Answer:
4.66 x 10^8 yr
Explanation:
The age of the rock can be calculated using the equation:
ln (N/N₀) = - kt where N is the quantiy of radioisotope decayed and N₀ is the initially quantity present of the radioisotope; k is the decay constant, and t is the time.
Now from the data , we have 78 argon-40 atoms for every 22 potassium-40 atoms, we can deduce that originally we had 22 + 78 = 100 atoms of potassium-40 so this is our N₀.
When we look at the equation, we see that k is unknown, but we can calculate it from the half-life which is given by the equation:
k = 0.693/ t half-life = 0.693/ 1.3 x 10⁹ yr = 5.33 x 10⁻¹⁰ yr⁻¹
Now we are in position to answer the question.
ln ( 78/100 ) = - (5.33 x 10⁻¹⁰ yr⁻¹ ) t
- 0.249 = - 5.33 x 10⁻¹⁰ yr⁻¹ t
0.249/ 5.33 x 10⁻¹⁰ yr⁻¹ = t
4.66 x 10^8 yr
