1. Limited time only! Sign up for a free 30min personal 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!

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