**What
you'll learn:**

**What parent isotopes and daughter products are, and their relationship.****How to caclulate, graph and use a radioactive isotope decay curve (exponential decay curve).****How to calculate an absolute geologic age from an isotope ratio,****The difference between absolute and relative ages in geology.****Beginning with geological relations among rocks and structures, how to apply the principles of relative dating i order to deduce a geologic history.****How to discern the basic types of unconformities.****How to refer to the geologic timescale.**

**What
you'll turn in: **

**Excel spreadsheets that contain your data and charts.****You must email your spreadsheets from your student (wenval.cc)****email to the instructor's wenval email address:**

rdawes@wenval.cc.**Completely labeled XY (Scatter) graphs, printed out with white (clear) backgrounds, produced in Microsoft Excel.****Answers to all written questions.**

**Open
up a new Excel spreadsheet (workbook).**

**Make
a graph of radioactive decay over the course of 10 half-lives, as follows. You
get to choose the wording of the labels.**

**Label the first column, which will be the number of half-lives that have elapsed. Enter the numbers 0 through 10.****Label the second column, which will be the fraction (out of 1) of parent isotope remaining. In next cell down of this column, in the cell to the right of 0 elapsed half-lives, enter the number 1.****In the next cell down after that, enter the mathematical formula =0.5*[click on cell above to enter its coordinates], then click the Enter button.****Copy that mathematical formula down the rest of the column. Each number should be half as big as the number above it.**

**Label the third column, which will be the fraction of daughter product isotope that has accumulated as a result of radioactive decay of the parent isotope.****In next cell down of this column, in the same row as 0 elapsed half-lives and 1 fraction of parent isotope, enter the mathematical formula =1-[click on the cell to the left, entering its coordinates]. This should result in the number 0.****Copy that mathematical formula down the rest of the column. Each number should equal one minus the parent isotope fraction.**

**Make your graph:****Highlight all 33 cells you have created. Click on the Graph Wizard.****Create an XY (Scatter) chart with data points connected by smoothed lines.****Click on the parent isotope curve and Add Trendline/ Exponential. You will see that for the first half-life, the true exponential curve is not the same as the crude line created by the smoothed line XY graph function.****Put the legend at the top of the chart.****Make sure that:****the axes of the graph are labeled****the legend is labeled****the chart has a title across the top that includes your name****The horizontal (X) axis runs only from 0 to 10. (To adjust it, right-click on the horizontal axis itself, or one of the numbers below it, choose Format Axis, and set maximum to Fixed 10.)****The vertical (Y) axis runs only from 0 to 1.0 (To adjust it, right-click on the horizontal axis itself, or one of the numbers below it, choose Format Axis, and set maximum to Fixed 1.0.**

**PRINT JUST ONE COPY OF YOUR GRAPH, WITH YOUR NAME ON IT, WITH DIFFERENT DATA SYMBOLS FROM ANYBODY ELSE AROUND YOU, TO TURN IN.**

**Questions
about radioactive decay. (Note: Answer all written questions on the separate
answer sheet.):**

**What is a half life?****After one half-life has elapsed, what fraction of the parent isotope will remain?****After two half-lives have elapsed, what fraction of the parent isotope will remain?****After three half-lives have elapsed, what fraction of the parent isotope will remain?****To the nearest 0.01, after 0.5 of a half-life has elapsed, what fraction of the parent isotope will remain? (If you think the answer is 0.75, look closer.)****To the nearest 0.01, after 1.3 half-lives, what fraction of the initial amount of a parent isotope will remain?****To the nearest 0.01, when 0.3 of the parent isotope remains, how many half-lives will have elapsed?**

**The
following table lists some of the main isotope systems used for radiometric
dating.**

Parent |
Daughter |
Half Life(years) |
Dating Range(years) |
Minerals/materials |

Uranium-238 | Lead-206 | 4,500 million | 10 - 4,600 million | Minerals include zircon, uraninite. Igneous or metamorphic rocks. |

Potassium-40 | Argon-40 | 1,300 million | 0.05 to 4,600 million | Minerals include muscovite, biotite, K-feldspar. Volcanic rocks. |

Rubidium-87 | Strontium-87 | 47,000million | 10 - 4,600 million | Minerals include muscovite, biotite, K-feldspar. Igneous or metamorphic rocks. |

Carbon-14 | Nitrogen-14 | 5,730 years | 100- 70,000 years | Not used for dating rocks, except carbonates from Earth's surface such as recent coral reefs. Used for young organic materials, or surface-water samples: Wood, charcoal, peat, bone, tissue, carbonate minerals from surficial environments, water containing dissolved carbon. |

**From
the last three questions in part A, you may get the sense that there are limits
to the eyeball method of reading a graph to get the number of half-lives from
the fraction of isotopes. **

