## ES 10 The Earth Homework 5 Geologic Time and Stratigraphy Answers Greg Anderson

This homework set was worth a total of 100 points. Most people did pretty well overall.

### Stratigraphy

Questions 1 and 2 were pretty simple, and few people had trouble with them.

#### Question 1 (4 points)

The proper order was, from oldest to youngest: C, B/I, A/F/H, E/G, D.

#### Question 2 (6 points)

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.

### Stratigraphy and the ``History of Rocks''

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...).

#### Question 3 (10 points)

Here's my history:

1. Layers D, C, and B were laid down (in that order).
2. D, C, and B were folded by compression from the ends.
3. Layer A was laid down on top of B.
4. The batholith (E) intruded into layers B-D and cooled.
Other interpretations were possible. One of the them would be simply switching the order of layers A and E. Another interpretation would be:
1. Layers D, C, B, and A were laid down (in that order).
2. D, C, B, and A were folded by compression from the ends.
3. Layer A was eroded flat.
4. The batholith (E) intruded into layers B-D and cooled.

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.

#### Question 4 (10 points)

Here's my history:

1. Layers D, E, F, and G were laid down (in that order).
2. After G was laid down, layers D-G were folded, tilted, and eroded to a flat plain.
3. After some unknown amount of time passed, layer C was laid down. There's an angular unconformity between layer C and the deformed layers D-G.
4. Layers B and A were laid down in that order.

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.

#### Question 5 (20 points)

Here's my history:

1. Layers M, L, K, J, I, H, G, and F were laid down (in that order).
2. After F was laid down, layers M-F were tilted and eroded to a flat plain.
3. After the tilting and erosion, but before layer E was laid down, a fault developed between layers H and I. This is a normal fault, as described in the lecture notes from Lecture 11.
4. After the fault stopped moving, layer E was laid down, followed by layer D.
5. After layers E and D were laid down, but before layer C was laid down, a fault developed between layers K and M. This is a normal fault also.
6. After the fault stopped moving, layer C was laid down, followed by layers B and A.
Also, the fault between H and I is oldest; it formed before the fault between K and L.

It is also possible to interpret the column slightly differently, as below:

1. Layers M, L, K, J, I, H, G, and F were laid down (in that order).
2. After F was laid down, layers M-F were tilted and eroded to a flat plain.
3. Layer E was laid down on the flat surface.
4. After layer E was laid down, a fault developed between layers H and I. This is a normal fault, as described in the lecture notes from Lecture 11.
5. After the fault stopped moving, erosion took place and planed layer E off to a flat surface.
6. After the erosion, layer D was laid down.
7. After layers E and D were laid down, but before layer C was laid down, a fault developed between layers K and M. This is a normal fault also.
8. After the fault stopped moving, layer C was laid down, followed by layers B and A.
If you wanted to give me this second interpretation, you must have told me about the erosion after E was laid down.

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.

### Dating Rocks Using Radioactive Decay

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.

#### Question 6 (10 points)

My solution to this question:

1. From simply looking at Table 1, you could find that the half-life of the decay of Polonium-218 (Po-218) to Lead-214 (Pb-214) is 3 minutes. No math necessary.

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.

2. Here you were to compute the decay constant (lambda in the homework, here let's call it R). In the notes from Lecture 14, there were a set of equations given (under the heading "Dating a Rock") which were all you needed to use.

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.

3. Here you were to compute the age of the sample, given the number of daughter and parent atoms, and your estimate of the decay constant from the part above. Again, the relevant equation is in the notes from Lecture 14.

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.

Overall, this problem gave people little trouble.

#### Question 7 (40 points)

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):

1. R = ln(2)/T. T = 48.8 billion years, or 48.8 × 10^9 years. Plug and chug:

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.

2. t = ln(1 + D/P) / R again. Here, R is 1.42 × 10^-11 from above, D is 323 and P is 15000. Again, it's plugging and chugging:

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.

3. R = ln(2)/T. T here is 1.25 billion, or 1.25 × 10^9 years.

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.

4. t = ln(1 + D/P) / R again. R here is 5.544 × 10^-10 from above, D is 500, and P is 1500. The work:

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.

5. Ahhhhh, here's a change in equations, though not a big one. Before, you were given the half-life (T) and asked to compute the decay constant (R). Here, you were given R and asked to compute T. However, you have the equation that relates R and T. All one needs to do is change the equation around to have T on the left side and R on the right, rather than the other way around. Here's the new equation:

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.

6. Here, you are back to the same equation as in part (d). Here's the work:

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.

So that's parts (a)-(f). You then had an additional part to solve. This is where most people got stuck for 5 points. Given the answers above, you had to tell me, to the best of your knowledge but no farther, the ages of layers A, B, E, G, and I in Figure 1.

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.