5

2 L laatelifir? of after carbon- half-lives? 2 5' Ll 5.730 points] 5 nof started 1 100.0 of carbon 14 how much...

Question

2 L laatelifir? of after carbon- half-lives? 2 5' Ll 5.730 points] 5 nof started 1 100.0 of carbon 14 how much

2 L laatelifir? of after carbon- half-lives? 2 5' Ll 5.730 points] 5 nof started 1 100.0 of carbon 14 how much



Answers

Carbon-14 has a half-life of approximately 5730 years. If $A_{0}$ is the original amount present, then the amount present after $t$ years is given by $A(t)=A_{0} 2^{-t / 5730} .$ If $55.0 \mathrm{mg}$ is present initially, how much is present after 3250 years?

So I have a half life of 57 30 for carbon 14. I'm starting out with five g. I want to know how long it will take to get to two g. So there's my formula right there for the half life. I'm starting out with five. I want to end up with two. So I divide both sides by five and that's what I get. And I want to put this in terms of log rhythms. So I'm going to do the log 0.5 of 2/5 equals T over 57 30. Now let's do the log a 0.5 log of two fists, base 0.5. And that's going to give us that. Now. I need to multiply it by 57 30 and I'm going to get 75 75 75 75. So 7575 years.

Um, this is one of the first of the poles of the radioactive carbon. Take a problem or the useful application, but determine the level of carbon, uh, to determine the age off Boston's. They can say that's a percentage of, uh, urban to find the age of wasn't This is a very a common application. They're useful. I understand the age off. A lot of things rocks organisms. Okay, so the general equation for this could be you can write em or concentration of the mass of the mount, whatever m equals and zero exponential. Negative. Katie XB. Uh, I guess the book is rt or peace. What for our for the bait of And they're given 1/2 like this off, like off the radio. Active carbon? Yes. 5730 years. C 14 is 5750 years, Which means that's for a given amount of carbon toe become half that amount. It takes 565,730. Okay. And we're going to use the, uh So how this is useful. We can use this number to calculate the are Well, if we need this expression and you can refer to page 3 98 Believes in the book where it gives but are it relates the art to the half life. A life off the carbon toe. This, uh, relation will be This is the hapless. Simply plug this in and you can get you determine our so and say our it once and then to you entered by I'm seven b, you know? So I want to use this and, uh, yes, this value. Plug it in here. Uh, so then, to determine find what is Or how long for the carbon to drop from? Bye, grams. Yeah, two grams. Okay, that's the question. So we have we're going to use to situation we're gonna plug in the initial years by this value is to be just determine the our value, and then you sell petite right. But we have everything we need, but it just didn't listen. You could use this. You could you shake out putting and delayed this and finally this value. But I won't try something different. I'm just a kid with hazardous, okay. And you're welcome. Great out and then plug it back in and write the master question. That's fine. But I want to leave it like this. Part time B and ah, just for the sake. Off variety A supposed apparently. And then say no. Let's say plug in the question. So if m equals m zero e to the are tee Okay. Been on, since I need find the value off yet which and becomes 22 I one in chill are tee okay r p and then So they could be like this. Has who do it by five equals e to the r p. Order Ellen off pictured right in enoughto over a not Solomon to over five. The Eleana to over five equals r p or or he equals we have a pistol in this guy, the work they want to find. Okay, if one over r times and then Ah, two over fight. And now I guess blow your your calculators are is Ellen two divided by 5730 So let's see. One war are is and then two divided by price errantly visited by 730 good upstairs times. And it can now do this creation and sold on this. And you should get something like B equals he equals 7000 570 uh, four or five years? Years doesn't make sense. Let's see if it takes five appellants 730 years for to drop from five to Is the half lifes off five to 2.5 would pick so many years So two dropped it too. It should take more than this. And so this is This is looking cancer Looks like a good

Okay So this problem is a little longer. So let's lay out a plan. Okay. First we're gonna find our K. And then we'll use that to find our ratio of our original amount to what we're left with okay. And then we'll find the partial pressure of co. two that's remaining okay And we'll use that to find the partial pressure of the n. 0. 2 that forms. So let's start with our planet's. Okay. Is the Allen of two over past life? So 693 Ln of two And a half life is 5730 years. So that gives us AK. 1.21. I'm sending negative four Years to the -1. And then we'll use this formula here to find that ratio of easier to A. That equals Katie. So that ratio of 802 a. Elena bit. So we've got our K. 1.21. So I'm sending negative four And we might find that by 20,000 years. So the Ln of that ratio easier over A. Is 2.419. So the ratio of a zero to A. But we started with to what we had remaining is 11 to Mhm. So the partial pressure of our CO. Two that's our A zero original. As compared to the partial pressure of Co. two. That's R. A. Equals 11 2. So we know the original partial pressure of CO. Two was one atmosphere. And we're looking for the partial pressure of co. two. That's 11.2 here. So the partial pressure of our co two is going to equal 0.8 93 ATM remaining. Okay. That's what we have left. Well we started with one And now we've used zero or we have this much left So we get .911 ATM. So that equals the partial pressure of the co. two. That has reacted well that's also going to be the partial pressure of the eno. To that's formed. So now that we've figured out how much you know to reform. Let's set up let's use that reaction to set up an icebox. So are partial look start. So are you know to This forming r. 204. So we'll set up on ice box here. So I have .911 minus two X. Zero. What's up? 2.911 -2. X. And X. Okay. And we know the K. Is one Time Santa -5. So that's going to equal X. Over .911 -2 x. All squared And six. Since K. is so small. We can assume that two x. Is much much smaller than the .911. So that will simplify our math by removing that. Thanks. So if we saw her ex here, We're going to get 8.3 Times 10 to the negative feet. I'm sorry, negative six ATM. And that's our partial pressure RN 204.

