What does radioactivity mean in this question numerically?

What does radioactivity mean in this question numerically? e radioactivity due to C-14 isotope t! = 6000 yr of a sample of wood from an 9 ancient tomb was found to be nearly half that of fresh wood; the tomb is, therefore, about (a) 3000 years old (c) 9000 years old (b) 6000 years old (d) 12000 years old

Dear Student,

We have to use the radioactive decay equations to solve this problem.Radioactivity means the activity.

Now, half-life is defined as the time taken for the radioactivity of an isotope to fall to half of its original value.

$T_{\frac{1}{2} }= \frac{\ln 2}{\lambda }=\frac{0.693}{\lambda }, where T_{\frac{1}{2} }is the half life and \lambda is the radioactive decay cons\tan t$
It is given that the radioactivity of the ancient wood is half the value of the radioactivity of the fresh wood, in the sample taken.
So, the time taken for  fresh wood to decay to ancient wood is its half-life.

We have already been given the half life as 6000 years.
Thus, the age of the ancient wood in the tomb is its half life. Thus, its age is 6000 years.

Thus the correct answer is option (b).

Hope it helps.

Regards