Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Raioactive Dating Problem

  1. Jan 20, 2010 #1
    Bones of the wooly mammoth have been found in North America. The youngest of these bones has a 14C activity per gram of carbon that is about 21% of what was present in the live animal. How long ago (in years) did this animal disappear from North America?

    I'm struggling with this problem - is it simply a mathematical problem - working out how many half-lives (5730 years) cause 21% to be left?
    Or, do i have top work out the Decay constant λ then use ΔN/Δt = -λ N ?

    If it is simply a mathematical Can anyone tell me how to do it please.
    If I have to find the Decay constant, I'm still stumped on the mathematics involved.

    Thanks for any help.

    Chawkdee
     
  2. jcsd
  3. Jan 20, 2010 #2

    mgb_phys

    User Avatar
    Science Advisor
    Homework Helper

    You just need the ratio of N_now, N_orig and the half life.
    The equation is derived here http://en.wikipedia.org/wiki/Half-life

    c737eed649e864cc426cfc4c133bb49d.png

    Hint, estimate how many half lives you would need to get 25% of the c14 left - it's easy to get logs the wrong way around in the calculator
     
    Last edited by a moderator: Apr 24, 2017
  4. Jan 20, 2010 #3

    cepheid

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Well, both methods are mathematical! There is no difference between them. The differential equation dN/dt = -λN has an exponentially decaying solution: N(t) = N0e-λt, where the constant N0 is the original amount.

    You can easily express this as an exponential function having base 2 instead of base e. That will tell you the relation between the half-life and λ. That is how the two methods are related. That having been said, since you already know the half-life, you can probably use the first method you suggested.
     
  5. Jan 22, 2010 #4
    Thanks a lot - great help!
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook