Due Thursday September 17, 1998.
Instructions: Read, follow the directions, fill in the blanks and type the short essay.
In your junior year as a geology major
at UK, you determined that Joltium (Jt), the element you discovered your
sophomore year, is radioactive and decays with a half-life of 69.3 Ma to
form Bleepium (Bp). Now in your senior project, you have measured
quantities of both Jt and Bp in numerous rock samples and need to figure
out how old these rocks are.
Two things you need to know:
1) The formula for calculating the ages of rocks is:
Age = 1.443
x H.L. x ln ( Nd/Np + 1
)
where:
H.L. = half-life of the radioactive decay series you are using
Nd = number of daughter atoms in the sample you are testing
Np = number of parent atoms in the sample you are testing
ln ( ) = the natural logarithm of the number within the parentheses
(in this case, Nd/Np +1 ).
2) Here is a table of natural logarithm values that might come
in handy (in case you don’t have a scientific calculator handy):
| Nd
----- + 1 Np |
Nd
ln ( ----- + 1) Np |
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Here are the problems:
1. Look carefully at the formula and figure some things out about
how it works. What happens if we sample a lava flow that is only
1 day old? Essentially zero daughter product will have formed in
one day, so the Nd/Np ratio = Zero. If so, what is the age of the
sample, according to the formula? 1.443 x H.L. (69.3) x ln
(1) = ______ . To get that answer, you had to look up the value of
ln (1) in the table above, or use a calculator, or you had to just know
that ln (1) = zero (many people do).
2. In rock Sample #1, a gabbro from an intrusive dike in Sweden, there are 3.3 million atoms of Jt and 1.1 million atoms of Bp. To calculate the age, do this (fill in the blanks, step by step):
Age = 1.443 x H.L. x ln ( Nd/Np + 1 ) First, What is Nd/Np? __________
What is 1.443 x H.L.? __________
What is ( Nd/Np +1) ? __________
What is ln ( Nd/Np +1) ? __________
Finally, what is 1.443 x H.L. x ln ( Nd/Np +1) ? __________ (your answer is the age of Sample #1!)
3. In Sample #2, a diorite from California, there are the same number of atoms of Jt as of Bp.
What is the ratio Nd/Np ? ________. What percentage of Jt has decayed to Bp? _______%
How old is Sample #2?_________
4. In Sample #3, a granite from Sweden, there are seven times more Bp atoms than Jt atoms.
Is the sample older or younger than one half-life? ___________
What percentage of the original Jt atoms have decayed to form Bp atoms? _________ %
What is the Nd/Np ratio? __________
What is the age of this rock? ___________
5. Sample #4 is also a granite, sampled in the same granite body in Sweden where Sample #3 was taken, but about 1km away. You expected the ages of these two rocks to be the same, but instead you found that Sample #4 has a Nd/Np ratio of 0.33. Is the age of Sample #4 younger or older than Sample #3? _________
Sample #4 however, was sampled immediately adjacent to Sample #1, the gabbro dike that cuts across this granite body sampled by rocks #3 and #4. Carefully read the section of the Wicander and Monroe textbook on pages 64 to 65 about radiometric dating to determine why Sample #4 differs from Sample #3. Write a short essay (two paragraphs) that: (a) explains this dilemma, and (b) discusses other sources of error and uncertainty in radiometric dating. Type this essay and attach it to this sheet for handing in.
6. Bonus question (worth 1 full extra point - possible 6 out of 5): If the atomic weights of Joltium and Bleepium are the same, what is the decay mechanism for Joltium? ___________________
(read the chapter for this one, see key terms like "alpha", "beta",
"electron capture" and you'll know you're in the right area.)