Age of Ax Handle from Dig: Calculating Half-Life of Carbon-14

[Soaring Crane]

An archaeologist digs up a piece of wood believed to be an ax handle from a dig. The wood is from an ash tree. The beta emission from the old piece of wood is 4 beta/min. A similar piece of wood that is freshly cut registers beta emission at 16 beta/min. The half-life of carbon-14 is 5,370 yrs. How old is the piece of wood from the dig?

Is it 5370yrs./2?

Thanks.

 

[faust9]

You need to look up half-life($\lambda$). How many half lives are required to reduce 16 to 4 (there's an elegant exponential function for doing these problems BTW)?

 

[greenman100]

5370*4, b/c the halflife is cut in half twice

 

[recon]

Is it 5370yrs./2?

No it isn't. That's not the way to think of half-life. Don't let the word 'half' confuse you.

5370*4, b/c the halflife is cut in half twice

Both your answer and reasoning are wrong. The halflife is never cut in half twice. The beta emission is cut in half twice.

It takes 5370 years for the beta emission to decrease from 16 to 8. Another 5370 years to decrease from 8 to 4. Soaring Crane, you should now be able to determine the total amount of time it takes for the beta emission to decrease from 16 to 4.

 

[HallsofIvy]

5370*4, b/c the halflife is cut in half twice

Your calculation is correct but, as recon said, your answer and your reasoning (as well as your wording!) are wrong.

"Halflife" is a constant- it doesn't get cut in half. You are correct that the beta emission has been cut in half twice. Each time it is cut in half is one half-life. Okay, "cut in half twice" requires how many half-lives?