerals (mica,
feldspar, hornblende)
Carbon-14 Nitrogen-14 5,730 100–70,000 Organic materials
Conversely, isotopes with very long half-lives, such as samarium-147, decay so slowly
that they can be used to date only very old rocks.
To calculate the numerical age of a rock, geologists first crush it and separate
out the mineral containing the desired isotope. A mass spectrometer determines
the parent:daughter ratio, and then a logarithmic equation is solved to calculate
the rock’s age. Your calculations will be easier: once you know the parent:daughter
ratio, you can use TABLE 12.2 to calculate age by multiplying the half-life by the
number in the fourth column.
Piecing together the 4.56-billion-year history of the Earth requires geologists to
combine all the methods presented in this chapter: the physical principles of relative
dating, fossil-based ages from sedimentary rocks, and numerical ages from igneous
and metamorphic rocks. In Exercise 12.7, you will use these methods exactly the
same way a professional geologist does.
TABLE 12.2 Calculating the numerical age of a rock from the half-life of an isotope
Parent atoms
remaining
(%)
Parent:
daughter
ratio
Number of
half-lives
elapsed
Multiply halflife
by
to determine
age
Parent atoms
remaining
(%)
Parent:
daughter
ratio
Number of
half-lives
elapsed
Multiply halflife
by
to determine
age
100 — 0 0 35.4 0.547 1½ 1.500
98.9 89.90 1
∕64 0.016 25 0.333 2 2.000
97.9 46.62 1
∕32 0.031 12.5 0.143 3 3.000
95.8 22.81 1
∕16 0.062 6.2 0.066 4 4.000
91.7 11.05 ⅛ 0.125
84.1 5.289 ¼ 0.250
70.7
50
2.413
1.000
½
1
0.500
1.000
0.05
0.025
11
12
Don’t bother!
There are too
few parent
atoms to
measure
accurately
enough.
12.4 DETERMINING NUMERICAL AGES OF ROCKS
317