Potassium- 40 decays to argon-40 with a half life of 1.27 ×10^9 yr. What is the age of a rock in

step 1 Hello students in the given problem problem 1 25 of chapter 11 we have asked that potassium 14 d

Potassium- 40 decays to argon-40 with a half life of 1.27...

Potassium- 40 decays to argon-40 with a half life of $1.27 \times 10^{9} \mathrm{yr}$. What is the age of a rock in which the mass ratio of ${ }^{10} \mathrm{Ar}$ to ${ }^{10} \mathrm{~K}$ is $3.6$ ? a. $2.8 \times 10^{10} \mathrm{yr}$ b. $1.4 \times 10^{9} \mathrm{yr}$ c. $1.4 \times 10^{10} \mathrm{yr}$ d. $2.8 \times 10^{9} \mathrm{yr}$

Potassium- 40 decays to argon-40 with a half life of $1.27 \times 10^{9} \mathrm{yr}$. What is the age of a rock in which the mass ratio of ${ }^{10} \mathrm{Ar}$ to ${ }^{10} \mathrm{~K}$ is $3.6$ ?
a. $2.8 \times 10^{10} \mathrm{yr}$
b. $1.4 \times 10^{9} \mathrm{yr}$
c. $1.4 \times 10^{10} \mathrm{yr}$
d. $2.8 \times 10^{9} \mathrm{yr}$

Key Concepts

Isotope Ratio Analysis

Isotope ratio analysis involves the measurement of the relative abundances of isotopes within a sample. In the context of radiometric dating, the parent-to-daughter isotope ratio provides the necessary information to apply decay equations and calculate the age of the sample.

Radiometric Dating

Radiometric dating is a method used to determine the age of rocks and other materials by measuring the ratios of parent isotopes to their daughter products. This technique utilizes the known half-life of the radioactive parent isotope to estimate the time elapsed since the material formed.

Decay Constant

The decay constant is a parameter that quantifies the probability per unit time that a given nucleus will decay. It is directly related to the half-life and appears in the exponential decay equations used to model radioactive decay.

Half-Life

The half-life of a radioactive isotope is the time required for half of the initial quantity of the decaying substance to transform into another element or isotope. It is a fundamental parameter in calculating the decay rate and is central to radiometric dating techniques.

Radioactive Decay

Radioactive decay is the spontaneous process by which an unstable atomic nucleus releases energy by emitting radiation. This process follows an exponential law where the number of undecayed nuclei decreases in a predictable manner over time.

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