**There
is a clear mathematical relationship between the amount of a radioactive isotope
(and the corresponding amount of daughter product), and the number of half-lives
that have elapsed. The relationship is non-linear, involving some sort of logarithm
or exponent. **

**The
mathematical formula can be used to determine exactly how many half-lives have
elapsed, for any fraction of parent/daughter isotope, without having to make
a visual estimate from a graph. In this next (and last) spreadsheet exercise,
you will use the mathematical formula.**

**Start
with the data below, from six different geological samples. **

Sample # |
Isotope system: Parent---Daughter | Daughter Isotope-Parent Isotope (D/P)
ratio |

1 |
C-14---N-14 | 1.51 |

2 |
C-14---N-14 | 2.48 |

3 |
K-40---Ar-40 | 0.655 |

4 |
K-40---Ar-40 | 0.358 |

5 |
U-238---Pb-206 | 0.296 |

6 |
U-238---Pb-206 | 0.015 |

**Open up a new Excel spreadsheet (workbook).****Enter the data from the preceding table, samples 1-6. You can cut and paste the data directly online, or else type it in.****Now calculate the six ages.****Given a half-life of an isotope and the daughter/parent isotope ratio (D/P), the age equals the half-life times the natural log of [(D/P)+1], the preceding result then divided by the natural log of 2.**

Age = (Half-life) X ln[(D/P) + 1]/ln2

(where the half-life is for the particular isotope, D/P is the**daughter/parent isotope ratio, and ln means natural log)**

**Enter this formula in Excel, to the right of the cell that has the number 1.51:**

**=(half life number)*LN([click on cell that has the D/P ratio of 1.51]+1)*(1/LN(2)).**

**If your data is set up in the same cells as this example, your actual formula may read as follows:**

**=(5730)*LN(E2+1)*(1/LN(2))**

**where 5,730 is the half life of the isotope in this sample.**

**E2 is the cell with the D/P ratio. If your D/P ratio of 1.51 is not in cell E2, change the formula to the cell address that contains 1.51.**

**LN means "natural logarithm." It must be in capital letters to work in an Excel formula.**

**This should return a result of 7,608 years. At the top of this column, label it. For example: "Age (yrs)."****Copy the formula down the same column five more times.****You should now have all 6 ages calculated.****However, at this point, 4 of the calculated ages are wrong, because they contain the C-14 half-life, but they do not have C-14 in the sample.**

**For samples 3 and 4, change the half life in the formula to the half-life of K-40 (see Table 1, above).****For samples 5 and 6, change the half-life in the formula to the half-life of U-238 (see Table 1, above).****Round each age off to three significant digits. The first age will round from 7,608 years to 7,610.****You may choose to type the rounded ages into the next column to the right, with a label such as "Rounded ages (yrs)."****These ages, rounded to three significant figures, are your true answers for the ages of the samples.**

**Now
answer the following questions on your lab answer sheet.**

**Why can't carbon-14 be used to measure the ages of rocks? Give two reasons.****Why can't carbon-14 be used to measure the ages of dinosaur bones?****What must have happened to an isotope system in a rock, since the rock formed, for a radioisotope age to be valid?**

**C.
Using Relative Dating to Deduce the Geologic History of the Grand Canyon.**

**The
following figure, "Generalized Rock Column of the Grand Canyon," comes
from a University of New Mexico geologic history project done in conjunction
with with Grand Canyon National Park, the "Trail of Time" exhibit,
at the Web site
http://www.trailoftime.org/.**

**Note:
There is further information, and another stratigraphic view, of the Grand Canyon
on the Kaibab Natural History Association's Web page on Grand Canyon rock layers
at:
Kaibab
Natural History (http://www.bobspixels.com/kaibab.org/geology/gc_layer.htm).**

**Get
some colored pencils.**

**On
a printout of the figure below (see if your instructor provides you with one),
mark a major nonconformity with green
lines, a major angular unconformity with
red X's along the unconformity, and a major disconformity
with a red line.**

**The following two paragraphs and geologic column (Table
3:) comes from a geology 101 online assignment at the University of North Dakota,
at http://www.und.edu/instruct/mineral/101intro/grandcanyon/grandcan.htm.**

Below is a geologic column for the Grand Canyon.Each formation is more or less described. This is the type information that geologists use to construct geological histories.

Note that squiggly lines in the column shown above and dashed lines below indicate unconformities. As you know, that means that something is missing, possibly because the land was high and being eroded at that time! I have only marked the most significant unconformities. They occur above and below the Zoroaster Granite, at the base of the Temple Butte Limestone, and at the base of the Surprise Canyon Formation.