So we can look at the relationship between the half life and the decay constant. Where we'd like to calculate a decay constant which is equal to lambda 9.693 divided by the half life. Where would like the half life in years in this instance? And so we get a decay constant of 1.21 times 10 to the minus four years to the minus one. While we sub in for the half life asked 5730 years. So the number of moles of radioactive element is N. T. That is present after time T. Which has the initial amount and not after the decay constant lambda. So we have N. T. Is equal to end, not multiplied by E. To the minus lambda T. So what we can soul for is and not multiplied by 9.9889 So the number of moles of N. 02 produced is as follows. And not take away and not multiplied by not point not 889 which is equal to 9.9111 and not. So the pressure of N 02 produced is not 0.9111 atmosphere. Yeah. And so the equilibrium for the reaction is as follows. We have two and 02 that's an equilibrium with and two oh four as a gas. So we construct an ice table, initial change equilibrium not 0.9111 minus two. X 9.9111 Subtract to exit equilibrium. Here we have zero X. And X. So we can solve for his ex where the K. Is equal to P N 204 divided by P N 02 squared. So we solve for X. After we put in the values so we have X divided by 9.9111 Subtract two X squared. Where we solve X. That is 8.3 times 10 to the minus six atmosphere. And that is the pressure of N 204


Similar Solved Questions

5 answers
Ralance thefollowing redorrexciion equation; Cr2072 - (aq) +/ (a9) _ ~Crst(eq) + Iz(s)Mrinm_ Tne 7 Maich ine species with it3 soichiometri cochicient in thzbalz 7C26PremiseRestoneeDrag and drop t0 matchFullsi020 ?
Ralance thefollowing redorrexciion equation; Cr2072 - (aq) +/ (a9) _ ~Crst(eq) + Iz(s) Mrinm_ Tne 7 Maich ine species with it3 soichiometri cochicient in thzbalz 7C26 Premise Restonee Drag and drop t0 match Fullsi 020 ?...
5 answers
A microwave oven is designed so that the electric field at the center of the oven oscillates with maximum amplitude. If the wavelength the oven operates is 12 cm, what may be the width of the oven:puan36 cm42 cmNone of them20 cm40 cm32 cm
A microwave oven is designed so that the electric field at the center of the oven oscillates with maximum amplitude. If the wavelength the oven operates is 12 cm, what may be the width of the oven: puan 36 cm 42 cm None of them 20 cm 40 cm 32 cm...
5 answers
Problem 2.8 Find the General Solution:ry 4xy'+6y =x" sin(x)
Problem 2.8 Find the General Solution: ry 4xy'+6y =x" sin(x)...
5 answers
Question 3 (3 points) Give the correct IUPAC name for the given molecule:H-C-C-c-HH-C-H H
Question 3 (3 points) Give the correct IUPAC name for the given molecule: H-C-C-c-H H-C-H H...
5 answers
Question 72 ptsNH; - 02 reacts?Nz HzO. How many grams of Nz are produced when 6.5 grams of 02
Question 7 2 pts NH; - 02 reacts? Nz HzO. How many grams of Nz are produced when 6.5 grams of 02...
5 answers
Problemfor each & € R; the set A € Rx R is defined by Suppose that_ Au {(I,9) :y z/ -al} Find U A and A ocr OCR
Problem for each & € R; the set A € Rx R is defined by Suppose that_ Au {(I,9) :y z/ -al} Find U A and A ocr OCR...
5 answers
Edoblerb #B: (4) (10 points) Show how to find the derivative f defined by Ja 3 f() Vil/s 21_ using the chain rule_ (b) (5 points) Suppose f(1) = 3.F'() = +5.9(2) = 1,9(2) = 2 Exkib L t0 find (f 0 9)' (2) ~using the chain rule.
Edoblerb #B: (4) (10 points) Show how to find the derivative f defined by Ja 3 f() Vil/s 21_ using the chain rule_ (b) (5 points) Suppose f(1) = 3.F'() = +5.9(2) = 1,9(2) = 2 Exkib L t0 find (f 0 9)' (2) ~using the chain rule....
1 answers
Use a graphing calculator to perform the indicated multiplications. $$\left[\begin{array}{rrr}-9.2 & 2.3 & 0.5 \\-3.8 & -2.4 & 9.2\end{array}\right]\left[\begin{array}{rr}6.5 & -5.2 \\4.9 & 1.7 \\ -1.8 & 6.9\end{array}\right]$$
