A Piece of wood, reportedly from king Tut's tomb was burnt and `7.32g ``.^(14)CO_(2)` was collected. The total radioactivity in the `.^(14)CO_(2)` was `10.8` dis `min^(-1)`. How old was the wood sample? `t_(1//2) = 5730 yrs` and `.^(14)C` isotope `= 15.3` dis `min^(-1) g^(-1)`.

Explanation

The mass of carbon in the simple is 44g of `CO""_(2)` contains = 12g of C
7.32g of `CO""_(2)` contains = `(12 xx 7.32)/(44) = 1.966gC`
`A""_(0) = 15.3 " dis" // "min " g`
`lambda = (0.693)/(t""_(0.5)) = (0.693)/(5730) year""^(-1)`
`A = (10.8)/(2.00) = 5.4 " dis" // "min " g`
As we know.
`t = (2.303)/(lambda) "log" (A""_(0))/(A) = (2.333 xx 5730)/(0.693) "log" (15.3)/(5.4) = 8.6127 " years"`