Answer:
The age of the rock is 2.23x10⁹ years.
Explanation:
The age of the rock can be calculated using the following equation:
[tex] t = \frac{t_{1/2}}{ln(2)}*\frac{K_{f} + \frac{Ar_{f}}{10.9\%}}{K_{f}} [/tex] (1)
Where:
t: is the age of the rock =?
[tex]t_{1/2}[/tex]: is the half-life of ⁴⁰K = 1.248x10⁹ years
[tex]K_{f}[/tex]: is the quantity of ⁴⁰K in the sample = 281.8x10⁻⁹ mol
[tex]Ar_{f}[/tex]: 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:
[tex] 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} [/tex]
[tex] t = 2.23 \cdot 10^{9} y [/tex]
Therefore, the age of the rock is 2.23x10⁹ years.
I hope it helps you!
