5

Dinosaur fossils are Often dated by using an element other than carbon; like potassium-40 that has ionger half life (in this case approximately 1.25 billion Years)....

Question

Dinosaur fossils are Often dated by using an element other than carbon; like potassium-40 that has ionger half life (in this case approximately 1.25 billion Years). Suppose the Minimum detectable amount 19 and dinosaur dated with 4K to be 66 million years old_ Is this possible?Yes_ it is possible to date this fossil with 4K.is not possible to date this fossil with 40K.What the maximum age of fossil that we could date using billion yrK? (Round your answerdecima place.)Need Help?Read luWhlch ltIel

Dinosaur fossils are Often dated by using an element other than carbon; like potassium-40 that has ionger half life (in this case approximately 1.25 billion Years). Suppose the Minimum detectable amount 19 and dinosaur dated with 4K to be 66 million years old_ Is this possible? Yes_ it is possible to date this fossil with 4K. is not possible to date this fossil with 40K. What the maximum age of fossil that we could date using billion yr K? (Round your answer decima place.) Need Help? Read lu Whlch lt Ielilo _ Tutor



Answers

Dinosaur fossils are often dated by using an element other
than carbon, such as potassium-40, that has a longer half-life
(in this case, approximately 1.25 billion years). Suppose the
minimum detectable amount is 0.1$\%$ and a dinosaur is dated with $^{40} \mathrm{K}$ to be 68 million years old. Is such a dating possible? In other words, what is the maximum age of a fossil
that we could date using $^{40} \mathrm{K} ?$

In the previous couple of problems, we talked about carbon 14 dating and in this problem, we're talking about potassium 40 dating and potassium 40 has a much longer half life, 1.25 billion years. We're going to use our exponential decay model and we're going to find the value of K. And then that will complete our model. And we can figure out whether or not we could use this particular kind of dating to date a dinosaur fossil. Okay, so if the half life is 1.25 billion years, then we can put 1/2 of em Not. And for the final amount I m not, is the initial amount and the K value we don't know, but the time is 1.25 billion. So we're substituting all of those numbers into our function, and now we're gonna solve that for K. So we start by dividing both sides by I am not and we get 1/2 which alright is 0.5 equals e to the 1.25 billion times K. Now we'll take the natural log of both sides and we have the natural log of 0.5 equals 1.25 billion times K and will divide both sides by 1.25 billion. And we get Kay is the natural log of 0.5 divided by 1.25 billion. So our model then is going to be m equals m not times e to the natural log of 0.5 over 1.25 billion times T. Okay, so let's use that model and figure out how long we would have if the minimum detectable level is 0.1% so 0.1% as a decimal is 0.1 So that means our final amount is going to be 0.1 times I'm not. We'll substitute that into our equation and will solve her time. So let's divide both sides by I am not. And we get 0.1 equals e to the natural log of point 5/1 0.0.25 1,000,000,000 times T. Now we're going to take the natural log of both sides. Natural log of 0.1 equals and natural log of 0.5 over 1.25 billion times. T now to get t by itself. We want to multiply both sides of the equation by the reciprocal of this fraction, and we end up with T equals 1.25 billion times of natural log of 0.1 over the natural log a 0.5 and we put that into a calculator and we end up with approximately 1.25 times 10 to the 10th power, and that translates into 12.5 billion. So what that saying is that we could date something that was as old as 12.5 billion years old using this technique of using potassium 40. So could you date the 68 million year old dinosaur fossil? Yes, you could.

We're going to assume that, uh, thank you. Why? Lefty represents the best thing 40 after time tea, and we're gonna know this radioactive. Okay, mention isn't of any use the expression. Okay, Well, and Jane here, these are getting constant, and we're gonna use that. We're gonna find that using the problem statements given that he buy best 40 is on Orange. 25 1,000,000,000 years. So what's fine? Org Carrie Wilson. You know that five sometime face for the Element treats 1/2 of its initial who tend ISS kay turns 4.25 10 9 years. So from this we find, act or help is to financial 11257 to 9. Okay, so are you. Jerry Constant is found to be negative. There. You are going to do it by hole today. Nine. Uh, so excuse that the minimal required some pens off. Um, but supporting should be borden point or percent off heads in show value. So what does that mean? Well, it means that is as long as plus the 40 content, uh, divided by its initials. Something is greater than point. Here's your one. With this method, we actually can did think that, um So what is white teeth? Well, what do you use? You should turn the financial They do one of two or 4 to 59 Oh, where you are? Zero. They should be greater than pulling beers or what? Oh, there's nothing about exponential Late to make love to you. Why did I will? 5 10 to mine should be greater than 40 years to earn every anti ballistic natural, lovable times. And we're gonna end up with two law. Negative. Open. It's a lover to t. Well, would you buy, can it, Darrin? So that should be greater than oh, from soaring. Should be great. Don't want one from this. You find that so as long as time is less than 12.5 the other one years, he actually knew. Respect it too. State, uh, Brussels. So in cold statement, it is given that it is asked that is possible King today, dinosaur Also what this matter from which is 60 80,000,000 years old. So the answer is yes. Since age 1,000,000 Is less things well going by? So yes,

