This homework set was worth a total of 100 points. Most people did pretty well overall.
Questions 1 and 2 were pretty simple, and few people had trouble with them.
The proper order was, from oldest to youngest: C, B/I, A/F/H, E/G, D.
The proper order was, from oldest to youngest: E, D, C, B/L, K, J, I, A/G/H, F. Layers I, J, and K are the missing layers between A and B.
Questions 3-5 were a bit more challenging, but still most people did fairly well. The places where the most points were taken off were in Questions 3 and 4 when people neglected to note the folding of some of the layers and in Questions 4 and 5 when people did not tell me how the angular unconformities formed (there were examples in the examples on the web page...).
Here's my history:
To get full credit, you had to mention folding and you had to have all the pieces in the right order.
Also, a side note. The phrase is "laid down", not "layed down". As far as I know, there's no such word as "layed". See the WWWebster Dictionary entry on "lay" for more details.
Here's my history:
A number of things tripped people up here. Several people had the wrong order for D-G, even though I told you that D was oldest. Several other people told me about layer H. There was no layer H in the homework problem - though there was one in the example. All I can say to these two groups is, read the homework more carefully.
Other common errors included not mentioning folding, or not mentioning tilting, or not mentioning erosion. Several people simply told me there was an angular unconformity between C and D-G. Yes, but I wanted you to tell me how it formed.
Another curiosity for me was the number of people who told me layers D-G were folded by wind or waves. Huh? I guarantee you that wind is not strong enough to fold solid rock. Erode, yes; fold, no way.
Overall, most people did fairly well.
Here's my history:
It is also possible to interpret the column slightly differently, as below:
The things which tripped most people up were having the wrong order for layers M-F (again, I told you that M was oldest; read the homework more carefully!) and leaving out the tilting and erosion.
These problems were more mathematical than the above. Despite that, most people did fairly well, though I will admit that these are definitely the questions which gave most people the most trouble.
My solution to this question:
Note that the half-life is the time it takes half of the parent atom (Po-218 in this case) to decay and become the daughter atom (Pb-214 in this case). Note that the half-life is not the amount of time it takes for there to be an equal number of parent and daughter atoms, in general. This second sentence is only true when you start with a pure sample of the parent atom.
In this case, the equation of interest is: R = ln(2)/T, where R is the decay constant, T is the half-life (in minutes here), and ln(2) is the natural logarithm of 2, which is 0.69314718....
To solve the problem, all you needed to do was plug 3 minutes in for T, and do the math on your calculator:
R = ln(2)/T = 0.693/3 minutes = 0.231 1/minute.
Some people were thrown off by my comment that I wanted you to give me the decay constant in units of 1/minute. If you notice above, that's already what the units are; no additional work was necessary. I'm sorry if this confused you.
The equation to use is: t = ln(1 + D/P) / R, where D is the number of daughter atoms (Pb-214 in this case), P is the number of parent atoms (Po-218), and R is the decay constant you computed above, and again ``ln'' means the natural logarithm.
Plug and chug as usual:
t = ln(1 + 537/1185)/0.231 minutes = ln(1.4532)/0.231 minutes
t = 0.3737/0.231 minutes = 1.618 minutes or about 2 minutes.
A number of people reversed the 537 and 1185. This will totally mess up your numbers. I'm not sure why they made this mistake, but as I said, it was fairly common; if I did something which made this unnecessarily unclear, please let me know so I can fix it in the future.
Parts (a), (c), and (e) of this question were very similar to part (b) of question 6. In fact, you use the same equation in both places. Parts (b), (d), and (f) of this question were very similar to part (c), and again, it's the same equation. Here's the summary (again, I use R instead of lambda, since I can't draw a lambda in HTML):
R = 0.693/(48.8 × 10^9 years) = 1.42 × 10^-11 1/year
The single most common mistake here was forgetting the, um, billion years part and simply dividing by 48.8. Another common mistake was not stating the units of the answer.
t = ln(1 + 323/15000)/(1.42 × 10^-11) years
t = ln(1.02153)/(1.42 × 10^-11) years
t = 0.0213/(1.42 × 10^-11) years
t = 1.5 × 10^9 or 1.5 billion years
So layer C is 1.5 billion years old.
If you had messed up part (a), clearly you will not get this answer; I didn't take any extra points off for that. On the other hand, again people inverted the daughter and parent atoms, 323 and 15000. Again, this will mess you up big-time.
R = 0.693/(1.25 × 10^9 years) = 5.544 × 10^-10 1/year
Again, people left off the billion part or forgot to state units.
t = ln(1 + 500/1500)/(5.544 × 10^-10) years
t = ln(1.333)/(5.544 × 10^-10) years
t = 0.2874/(5.544 × 10^-10) years
t = 518.3 million years or 5.183 × 10^8 years
So layer D is about 518 million years old.
R = ln(2)/T
R × T = ln(2)
T = ln(2)/R
So plug in R = 4.9511 × 10^-11 and do the math.
T = 0.693/(4.9511 × 10^-11) years = 1.4 × 10^10 or 14 billion years
All there was to it.
t = ln(1 + 302/10000)/(4.9511 × 10^-11) years
t = ln(1.0302)/(4.9511 × 10^-11) years
t = 0.02975/(4.9511 × 10^-11) years
t = 600.8 million or 6.008 × 10^8 years
So layer E is about 600 million years old.
From your answer to 1, you know that layers B and I were the same, layers E and G were the same, and layers A, F, and H were the same. Also, you know that C is older than B/I, B/I are older than A/F/H, A/F/H are older than E/G, and D is younger than anything. From these facts and the answers to parts (a)-(f), you can give ages for these layers.
Note, however, that you don't have enough information to give exact ages for some layers. You can't give exact ages for layers B/I, or A/F/H. You can't. You can't average across layers or guess how old they are; you can't do it.
The best you can do for B/I and A/F/H is state that the layers are in the range of age between C and E/G, and that B/I is older than A/F/H. That is all you can say. Anything else is wrong.
So here's my answer:
A/F/H: between 600 million and 1.5 billion years old
B/I: between 600 million and 1.5 billion years old, but older than A/F/H
E/G: 600 million years old.
A few quick-eyed folks caught the mistake I made in writing this question. In the beginning of the question, I said you were going to date layers C, D, and F from Figure 1. However, later in the question (parts e and f), I said layer E. Ooops! Unfortunately, if I had caught it, the problem would have worked better, because you would have been able to get an exact age for layer F, and thus A and H, and would've been better able to bracket the ages of B/I and E/G. If you caught this one, I graded it appropriately; kudos to you for catching me!