I finished all my ap environmental work for the summer the other night, but I passed over a question since I had no idea how to approach it.

If someone could explain how to do this, it would help me out a lot.

57. An archeologist digs up a piece of wood believed to be an ax handle from a dig. The wood is characterized as being from an ash tree. The beta emission from the old piece of wood is 4 beta/minute. A similar piece of wood that is freshly cut registers beta emission at 16 beta/minute. The half life of carbon 14, a radioisotope of carbon present in all living things, is 5370 years. How old is the piece of wood from the dig?

i would imagine it would be 10740 years old. the decay of radiation is measured by the decay, which is only a quater of what it was at year zero. with the half life of 5300 years, you would get half the radiation after that, and half of that 5300 years later.

there is an equation that works it out in the case you don't get nice easy whole numbers, but thats out of my field.

http://en.wikipedia.org/wiki/Half-life

not the video game!

RAOVQ is right, but here is a more comprehensive explaination for if you get more trickier questions

a HL of 5370 years means it loses half its C-14 in 5370 years

you can figure out the equation of this as

current carbon14 = original carbon 14 * (0.5^number of half lives)

ie. if its one HL old, its half the original, if its 2 HL's old its a quarter of the original

An archeologist digs up a piece of wood believed to be an ax handle from a dig. The wood is characterized as being from an ash tree. The beta emission from the old piece of wood is 4 beta/minute. A similar piece of wood that is freshly cut registers beta emission at 16 beta/minute.
from here, it tells us the original (ie the one that is freshly cut) is 16 and the current is 4

4 = 16 * (0.5^n)------->where n is the number of HL's
0.5^n = 4/16 = 0.25
n = log(to base 0.5)0.25

your calculator cant do this, so use the change of base formula for logs and change it to something your calculator can do, such as base 10 or base exponential

log(base b)x = log(base a)x/log(base a)b

n = ln0.25/ln0.5
n = 2
it has been through 2 half lives
one half life is 5370 years
therefore, the sample is 2*5370 years old

10740 years

youre welcome

Simply put: Half life means that over that period of time half of the isotope decays. So if it's 16 beta/min when fresh, it will be 8 beta/min after 5370 years, and after another 5370 years, it would be 4 beta/min. So a total of 10,740 years old.

Yes, Mantikore gave a more thorough explination, which is useful for more difficult versions of the same problem. Props to him for it.