**Table
3**

Permian | Kaibab Limestone | Gray, sandy, massive, limestone up to 320' thick. Abundant fossils include corals, squids, sponges, and shellfish. |

Toroweap Formation | Red and Yellow sandstones at the top and bottom of the formation, and some limestone between. Common fossils include corals, sponges, sharks teeth, and many kinds of clams, etc. | |

Coconino Sandstone | A massive white to buff colored, cross-bedded sandstone about 400' thick. Almost all quartz, well sorted, fine grained, and displays huge aeolian cross-bedding. Trails of quadrupeds, either reptiles or amphibians, have been found. | |

Hermit Shale | 100-300' thick, predominantly shale but also includes some sandstone strata. The sandstones have a deep red color. Some shale shows mud cracks and ripple marks. Fossils of plants, mostly ferns, and quadruped footprints have been found. | |

Pennsylvanian | Supai Group: Esplanade Sandstone |
1000' thick series (group) of alternating red cross-bedded sandstones and shales. The upper part of the group is non-marine and tracks of quadrupeds are found on bed tops. These tracks are believed to have been made by amphibians or primitive reptiles. Sediments appear in many places to be thin beds spread over wide areas in short periods of time. The lower part of the Supai includes calcareous sandstones and shales which many believe are of marine origin. |

Mississippian | Surprise Canyon Formation |
Variable deposits include sands and conglomerates. Cross bedding is common but localized. Great horizontal variation in stratigraphy. |

Redwall Limestone | Thick to massively bedded, bluish-gray limestone beds up to 600' high. The most conspicuous cliff in the canyon. It appears red, but that is only on the surface. Various invertebrates, including corals, shellfish, and crinoids are present as fossils. | |

Devonian | Temple Butte Limestone -- unconformity -- |
A calcareous sandstone, lavender to purplish colored, 50-100' thick. Fossils of armored fish, corals, shellfish and snails have been found. |

Cambrian | Tonto Group: Muav Limestone |
The Muav Fm. is a gray to buff limestone
300-400' thick. At its base, the limestone is interbedded with green shale
and sandstone. At its top the limestone grades into brown shales and sandstone.The Bright Angel Shale is mostly thinly bedded sandstones,
but conspicuous micaceous shales and dolomite beds are also present. It
varies between 350 and 400' thick.The Tapeats Sandstone is massive, coarse to medium grained,
100-300' thick. It is generally chocolate brown, but is lighter colored
in some areas. Cross beds are very common. Ripple marks, showing strong
currents in one direction can also be found. Trilobite (an extinct early
crab like critter) trails and worm tracks are present. |

Late and Middle Precambrian | Dox Sandstone | Sandstone mixed with limey shale. Ripple marks and cross bedding are present. Up to 1700' thick but variable. |

Shinumo Quartzite | Thick bedded, massive, white, variable color, 1100' thick in some places. Many cross beds and ripple marks on a fine scale. May form cliffs locally. | |

Hakatai Shale | 800' thick reddish and vermilion mudstones and shales interbedded with minor sandstone. Ripple marks, mud cracks, raindrop impressions are common. This formation is generally eroded to a smooth slope. | |

Bass Limestone on top of |
Mostly gray dolostones, weathered dark brown in places. Up to 200' thick. Interbedded shales and sandstones are present, often showing ripple marks. Fossil algae have been found. | |

Early Precambrian | Zoroaster Granite |
Although stratigraphically below the Vishnu Schist in many parts of the canyon, this intrusive igneous rocks is actually younger in age. Granites of this sort are associated with uplift and formation of mountain ranges. |

Vishnu Schist | Oldest rock in the canyon. Formed by metamorphism of rocks that were originally sedimentary. The metamorphism occurred after the rocks were buried to great depth by mountain building. This formation is now tilted up and in places approaches vertical. Thickness unknown. |

**Your
last assignment, the final part of the lab, is to write a geologic history of
the Grand Canyon's rocks, based entirely on the
Generalized Rock Column (above), Table 3 (above), and the Kaibab Natural History
Association Web page,
http://www.kaibab.org/geology/gc_layer.htm.
To perform the assignment:**

**Proceed from oldest to youngest.****Do NOT use absolute ages. Just use relative time terms such as "next," "followed by," "in the Late Precambrian," or "during the Devonian period."****In e very statement about time that you make, such as what came next in the sequence, you must explicitly point out which principle of relative dating is the basis of your logic. For example, "next, based on the principle of superposition, the land rose above sea level..." Or, "next, the __ granite intruded the __ schist, based on the principle of cross-cutting relationships." Or, "next, the ________ was tilted, based on the principle of original horizontality."****You will need to identify several major unconformities in your geologic history, such as "after tilting of the strata, a long interval of erosion occurred, which created an angular unconformity after the landscape was buried under more sediment."****To speed the process up, you can lump the Precambrian stratified (sedimentary) rocks into one supergroup, the Precambrian Grand Canyon Supergroup, and describe them in one paragraph.****End your geologic history at the Moenkopi Formation. Recent basalt eruptions, and the recent erosion that created the Grand Canyon, need not be included in your history.****Your written geologic history of the Grand Canyon must be typed.****Your written geologic history of the Grand Canyon is due before next week's lab.****The rest of this lab is due today.**