Question

The half life for the radioactive decay of potassium-40 to argon-40 is 1.26×109 years. Suppose nuclear chemical analysis shows that there is 0.359 mmol of argon-40 for every 1.000mmol of potassium-40 in a sample of rock. Calculate the age of the rock.

Answer 1

2.42x10⁹ years is the age of the rock

Step-by-step explanation:

The decay of an isotope follows the equation:

Ln[A] = -kt + Ln[A]₀

Where [A] is amount of isotope after time t, k is decay constant and [A]₀ is the initial amount of the isotope

To find decay constant from half-life:

k = ln2 / half-life

k = ln2 / 1.26x10⁹years

k = 5.501x10⁻¹⁰ years⁻¹

As in the reaction, K-40 produce Ar-40:

[A] = 0.359mmol

[A]₀ = 0.359mmol + 1.000mmol = 1.359mmol

Replacing:

Ln[0.359mmol] = -5.501x10⁻¹⁰ years⁻¹t + Ln[1.359mmol]

-1.3312 = -5.501x10⁻¹⁰ years⁻¹t

t = 2.42x10⁹ years is the age of the rock