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
`lambda=(0.693)/(5760)t`
Now `t=(2.303)/(lambda)"log"(""^(14)C"origianl")/(""^(14)C " after time t")`
`=(2.303 xx 5760)/(0.693)"log" (100)/(12.5)`
`=(2.303xx5760xx0.9030)/(0.693)`
`=17281=172.81xx10^(2)` years