Question

Earth Science help PLEASE! Need help filling out a table.

Study Data Table 1 below. It contains information about the parent-daughter ratios of the isotope uranium-235 (U-235) for several of the rock layers in the block diagram.

ROCK LAYER %of U-235 ABSOLUTE AGE PERIOD
g 94 ? ?
f 90 ? ?
d 65 ? ?
b 60 ? ?

Answer 1

I know this isn't completely mathematical but I really need help! Im attaching the resource pages now!

Answer 2

rock layers

Answer 3

Do you have a formula for finding the absolute age from the percentage of U-235 remaining?

Answer 4

That's the only interesting part here; writing the name of the period is just a matter of looking up the age in a table.

Answer 5

no i don't, no formulas were given which is why i am lost

Answer 6

how do i know what age to look up though?

Answer 7

Ah, never mind, I can derive it for you!

\[P(t) = P_0 (2)^{-t/t_{1/2}}\]will give you the amount remaining at \(t\) years, assuming you start with \(P_0\). We only care about the fraction, so we can write\[\frac{P(t)}{P_0} = (2)^{-t/t_{1/2}}\]and put our percentage (expressed as a decimal) in place of the fraction on the left.

If we take the log base 2 of each side,
\[\log_2(\frac{P(t)}{P_0}) = -\frac{t}{t_{1/2}}\]Multiply both sides by \(-t_{1/2}\):
\[-t_{1/2}\log_2(\frac{P(t)}{P_0}) = t\]Using the change of base formula for logs
\[-t_{1/2}\frac{\log_{10}(\frac{P(t)}{P_0})}{\log_{10}(2)} = t\]

Answer 8

So, if we want to find the age of a rock sample which has 50% of its U-235 remaining (which will allow us to check the formula), we plug in \(t_{1/2} = 704*10^6\text{ years}\), \(\dfrac{P(t)}{P_0} = 0.5\) and \(\log_{10}=0.30103\)

\[t = -704*10^6 \text{ years} * \frac{(-0.30103)}{0.30103} = 704*10^6\text{ years}\]

Half life of U-235 is 704 million years, so after 704 million years, we'll have half the amount we started with. Log base 10 of 0.5 = log base 10 of 1/2 which = -log base 10 of 2, so you could do this in your head if you know that log base 10 of 2 = 0.30103, as I do :-)

Answer 9

So 704 mya would translate to Precambrian era, according to your last resource page.

Do you understand how to use the formula?

Answer 10

sorry @whpalmer4 I was picking up my brother from school. I kind of understand the formula that you are using, but how do you know where to plug in which numbers?

Answer 11

would I do half of 94 to find the absolute age and period for rock layer G?

Answer 12

\(t_{1/2}\) is the half-life of the element that is decaying. I got the value for U-235 by asking WolframAlpha: http://www.wolframalpha.com/input/?i=half-life+uranium+235

Answer 13

the fraction \[\frac{P(t)}{P_0}\]is just the fraction of the original amount in the rock layer. If your data says 65%, you put 0.65 in place of that fraction.

Answer 14

No, for rock layer g, you have 94% of the original amount, so you use 0.94.

Answer 15

so to find rock layer G with a percentage of 94 I would do .94/.94(0)?

Answer 16

I'm sorry, I'm just really confused because I'm doing this class online so i don't really have a teacher or a textbook :o

Answer 17

No, P(t) is the amount of the element at time t. P_0 is the initial amount, or the value of P(0). P(t)/P_0 is the percentage remaining, so you put 0.94 where it says P(t)/P_0

Answer 18

Sorry, I didn't type the formatting commands.

\(P(t)\) is the amount of the element at time \(t\). \(P_0\) is the initial amount, and \(P(0) = P_0\). \(P(t)/P_0\) is the percentage remaining (expressed as a decimal), so you put \(0.94\) where it says \(P(t)/P_0\) when computing the age of rock layer g.

Answer 19

I'm reasonably certain that they must have covered this formula at some point, and you aren't just expected to derive it on your own, but now you have it, whether they did or not :-)

Answer 20

so would it be .94(94)/.94(0)?

Answer 21

I'm sorry i just don't understand, but I'm really trying!

Answer 22

No...

Sigh. Let me give you a new formula.

\[-t_{1/2}\frac{\log_{10}(R)}{\log_{10}(2)} = t\]

R is the percentage remaining, expressed as a decimal.

Answer 23

-t_1/2 log10(.94)/log10(2) would give me its absolute age?

Answer 24

Try it out, see what you get, decide whether the result seems reasonable. I'll check your answer if you tell me.

Answer 25

Remember, R = 0.5 is the amount after 1 half-life. R = 0.25 is the amount after 2 half-lives. What does the formula give you for those values?