Use a graphing calculator to perform the indicated multiplications. $$\left[\begin{array}{rrr}-9.2 & 2.3 & 0.5 \\-3.8 & -2.4 & 9.2\end{array}\right]\left[\begin{array}{rr}6.5 & -5.2 \\4.9 & 1.7 \\ -1.8 & 6.9\end{array}\right]$$...
1 answers
Evaluate the integral by making a substitution that converts the integrand to a rational function. $$\int \frac{e^{t}}{e^{2 t}-4} d t$$
Evaluate the integral by making a substitution that converts the integrand to a rational function. $$\int \frac{e^{t}}{e^{2 t}-4} d t$$...
5 answers
Sump ; € 7 as much 6 $ 0oss_ 15le 4 5 = x+3 Li 7 - X+3
Sump ; € 7 as much 6 $ 0oss_ 15le 4 5 = x+3 Li 7 - X+3...
5 answers
19. Polonium-214 undergoes radioactive decay to produce lead-210. Write the balanced nuclear reaction for this processYour answer20. Lead-211 undergoes radioactive decay to produce bismuth-2111 Write a balanced nuclear reaction for this process.Your answer
19. Polonium-214 undergoes radioactive decay to produce lead-210. Write the balanced nuclear reaction for this process Your answer 20. Lead-211 undergoes radioactive decay to produce bismuth-2111 Write a balanced nuclear reaction for this process. Your answer...
5 answers
DucSTiONpopuujton GmtnJrwuoolonalo Ina lgalc Toj Ouernat173 707s50 . Hom Nanyue pmaet nllerGlt)QUEsTion "bestscllcr" Ihc Iolul sllce ny[ logisile Iunction below: Alter Ihe 'feleusc of4 350000 S(t) 100; montles the number of books sold and [ Is ttk' Ulne whcre S() represents Ihe nle of inereasc ol the function - WIS grceetest: Estimale the timc, alicr thc initial rclease , whcn amotana ronn monini Jmontne
DucSTiON popuujton Gmtn Jrwuoolonalo Ina lgalc Toj Ouernat 173 707s 50 . Hom Nany ue pmaet nller Glt) QUEsTion "bestscllcr" Ihc Iolul sllce ny[ logisile Iunction below: Alter Ihe 'feleusc of4 350000 S(t) 100; montles the number of books sold and [ Is ttk' Ulne whcre S() represen...
5 answers
Show all your work!Question 3 (10 points). Let A =k+1For which values of k is A invertible?Show all your workl
Show all your work! Question 3 (10 points). Let A = k+1 For which values of k is A invertible? Show all your workl...
5 answers
Why is pentose phosphate pathway important?
Why is pentose phosphate pathway important?...
5 answers
How has increased knowledge about plant growth been applied to improving the resistance of some plants t0 pests 5 marks) and allowed those plants to be used in non-native areas? (5 marks) What are (he positive and negalive impacts of such applications? (10 marks) (20 marks total)
How has increased knowledge about plant growth been applied to improving the resistance of some plants t0 pests 5 marks) and allowed those plants to be used in non-native areas? (5 marks) What are (he positive and negalive impacts of such applications? (10 marks) (20 marks total)...
5 answers
Question Completion Status;QUESTION 10Tor F it Is possible that there are galaxies 18 billion light-years away Which we cannot see, True FalseQUESTION 11Which dlstance mcasuring technique cannot be Used for measuring thie distonce o1 _ gulaxy? ParallaxCepheld variables White dwart SupernovaHbble $ Law
Question Completion Status; QUESTION 10 Tor F it Is possible that there are galaxies 18 billion light-years away Which we cannot see, True False QUESTION 11 Which dlstance mcasuring technique cannot be Used for measuring thie distonce o1 _ gulaxy? Parallax Cepheld variables White dwart Supernova Hbb...
5 answers
The highway mileage (mpg) for a sample of 8 different models of car company canbe found below; Find the mean, median, mode, and standard deviation Round t0 one decimal place as needed19,22,25,27,30,31,33,33Mean =MedianModeStandard DeviationQuestion H elp: Omessdle unstructorSubmit Qucstlon
The highway mileage (mpg) for a sample of 8 different models of car company canbe found below; Find the mean, median, mode, and standard deviation Round t0 one decimal place as needed 19,22,25,27,30,31,33,33 Mean = Median Mode Standard Deviation Question H elp: Omessdle unstructor Submit Qucstlon...

-- 0.030757--