The half life for the radioactive decay of potassium- to argon- is years. Suppose nuclear chemical analysis shows that there is of argon-

Therefore, the age of the rock sample is 2.7 * 10⁹ years

Note: The question is missing some parts. The complete question is:

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.

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

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