If I begin with 100 atoms, how many atoms will be left of carbon 12 in 17,190 yrs if the half life of C12 is 5,730 yrs?

1 answer

It is not possible to answer this on such a small sample, as the disintegration is NOT precise: the half-live is an average of many. On a sample such as this...

Think of flipping six coins: will you get three heads and three tails? No.

But if you flip them 1 million times, you get darn close to half heads, half tails.

You teacher probably didn't want you to think on that issue.

so, if you had a 100 million atoms

Nleft= 100,000,000*(1/2)^(17,190/5,730)
= 12,500,000 or 1/8 of the original amount.
In your silly case, of 100 atoms, you would often get 12, or 13, and a few times get 11, or 14, or fewer still, 10, or 15

Radioactivity is not a precise schedule atom by atom.