Question

The decay of 40K to 40Ar is used to date igneous rocks around fossil deposits to bracket the age of the fossils. When 40K decays, 10.9% of the time it produces 40Ar. The half-life of 40K is 1.248 x 109 years. In a given rock sample, 281.8 nmol of 40K is measured and 7.25 nmol of 40Ar is measured. What is the age of the rock in years

Answer 1

Answer:

The age of the rock is 2.23x10⁹ years.

Explanation:

The age of the rock can be calculated using the following equation:

$t = \frac{t_{1/2}}{ln(2)}*\frac{K_{f} + \frac{Ar_{f}}{10.9\%}}{K_{f}}$   (1)          

Where:

t: is the age of the rock =?

$t_{1/2}$: is the half-life of ⁴⁰K = 1.248x10⁹ years

$K_{f}$: is the quantity of ⁴⁰K in the sample = 281.8x10⁻⁹ mol

$Ar_{f}$: is the quantity of ⁴⁰Ar in the sample = 7.25x10⁻⁹ mol

10.9%: is the percent of ⁴⁰Ar production by the decay of ⁴⁰K

By entering the above values into equation (1) we have:

$t = \frac{1.248\cdot 10^{9} y}{ln(2)}*\frac{281.8 \cdot 10^{-9} mol + \frac{7.25 \cdot 10^{-9} mol}{0.109}}{281.8 \cdot 10^{-9} mol}$

$t = 2.23 \cdot 10^{9} y$

Therefore, the age of the rock is 2.23x10⁹ years.

I hope it helps you!