OLD WOODWoodenit

Atomic physics… Help.?

One gram of living wood has a radioactivity of 16 counts per minute. The half life of Carbon-14 is 5730 years. Given the decay constant
k=ln 2/t_half calculate the age of a piece of old timber from a snip which was found to have a radioactivity of 13 counts per minute.

The basic equation is

dN / dt = – k N(t)

N(t) = N(0) exp ( -k t)

the initial decay is then given by the piece of living wood, that is

dN / dt = – k N(0) = – 16 counts per minute

Thus N(0) = 16 / k

k needs to be obtained from k=ln 2/t_half , you need to convert 5730 years into MINUTES to obtain k. dN/dt can also be expressed as

dN / dt = – k N(0) exp( -k t)

or

dN / dt = – 16 exp( -k to ) = – 13

where to is the value in minutes of your answer. You already calculated k (in 1/minutes) so go ahead and solve for to. I get an answer of about 1600 years, but I might be mistaken in my calculation so do this carefully.

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