A meteor has a Pb-206:U-238 mass ratio of 0.855:1.00. What is the age of the meteor? (Assume that the meteor did not contain any Pb-206 at the time of its formation.)

Name: Chemistry: A Molecular Approach
Author: Tro
ISBN: 9780134112831

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Understand that the problem involves radiometric dating using the decay of Uranium-238 (U-238) to Lead-206 (Pb-206).

Use the decay equation: \( N_t = N_0 e^{-\lambda t} \), where \( N_t \) is the number of parent atoms remaining, \( N_0 \) is the initial number of parent atoms, \( \lambda \) is the decay constant, and \( t \) is the time elapsed.

Recognize that the ratio given (Pb-206:U-238 = 0.855:1.00) implies that for every 1.00 part of U-238, there are 0.855 parts of Pb-206 formed.

Use the relationship \( \frac{N_0 - N_t}{N_t} = \frac{Pb-206}{U-238} \) to express the ratio in terms of the decay equation, where \( N_0 - N_t \) is the amount of U-238 that has decayed to Pb-206.

Calculate the decay constant \( \lambda \) using the half-life of U-238, which is approximately 4.468 billion years, and solve for \( t \) using the rearranged decay equation.

주요 개념

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Radioactive Decay

Radioactive decay is the process by which unstable atomic nuclei lose energy by emitting radiation. This decay occurs at a predictable rate, characterized by the half-life, which is the time required for half of the radioactive substance to decay. Understanding this concept is crucial for determining the age of geological samples through radiometric dating.

Uranium-Lead Dating

Uranium-lead dating is a radiometric dating method that uses the decay of uranium isotopes (U-238 and U-235) into stable lead isotopes (Pb-206 and Pb-207) to determine the age of a sample. The ratio of lead to uranium in a sample can indicate how long the decay process has been occurring, allowing scientists to estimate the age of the meteor in this case.

Mass Ratio and Isotope Ratios

The mass ratio of isotopes in a sample provides insight into the relative amounts of each isotope present. In this question, the Pb-206:U-238 mass ratio of 0.855:1.00 indicates the proportion of lead to uranium, which is essential for calculating the age of the meteor. This ratio helps in applying the decay equations to find the time elapsed since the formation of the meteor.