1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Carbon dating

  1. Aug 6, 2007 #1
    Carbon dating!!!!!

    A 5g charcoal sample from an ancient fire pit has a 14C activity of 63 disintegrations
    per minute. A living tree has a 14C activity of 15 disintegrations per minute per 1g.
    The half-life of 14C is 5730 years. How old is the charcoal sample from the ancient fire
    pit?


    2. Relevant equations
    dont think that any are necessary (I think!!)


    3. The attempt at a solution
    63/5 =12.6
    12.6/15 = 0.84
    5730*0.84 = 4813.2 years

    This isnt the right answer im sure. This is taken from a previous exam paper im doing to revise for my exams, and carbon dating is defintly gona come up, but cant find a method for doing this kind of question any where can somone pleeease help!!!
     
  2. jcsd
  3. Aug 6, 2007 #2

    mgb_phys

    User Avatar
    Science Advisor
    Homework Helper

    You haven't understood half-life correctly.
    The activity is halved every 5730years, so if you start with 15/s then after 5370 years you will have 7.5/s and after 10740 years 3.75/s.
    If you draw this on a graph you will see that it isn't a stright line.

    If you haven't studied enough maths to work this out the exam will normally 'cheat' and use answers that are whole numbers of half-lives. Because this doesn't you should have come accross the equation for exponential decay.
    Look up half-life or exponential decay.
     
  4. Aug 7, 2007 #3

    andrevdh

    User Avatar
    Homework Helper

    When the tree is alive it absorbs carbon (dioxide) from the atmosphere. This keeps the ratio of radioactive carbon in it (per gram) constant. When it dies the absorption (respiration) process stops and the remaining radioactive carbon (14) starts to decrease due to decay.

    The given data gives you the half-life of the decay process. The relation between the half-life and the decay constant is

    [tex]T_{1/2}\ \lambda = \ln(2)[/tex]

    so the initial activity is 15 disintegrations per minute per gram. The question requires you calculate the amount of time that elapsed to bring it down to 12.6. The decay decreases exponentially with time.
     
    Last edited: Aug 7, 2007
  5. Aug 7, 2007 #4

    Chronos

    User Avatar
    Science Advisor
    Gold Member
    2015 Award

    Agreed. The formula for radioactive decay was logarithmic last time I checked.
     
  6. Aug 7, 2007 #5

    andrevdh

    User Avatar
    Homework Helper

    Yes, the exponential formula can be changed into a (natural) logarithmic one that is linear in time.
     
  7. Aug 7, 2007 #6

    mgb_phys

    User Avatar
    Science Advisor
    Homework Helper

    I assumed that since the OP wasn't given simple times they must have studied decay laws and was trying to give hints on what to look up.
    If they haven't studied decay laws then quoting formulae with log(2) and lamba weren't going to help.
     
  8. Aug 8, 2007 #7

    andrevdh

    User Avatar
    Homework Helper

    I am not sure how one would do this without decal laws. What other approach is there? Using half-lifes?

    [tex]\frac{A_o}{2^n} = A_{now}[/tex]
     
  9. Aug 8, 2007 #8

    mgb_phys

    User Avatar
    Science Advisor
    Homework Helper

    If this is in an intro course before they have studied the necessary maths to use log funtions the decay rate is often chosen to be a whole number of half-lives, or you draw a graph and pick numbers off the curve.
     
  10. Aug 8, 2007 #9

    andrevdh

    User Avatar
    Homework Helper

    To my knowledge the decay rate (or activity) is

    [tex]A = \frac{dN}{dt} = -\lambda\ N[/tex]

    which also decreases exponentially with time.
     
  11. Dec 11, 2011 #10
    Re: Carbon dating!!!!!

    this is how the solution should be,
    Equation : R = R0e-λt

    t = (1/λ) (ln R0/R) = (5730 y/ ln 2) ln[(15.3/63.0)(5.00/1.00)] = 1.61x103 y
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Carbon dating
  1. Carbon-14 dating (Replies: 1)

  2. Carbon 14 Dating (Replies: 1)

  3. Carbon dating (Replies: 4)

Loading...