I don't know hot to work backwards to find the time elapsed in radioactive decay PLEASE HELP!!

Question

One fossil of a woolly mammoth is found to have 1/32 of the amount of C-14 found in a living organism. Determine the total time elapsed since this woolly mammoth died.

I got this question from the June 2007 Chem regents, #81. I don't know how to solve this, please help me! =(

Answer 1

I did something similar in physics. It's all to do with the half life of C-14.

Say you start with 100 C-14 atoms and after a time your left with 50 of them because 50 have radioactively decayed. The time taken for this to happen (for the amount of C-14 to half) is called the half life and it doesn't change depending on how much C-14 you have.  

The half life of C-14 is 5730 years (chech that i'm not too sure). So if you have a ceartain amount of C-14 in the mamoth after 5730 years you'll have half.

After 2 half lives you have 1/4 of what you stated with. Ater 3 half lifes you have 1/8 and so on ... after 5 half lives you have 1/32 of the origonal amount of C-14 that would be in a living organism.

So basically it takes 5 half lives to reduce to 1/32 and each half life took 5730 years so it died about (5x5730=28650) 28650 years ago. Hope that helps.

Answer 2

the formula is t = [ ln (Nf/No) / (-0.693) ] x t1/2

here, ln = natural algorithm

        Nf = percent of Carbon 14 present in the fossil

        No = percent of Carbon 14 present in the living tissue.

        t1/2 = half life of Carbon 14 = 5,730 years.

    

now, the calculation

  let time elapsed be t

so, t = [ln(1/32)/(-0.693) ] x 5730

        t = [ (-3.466)/(-0.693)] x 5730

        t = 28658 years

because the years value is more than 25000 therefore, the error is ± 50 years.

so, the answer is 28658  years ± 50

Answer 3

They made it easy for you, actually, as 32 is 2^5.

Each half life reduces the remaining C14 by half. 1/2 after one half life, 1/4 after the second, and so on. So with 1/32 remaining, 5 half lives have gone by. C14's half life is 5730 years, so that mammoth is around 28650 years old.