The decay of Rb-87(t1 / 2=4.8 ×10^10 y) to Sr-87 has been used to determine the age of ancient r

step 1 field of chemistry that deals with radioactivity, nuclear processes and the transformations of t

The decay of Rb-87(t1 / 2=4.8 ×10^10 y) to Sr-87 has been...

The decay of $\mathrm{Rb}-87\left(t_{1 / 2}=4.8 \times 10^{10} \mathrm{y}\right)$ to $\mathrm{Sr}-87$ has been used to determine the age of ancient rocks and minerals. a) Write the balanced nuclear equation for this decay. If a sample of rock is found to be $0.100 \%$ by mass $\mathrm{Rb}-87$ and $0.00250 \%$ by mass $\mathrm{Sr}-87,$ what is the age of the rock? Assume that there was no $\mathrm{Sr}-87$ present when the rock formed.

The decay of $\mathrm{Rb}-87\left(t_{1 / 2}=4.8 \times 10^{10} \mathrm{y}\right)$ to $\mathrm{Sr}-87$
has been used to determine the age of ancient rocks and minerals.
a) Write the balanced nuclear equation for this decay. If a sample of rock is found to be $0.100 \%$ by mass $\mathrm{Rb}-87$ and $0.00250 \%$ by mass $\mathrm{Sr}-87,$ what is the age of the rock? Assume that there was no $\mathrm{Sr}-87$ present when the rock formed.

Key Concepts

Radioactive Decay

Radioactive decay is a spontaneous process by which an unstable atomic nucleus loses energy by emitting radiation in the form of particles or electromagnetic waves. This concept is essential for understanding how a parent isotope transforms into a daughter isotope, and it underpins many methods in nuclear chemistry and geochronology used for dating materials.

Nuclear Reaction Equation

A nuclear reaction equation represents the transformation of one or more nuclei into another, showing the changes in atomic and mass numbers. In decay processes, it accounts for the conversion of a parent isotope into a daughter isotope while indicating the emission of particles such as beta particles, which is fundamental to identifying the type of decay involved.

Half-life

The half-life of a radioactive isotope is the time required for half of a given amount of the isotope to decay. It is a crucial parameter in determining how rapidly a radioactive substance diminishes over time, and is directly used in calculations to convert measured isotope abundance ratios into an age estimate.

Decay Constant and Exponential Decay Equation

The decay constant, related to the half-life, is used in the exponential decay law which governs the rate of radioactive decay. The equation N = N?e^(??t) describes how the quantity of a radioactive substance decreases over time. This concept is critical for solving problems where the elapsed time since a rock or mineral formed is determined from the remaining parent isotope or produced daughter isotope.

Isotope Ratio Dating

Isotope ratio dating is a method used in geochronology that involves measuring the relative abundances of parent and daughter isotopes in a sample. By assuming an initial condition (such as the absence of the daughter isotope) and applying the principles of radioactive decay, the time elapsed since the formation of the rock or mineral can be calculated. This approach is widely used for dating ancient geological samples.

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