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Chapter 21: Problem 22

Outline the principle for dating materials using radioactive isotopes.

Short Answer

Expert verified
Radioactive dating is a method used to calculate the age of materials. It is based on the principle of radioactive decay. Scientists measure the ratio of parent isotope to daughter isotope within a sample, knowing the half-life of the parent. These measurements allow them to calculate the elapsed time since the death of an organism or formation of a rock.

Step by step solution

01

Understanding Radioactive Dating

Radioactive dating refers to the process of determining the age of an object based on the amount of a certain radioactive isotope it contains. It is premised on the principle of radioactive decay, where isotopes decay at a constant rate known as half-life, which is the time taken for half of the radioactive atoms to decay into a more stable form.
02

Unstable Isotopes and Half-life

Radioactive isotopes or radionuclides are unstable due to the excess nuclear energy. This energy must be released, and it does so through radioactive decay. During this process, the radioactive isotope loses particles and turns into a more stable element. The half-life is the time taken for half of the radioactive isotope in a given sample to decay.
03

Procedure for Radioactive Dating

In radioactive dating, scientists determine the amount of the parent and daughter isotopes in a sample. By knowing the half-life of the parent isotope and the proportions of parent and daughter isotopes, scientists can calculate the time that has elapsed since the living organism died or the rock was formed. This is done by using the ratio of parent to daughter isotopes and the known half-life of the parent radioactive isotope.
04

Examples in Practice

There are several examples of radioactive dating. One of the most commonly known is Carbon-14 dating (used in dating organic materials). Another method is Uranium-Lead Dating (used for dating rocks).

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Most popular questions from this chapter

Sources of energy on Earth include fossil fuels, geothermal, gravitational, hydroelectric, nuclear fission, nuclear fusion, solar, and wind. Which of these have a "nuclear origin," either directly or indirectly?

Write balanced nuclear equations for these reactions and identify \(\mathrm{X}:\) (a) \(\mathrm{X}(\mathrm{p}, \alpha){ }_{6}^{12} \mathrm{C},\) (b) \({ }_{13}^{27} \mathrm{Al}(\mathrm{d}, \alpha) \mathrm{X}\) (c) \({ }_{25}^{55} \mathrm{Mn}(\mathrm{n}, \gamma) \mathrm{X}\)

For each pair of elements listed, predict which one has more stable isotopes: (a) Co or \(\mathrm{Ni},\) (b) \(\mathrm{F}\) or \(\mathrm{Se}\) (c) Ag or Cd.

Nuclear waste disposal is one of the major concerns of the nuclear industry. In choosing a safe and stable environment to store nuclear wastes, consideration must be given to the heat released during nuclear decay. As an example, consider the \(\beta\) decay of \({ }^{90} \mathrm{Sr}\) \((89.907738 \mathrm{amu})\) $$ { }_{38}^{90} \mathrm{Sr} \longrightarrow{ }_{39}^{90} \mathrm{Y}+{ }_{-1}^{0} \beta \quad t_{\frac{1}{2}}=28.1 \mathrm{yr} $$ The \({ }^{90} \mathrm{Y}(89.907152 \mathrm{amu})\) further decays as follows: $$ { }_{39}^{90} \mathrm{Y} \longrightarrow{ }_{40}^{90} \mathrm{Zr}+{ }_{-1}^{0} \beta \quad t_{\frac{1}{2}}=64 \mathrm{~h} $$ Zirconium-90 (89.904703 amu) is a stable isotope. (a) Use the mass defect to calculate the energy released (in joules) in each of the preceding two decays. (The mass of the electron is \(5.4857 \times\) \(10^{-4}\) amu. ( b) Starting with 1 mole of \({ }^{90}\) Sr, calculate the number of moles of \(9^{9}\) Sr that will decay in a year. (c) Calculate the amount of heat released (in kilojoules) corresponding to the number of moles of \({ }^{90} \mathrm{Sr}\) decayed to \({ }^{90} \mathrm{Zr}\) in \((\mathrm{b})\)

Write balanced nuclear equations for these reactions and identify \(X:(a){ }_{34}^{80} S e(d, p) X,(b) X(d, 2 p)_{3}^{9} L i,\) (c) \({ }_{5}^{10} \mathrm{~B}(\mathrm{n}, \alpha) \mathrm{X}\).
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