An archaeologist finds only one eighth of the cells found in living plants in a carved piece of wood. How old is the piece? (half-life period of C14 = 5200yrs) [olympiad ques]

Dear Student,

 

This is an exponential decay problem:

 

 

Where,      

 

Given half life = 5200 yrs

Thus, decay constant λ = ln(2) / 5200 = 1.3 x 10^-4  (year^-1)

 

N_t = N₀/8

 

Therefore, N₀/8 = N₀ e^-λt 

              ln (1/8) = -λ t

             t =  ln (8) / λ = 1.599 x 10⁴ years !

 

Hope that satisfies your query.

 

Team

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