The half-life for the (first order) radioactive decay of 14c is5730
years. an archeological sample
contained wood with only 72% of the 14c found in living trees.
whatwas the age of this archeological sample?

The age of this archeological sample is 2737.53 years

Explanation:

Given that:

Half life = 5730  years

Where, k is rate constant

So,  

The rate constant, k = 0.00012 year⁻¹

Using integrated rate law for first order kinetics as:

Where,  

is the concentration at time t

is the initial concentration

Given that:

The rate constant, k = year⁻¹

It is given that 72 % of the 14C remains. So,

= 0.72

Applying values as:-

The age of this archeological sample is 2737.53 years