The radioisotope potassium-40 decays to argon-40 by positron emission with a half-life of 1.3 ã 109 yr. a sample of moon rock was found to contain 78 argon-40 atoms for every 22 potassium-40 atoms. the age of the rock is:

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

every chemical equation adheres to the law of conservation of mass, which states that matter cannot be created or destroyed. therefore, there must be the same number of atoms of each element on each side of a chemical equation.