Answer 26

okay, but one last question! for -t_1/2 would t be .94?

Answer 27

-.041955648906 is what I got... is that somewhat close or what?

Answer 28

No, the \(t_{1/2}\) value is the half-life of the isotope. It is the same for all of the computations you do. 704 *10^6 million years (or you could just do 704, with the understanding that the answer is in millions of years)

Answer 29

sorry, that was a bit redundant: 704 million years, or 704 *10^6 years

Answer 30

I'm sorry I've been re reading the entire assignment, and I don't know if this will make a difference or not but it says what my original question was: "Study Data Table 1 below. It contains information about the parent-daughter ratios of the isotope uranium-235 (U-235) for several of the rock layers in the block diagram." and then it shows the table that I created in the original question,

right underneath that is #3. Study the graph Half-life of U-235 below. The half-life graph is plotted on a logarithmic scale, which straightens the curved line for radioactive decay. This scale can make it easier to plot data, as well as easier to use when the parent-daughter ratio represents less than a single half-life. Use the graph to determine the absolute ages of the rock layers in the chart." and then it has this graph..

Answer 31

No problem, the graph gives the same results as my formula, just not as accurately :-)

Answer 32

then #4. It takes 713 million years for half of a sample of U-235 to decay to lead-207. Use the Geologic Time Scale (Resource 10 in the DataBank) to complete Data Table 1 with the period during which each rock layer formed.

Answer 33

so according to the graph, rock layer G would be about 70 million years for the absolute age in the cambrian period?

Answer 34

or would that be the cretaceous period?

Answer 35

Right, that was the 3rd attachment you posted, I believe.

So, you take the percentage of U-235 remaining, either find it on the y-axis of the graph and drop down to the age on the x-axis, or plug it into my formula to get the age. Then look up the age on the column on the 3rd attachment.

70 mya is Cretaceous

Answer 36

can you wait until i post the rest of the answers that i get just to make sure they are right and that i am understanding correctly now? :)

Answer 37

im so sorry it took me so long to understand something that should be so simple!

Answer 38

so according to the graph that i posted, rock layer F would also be 70 mya and in the cretaceous period even though it is a different layer?

Answer 39

rock layer D I got was 350 mya in the Mississippian period

rock layer B is also 350 mya in the Mississippian period... according to the graph I posted.. is that correct or am I missing something?

Answer 40

Wait, if they have different percentages of U-235, it can't be the same age

Answer 41

look at the graph that i posted though, its confusing me because it shows it like they are in the same period because they are close in number

Answer 42

did you see what I mean?

Answer 43

before you worry about period, you need to get a decent number for age.

Answer 44

is there any way that i can get a more decent number from the graph provided in my book or do I have to do it the mathematical way? because i haven't learned that in this class or in my math class yet :O

Answer 45

Here, let me draw a line on a copy of the attachment, maybe that will help.

Answer 46

rock layer F has 90% U-235 which is about 107 mya.

Ah, I found your workbook online! http://www.lawndalehs.org/ourpages/auto/2008/1/16/1200519609497/Investigation%2013%20-%20Determining%20Geologic%20Ages.pdf

Let me mark up a copy of the chart so you can see what I mean.

Answer 47

okay, thanks!!

Answer 48

@whpalmer4 wouldn't 107 mya still be in the cretaceous period?

Answer 49

Okay, that took longer than I wanted, but hopefully you'll be able to read it easily.

Answer 50

Successive colored lines (red, purple, blue, green) are the percentage values for your layers

You still have to estimate the value along the x-axis, however

Answer 51

so G would be about 68 mya, F is about 107 mya, D is about 425 mya, B is about 500 mya??

Answer 52

I'd say D is closer to 450 mya, looking at the graph (remember each "block" is 200 mya across, and it's about 1/4 of the way across the block that starts at 400 mya)

Answer 53

oh okay that seems more reasonable! did the rest seem okay?

Answer 54

Do you mean the rest of the ages? Yes, I only commented on the one I thought was a bit too far off to be acceptable.

Answer 55

okay, so now for the periods, G and F would both be cretaceous and D would be siluruian and B would be cambrian correct?

Answer 56

1st two are Cretaceous, I agree...D at 450 mya I would say is just into Ordovician, rather than Silurian (you're still using 425 mya, I bet), B is Cambrian

Answer 57

i did use 425 on accident, I'm sorry!
THANK YOU SO MUCH!!! for all of your help! I appreciate it SO much!!!!!

Answer 58

You're welcome.

Answer 59

By the way, here's a non-logarithmic chart showing the decay of U-235 vs. time. The y-axis is the percentage remaining, and I put in grid lines at 90%, 50%, and 10%.

Answer 60

thank you!! :)