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A piece of wood form the ruins of an nuc...

A piece of wood form the ruins of an nuclei an ancient building was found to have a `.^(14)C` activity of 12 disintegrations per minute per gram of its carbon content. The `.^(14)C` activity of the living wood is 16 disintegrations/minute/gram. How long ago did the trees, form which the wooden sample came, die? Given half-life of `.^(14)C is 5760yers`.

Text Solution

Verified by Experts

Here, `T=5760 yrs. T=?`
`R_(0)=16` disintegrations/minute/gram
R=12 disintegrations/minute/gram
form `t=1/lambda log_(e) (R_(0)/R)=T/0.693xx2.303 log_(10) (R_(0)/R)=5760/0.693xx2.303 log _(10) (16/12)`
`t=5760/0.693xx2.303(0.602-0.477)=(5760xx2.303xx0.125)/0.693 yrs=2392.7yrs`
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