The activity of carbon-14 in a piece of ancient wood is only 12.5 % . If the half life period of carbon-14 is 5760 years, the age of the piece of wood will be

Options

A. `17.281 xx 10^(2)` years
B. `172.81 xx 10^(2)` years
C. `1.7281 xx 10^(2)` years
D. `1728.1 xx 10^(2)` years

Answer

B

Explanation

`t_(1//2) " of " C - 14 = 5760` years, `lamda = (0.693)/(5760)`
Now, `t = (2.303)/(lamda) "log" (.^(14)C " original")/(.^(14)C "after time" t)`
`= (2.303 xx 5760)/(0.693) "log" (100)/(12.5) = (2.303 xx 5760 xx 0.9030)/(0.693)`
` = 17281 = 172.81 xx 10^(2)` years