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.

2.42x10⁹ years is the age of the rock

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

answer : one can design an experiment using a liquid and an additive that can be added to the liquid and observe the chemical changes in the reaction species.

one would need a beaker which is filled with a known amount of the liquid in which thermometer is placed to measure the temperature changes; after addition of the additive to the liquid solution one can note down the temperature change and find whether the reaction is endothermic or exothermic in nature. by subtracting the initial temperature value with the final temperature one can find the temperature changes.

various combinations of liquid and additive can be used. liquid in this case can be a known quantity of water and additives can be epsom salt or without epsom salt the experiment can be conducted to notice the changes. water and ice, hydrogen peroxide and dry yeast, vinegar and baking soda,etc.