Answer:
Therefore, the age of the rock sample is 2.7 * 10⁹ years
<em>Note: The question is missing some parts. The complete question is:</em>
<em>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 0.771 mmol of argon-40 for every 1.000 mmol of potassium-40 in a certain sample of rock. Calculate the age of the rock. Round your answer to significant digits.</em>
Explanation:
Half-life is defined as the amount of time it takes a given quantity to decrease to half of its initial value.
In radioactive isotopes of elements, the half-life is used to calculate the age of the materials in which the radioisotopes are found.
The half-life is related to the age of a material through the following formula:
t = t½㏑(Nt/N₀) / -㏑2
where t is the age of the material;
t½ is the half-life of the material
Nt is the amount of material left after time t
No is the starting amount of material
From the question:
t½ = 1.26 * 10⁹ years
Nt = 1.000 - 0.771 = 0.229
N₀ = 1.000
-㏑2 = -0.693
t = {1.26 * 10⁹ * ㏑(0.229)} / -0.693
t = 2.68 * 10⁹ which is approximately 2.7 * 10⁹ years to two significant digits.
Therefore, the age of the rock sample is 2.7 * 10⁹ years
