Assume that when Earth formed, uranium-238 and uranium-235...

Assume that when Earth formed, uranium-238 and uranium-235 were equally abundant. Their current percent natural abundances are $99.28 \%$ uranium- 238 and $0.72 \%$ uranium- $235 .$ Given half-lives of $4.5 \times 10^{9}$ years for uranium-238 and $7.1 \times 10^{8}$ years for uranium-235, determine the age of Earth corresponding to this assumption.

Key Concepts

Radioactive Decay

Radioactive decay refers to the process by which unstable atomic nuclei lose energy by emitting radiation, resulting in the transformation of elements over time. This process is stochastic in nature and follows a predictable exponential law, enabling scientists to model and predict the reduction of radioactive isotopes in various materials.

Half-Life

Half-life is the time it takes for half of the initial quantity of a radioactive isotope to decay. This concept is fundamental in understanding the rate at which radioactive decay occurs, and it directly influences calculations used in determining the age of rocks, fossils, or other samples through radiometric dating.

Decay Constant

The decay constant quantifies the probability per unit time that a given nucleus will decay, and it is mathematically related to the half-life by the equation ? = ln(2)/half-life. This constant is essential for solving decay equations and modeling the exponential decrease of the parent radioactive isotope.

Radiometric Dating

Radiometric dating is a method used to estimate the age of objects by measuring the abundance of radioactive isotopes and their decay products. By comparing the observed isotope ratios with the known decay rates, scientists can back-calculate the time elapsed since the formation of the sample, making it a vital tool in geology and archeology.

Exponential Decay Law

The exponential decay law describes how the quantity of a radioactive substance decreases over time. It is expressed by an equation that relates the remaining amount of the substance to its initial quantity, the decay constant, and time, forming the basis for calculations in radiometric dating and assessments of natural processes.

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