One method of dating rocks is based on their ^87 Sr /^87 Rb ratio. ^87 Rb is a β^- emitter with

step 1 Let here initially 1 milligram of rubulium present. So we have 1MG of 87 present. Let x milligra

One method of dating rocks is based on their ^87 Sr /^87 Rb...

One method of dating rocks is based on their $^{87} \mathrm{Sr} /^{87} \mathrm{Rb}$ ratio. $^{87} \mathrm{Rb}$ is a $\beta^{-}$ emitter with a half-life of $5 \times 10^{11}$ years. A certain rock has a mass ratio $^{87} \mathrm{Sr} /^{87} \mathrm{Rb}$ of $0.004 / 1.00 .$ What is the age of the rock?

One method of dating rocks is based on their $^{87} \mathrm{Sr} /^{87} \mathrm{Rb}$ ratio. $^{87} \mathrm{Rb}$ is a $\beta^{-}$ emitter with a half-life of
$5 \times 10^{11}$ years. A certain rock has a mass ratio $^{87} \mathrm{Sr} /^{87} \mathrm{Rb}$ of $0.004 / 1.00 .$ What is the age of the rock?

Key Concepts

Radiometric Dating

Radiometric dating is a method used to determine the age of rocks and other materials by examining the relative proportions of parent and daughter isotopes. This technique relies on the predictable nature of radioactive decay, where unstable isotopes transform into stable ones at a constant rate, providing a 'clock' that can be used to calculate the age of a sample.

Radioactive Decay

Radioactive decay is the process by which unstable atomic nuclei lose energy by emitting radiation in the form of particles or electromagnetic waves. This decay typically follows a first-order kinetic process, meaning that the rate of decay is proportional to the number of unstable nuclei present, resulting in an exponential decrease over time.

Half-Life

The half-life of a radioactive isotope is the time required for half of the original number of radioactive atoms to decay. It is a critical parameter in radiometric dating as it provides a fixed time scale that allows scientists to calculate the age of a sample based on the remaining proportion of the original isotope.

Decay Constant

The decay constant is a value that quantifies the likelihood of a single atom decaying per unit time. It is mathematically related to the half-life through the equation ? = ln(2)/half-life, and it is an essential component in the mathematical formulation of radioactive decay and age determination.

Parent-Daughter Isotope Ratio

The ratio of parent isotopes to daughter isotopes in a sample is a fundamental measurement in radiometric dating. By knowing the initial amount of the parent isotope and measuring the current amounts of the parent and daughter isotopes, one can use the decay equation to calculate the elapsed time since the rock or mineral formed.

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