Question on Radioactivity, Activity and Age Estimations.

[Wesc]

Hi all, my end of year Physics exam is tomorrow and I need some help on this question and if someone could help I'd appreciate it.

Carbon-14 has a half life of 5730 years, and an equilibrium concentration in the Earth’s lower atmosphere of approximately one atom per 8.3 x 1011 atoms of normal Carbon-12. The body of a Neolithic traveller – Ötzi, the Ice-Man – was discovered emerging from a glacier in the Italian Alps in 1991. Material found with the body had an activity of approximately 121 Bq per kg of Carbon. Ignoring any possible calibration errors, calculate the approximate age of the body.

So far I found the decay constant to be 0.000121 y^-1 from the Half-life formula.
I also used the activity equation A = -λn to get this: 121 Bq/kg = -0.000121.N ... So 1,000,000 Bq/kg = N

So now, I think what I'm meant to do is use X = Xo.e^(-λt) ... and get a ratio for how much Carbon is left? But I'm unsure how to do so. Thanks for reading and I hope you can help :)

 

[mfb]

The decay constant has a unit, 1,000,000 Bq/kg = N does not make sense.
You should get the amount of Carbon-14-atoms per kg there (it is not 10^6!). You can calculate the initial amount of Carbon-14-atoms per kg, and the difference between the two values is related to the age of Ötzi.

 

[Wesc]

The decay constant has a unit, 1,000,000 Bq/kg = N does not make sense.
You should get the amount of Carbon-14-atoms per kg there (it is not 10^6!). You can calculate the initial amount of Carbon-14-atoms per kg, and the difference between the two values is related to the age of Ötzi.

I figured out another way anyway, thanks though ! :)