So they tell us that that c. 14 because the half life is only you know roughly 5000 years. It's not you can't use it for Uh dating dinosaur bones. Although you know technically you know dinosaur should have had carbon 14 in their bodies and it would decay. But the problem is is they basically they ask us to take find how much carbon would be left If a dinosaur was 68 million years old. So we plug t equals -68 million into here. And even with you know extremely high precision that's gonna that's zero for all practical purposes that is zero. There's nothing left because this is such a small number. It's you know just ridiculously small. And in fact even Mathematica basically said it's too small for a machine precision Which I think is in mathematica is like 18 digits or something. So anyway it's It's basically zero. So you look for c. 14 dinosaur bone and you're not gonna see any, you're not going to measure any. So they ask us, well if the minimum we can get It's about 1% .1% of what the original value was. How long how far back can we use Um carbon 14 dating? So we want we want 0.001 of the original amount. So that's what we can measure. That's the limit of what we can measure. And so we set that equal to c. 14 star. Um we c. 14 is here with K. Here. That's all for T. Um And we get that how far back we can go is about 57,000 years. About 57,000 years. If we if we have we can measure the c. 14 down to about .1% of what it wouldn would be in the body in a living body. Um We can get things back to about 57,000 years.

All right, so in this problem, we're talking about carbon dating again. And so we have our exponential decay model. M equals M, not each of the K T. And from problem number 11 we have are carbon dating model in specific with its K value of natural log 110.5 over 5730. And that value of K came from the half life of carbon 14 being 5730 years. So what we want to do is show that this is unreliable as a method for finding the age of the dinosaur. So imagine that the dinosaur fossil is thought to be 68 million years old. So the time is 68 million. What will happen if we substitute that number into this model? So we have m equals m not times E to the natural log of 0.5, over 5730 times 68 million. What you're going to put in the calculator is not the M not but the rest of it. And what happens is you end up with zero now it's not technically zero, but as far as the calculator can handle, it thinks it zero. So that shows us that we can't use carbon dating for something that old. So then the question is, what's the limit on carbon dating? What's the minimal or the minimum detectable if the minimum detectable level is 0.1% than what's the maximum age? So let's let em be 0.1% of M not, And that would be M equals 0.1 times m Not if we substitute that into our model. We can solve for the age. So we get bring it over here. 0.1 am not equals m not times e to the natural log of 0.5 over 57 30 times t Let's divide both sides by m not and we have 0.1 equals e to the natural log of your 0.5 over 5730 times T. Now we're going to take the natural audible sites. So the natural law gives your 0.1 equals and natural log of 0.5 over 5730 times t. Now our goal is to solve for T, so we need to multiply both sides by the reciprocal of this fraction, and we will get T equals 5730 times the natural log of 0.1 over the natural log of 0.5. And when you put that into a calculator, you get approximately 57,104. So that means that the maximum age of a fossil that you could date using carbon 14 is 57,104 years.


