Carbon-14 has a half-life of 5720 years and this is a first-order reaction. If a piece of wood has converted 11.5% of the carbon-14, then how old is it? 4290 years 2375 years 17160 years 4750 years 1008 years

1008 years

Explanation:

Given that:

Half life = 5720 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:

11.5 % is decomposed which means that 0.115 of is decomposed. So,

= 1 - 0.115 = 0.885

t = ?

t = 1008 years

it's all four options.