Radioacitivity question, I don't understand?

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You have a 20g sample of a cross, you have to date it, has an activity of 15 counts per second. 20g of living wood had an activity of 16 counts per second, estimate the age of the wood of the cross.

Sounds like you're talking about Carbon 14 dating.

Carbon 14 is an isotope of carbon- naturally occuring varient of carbon atoms that has two too many neutrons in the atoms-but has the same chemical properties as regular old carbon 12.

It has a half life of 5730 years (give or take 40).

A half life being the time it takes for half of the carbon14 to decay to carbon12.

So if the wooden cross had only 8 beeps on there geiger counter it would mean that it used up one half life. So the cross would be 5730 years old.

If there were four units of activity that would mean there was only half of half- so it would be two half lives old (2X 5730, or about 12K years old).

And so on.

So if you go the other way- if it has 15/16 of the original isotope, then it has only lost one sixteenth. Which means one half, of one half,of one half, of a half life as elapsed. Or one eighth of 5730 years. That being about 716 some years old.

As mentioned, its a carbon dating problem. Basically, you know what the ratio of carbon 14 to carbon 12 should be if it were new. As time goes on, the carbon 14 decays to carbon 12 - so if you measure the ratio of the two you can tell how much of the carbon 14 has decayed to carbon 12. So from that you can say the carbon has decayed by half, by 1/3rd, by 3/4ths, or whatever. You can then use logarithms to determine how many half lifes it would take to decay down that much. Then once you have the number of half lifes required, you multiply that by the known half-life time of carbon 14 to get the # of years old that it must be.