Given:
Half life t1/2 for K-40 = 1.26*10⁹ years
Initial amount of K-40, A₀ = 1.000 mmol
Amount of Ar-40 formed = 0.771 mmol
To determine:
The age of the rock
Explanation:
The radioactive decay can be expressed mathematically as:
A = A₀exp(-kt)------(1)
where A₀ = initial amount
A = amount after time t
k = decay constant = 0.693/t1/2 ----(2)
Here: k = 0.693/1.26*10⁹ yr = 0.55 *10⁻⁹ yr⁻¹
Now:
A₀ of K-40= 1.000 mmol
A of K-40 = 1.000 - 0.771 = 0.229 mmol
Based on eq(1)
0.229 = 1.000 exp(-0.55*10⁻⁹t)
t = 2.68*10⁹ years
Ans: Age of rock = 2.7*10⁹ yrs
