Awooden tool is found at an archaeological site. estimate the age of the tool using the following information: a 100 gram sample of the wood emits 1120 β-particles per minute from the decay of carbon-14. the decay rate of carbon-14 in living trees is 15.3 per minute per gram. carbon-14 has a half-life of 5730 years.

2578.99 years

Explanation:

Given that:

100 g of the wood is emitting 1120 β-particles per minute

Also,

1 g of the wood is emitting 11.20 β-particles per minute

Given, Decay rate = 15.3 % per minute per gram

So,

Concentration left can be calculated as:-

C left =

Where,  

is the concentration at time t

is the initial concentration

Also, Half life of carbon-14 = 5730 years

Where, k is rate constant

So,  

The rate constant, k = 0.000120968 year⁻¹

Time =?

Using integrated rate law for first order kinetics as:

So,  

t = 2578.99 years