Similar Solved Questions

5 answers
Consider the difference equation Tu+lAxn , whereA= Classify the origin as an attractor. repeller , saddle point . Explain your reasoning: Find the general solution of the difference equation
Consider the difference equation Tu+l Axn , where A= Classify the origin as an attractor. repeller , saddle point . Explain your reasoning: Find the general solution of the difference equation...
5 answers
Chapter 23, Problem 045Two charged concentric spherical shells have radii 7.75 cm and 15.0 cm_ The charge on the inner shell is 3.01 x 10- 8 C and that on the outer shell is 2.56 x 10- 8 C; Find the electric field (a) at r = 11.1 cm and (b) at r = 23.1 cm.(a) NumberUnits(6) NumberUnits
Chapter 23, Problem 045 Two charged concentric spherical shells have radii 7.75 cm and 15.0 cm_ The charge on the inner shell is 3.01 x 10- 8 C and that on the outer shell is 2.56 x 10- 8 C; Find the electric field (a) at r = 11.1 cm and (b) at r = 23.1 cm. (a) Number Units (6) Number Units...
5 answers
14 What is the equilibrium concentration of HCP The reaction is run at 258C and all data is collected at :25*C. Hz(g) Clzkg) 5 2HCll) AG;_= -6.38kJ [nitialj M 0.050 0.050 0.440 0.21 M 0.32 M 05 0.48 M 0.57 M
14 What is the equilibrium concentration of HCP The reaction is run at 258C and all data is collected at :25*C. Hz(g) Clzkg) 5 2HCll) AG;_= -6.38kJ [nitialj M 0.050 0.050 0.440 0.21 M 0.32 M 05 0.48 M 0.57 M...
5 answers
NmnenmETnmIninn Hpmlmna Vaian Jod One uon36) The lollowlng Verilog code describes some slmplc hardwarc_ Sketch the circuit dlagram of (hal hardware:Ftce exanale inpol Cocki output Q1. 02 :clock:02) ;aluay: A(posrdge €lock) beainendmodule
nmnenm ETnm Ininn Hpmlm na Vaian Jod One uon 36) The lollowlng Verilog code describes some slmplc hardwarc_ Sketch the circuit dlagram of (hal hardware: Ftce exanale inpol Cocki output Q1. 02 : clock: 02) ; aluay: A(posrdge €lock) beain endmodule...
5 answers
Find the pH of a 0.065 M solution of Sr(OH)2 Type your final answer below with correct units and sig figs.
Find the pH of a 0.065 M solution of Sr(OH)2 Type your final answer below with correct units and sig figs....
5 answers
11) (61 If 12kg of oxygen combusted with hydrocarbon fue produce 1Skg of products (carbon dioxide and Vater vapor) how much hydrocarbon fuel in kg was combusted?12) (41Write the nuclide symbol helaworan isotope of the element that has proton and neutrons.
11) (61 If 12kg of oxygen combusted with hydrocarbon fue produce 1Skg of products (carbon dioxide and Vater vapor) how much hydrocarbon fuel in kg was combusted? 12) (41 Write the nuclide symbol helaworan isotope of the element that has proton and neutrons....
5 answers
Solve the equation. (Enter your answers as comma-separated Iist . Use a5 &n Integer constant Enter your response retlans tan? (x) tanfx)Need Help?Hrd (1[0/1 Points]DETAILSPREVIOUS ANSWERSLARTRIG1O 2.3.062. 2F100 Submissions Used(Enter vour answers 15 comma-separated Ils . Use Jsan Integer constant. Enter Your response rdlans Solve the equation 2(x) tun(x)Need Help?
Solve the equation. (Enter your answers as comma-separated Iist . Use a5 &n Integer constant Enter your response retlans tan? (x) tanfx) Need Help? Hrd (1 [0/1 Points] DETAILS PREVIOUS ANSWERS LARTRIG1O 2.3.062. 2F100 Submissions Used (Enter vour answers 15 comma-separated Ils . Use Jsan Integer...
5 answers
Whol tne currenti Inthe dlGram below?
Whol tne currenti Inthe dlGram below?...
5 answers
Uad ountaderotrnracd macniricmFunenetleObl DIIAnducD @o44AlOmMananinARale Hanenneneintaa
Uad ountaderotrnracd macniricm Fune netle Obl DIIAnducD @o44 AlOm Mananin A Rale Hanenneneintaa...
5 answers
Solve the following equations for the given domain: Ztan?0 cos 0 = 3, 0" < 0 < 360" 3 tan(Zx + 152) = 4, 0' <x <180? (sin x + cosx)(1 sin X COS x) = 9sin? x, 0" < * < 3609 3(2 sin x cos x) = 2(sin x - 3cosx), 0" <x <360" sin x tanx 2 sin x tanx + 3 = 0, 0" <x <360" +2 = 0, 0' < x < 3609 cosx
Solve the following equations for the given domain: Ztan?0 cos 0 = 3, 0" < 0 < 360" 3 tan(Zx + 152) = 4, 0' <x <180? (sin x + cosx)(1 sin X COS x) = 9sin? x, 0" < * < 3609 3(2 sin x cos x) = 2(sin x - 3cosx), 0" <x <360" sin x tanx 2 sin x tanx +...
1 answers
Breathing is cyclic and a full respiratory cycle from the beginning of inhalation to the end of exhalation takes about 5 s. The maximum rate of air flow into the lungs is about $0.5 \mathrm{L} / \mathrm{s} .$ This explains, in part, why the function $f(t)=\frac{1}{2} \sin (2 \pi t / 5)$ has often been used to model the rate of air flow into the lungs. Use this model to find the volume of inhaled air in the lungs at. time $t$
Breathing is cyclic and a full respiratory cycle from the beginning of inhalation to the end of exhalation takes about 5 s. The maximum rate of air flow into the lungs is about $0.5 \mathrm{L} / \mathrm{s} .$ This explains, in part, why the function $f(t)=\frac{1}{2} \sin (2 \pi t / 5)$ has often be...
5 answers
Usc thc Shcll Mcthod to computc thc volumc obtaincd by rotating thc region cncloscd by thc graphs as indicated, about thc y-axis. y = 31 _ 1,y = 7 _ €,€ = 0 (Use symbolic notation and fractions where needed )
Usc thc Shcll Mcthod to computc thc volumc obtaincd by rotating thc region cncloscd by thc graphs as indicated, about thc y-axis. y = 31 _ 1,y = 7 _ €,€ = 0 (Use symbolic notation and fractions where needed )...
5 answers
(c) Estimate the P-value P-value 0.250 0.100 P-value 0.250 0.050 P-value 0.100 0.010 P-value 0.050P-value 0.010
(c) Estimate the P-value P-value 0.250 0.100 P-value 0.250 0.050 P-value 0.100 0.010 P-value 0.050 P-value 0.010...
5 answers
FS0283ExpzFind the IQ score corresponding to z = 2.83, when average of IQ's is 100 and standard deviation is 12Use me t0 enter the answBacDoneDeleCle:
FS0283Expz Find the IQ score corresponding to z = 2.83, when average of IQ's is 100 and standard deviation is 12 Use me t0 enter the answ Bac Done Dele Cle:...

-- 0.019126--