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Key concepts and summary

Nuclei that have unstable n:p ratios undergo spontaneous radioactive decay. The most common types of radioactivity are α decay, β decay, γ emission, positron emission, and electron capture. Nuclear reactions also often involve γ rays, and some nuclei decay by electron capture. Each of these modes of decay leads to the formation of a new nucleus with a more stable n:p ratio. Some substances undergo radioactive decay series, proceeding through multiple decays before ending in a stable isotope. All nuclear decay processes follow first-order kinetics, and each radioisotope has its own characteristic half-life, the time that is required for half of its atoms to decay. Because of the large differences in stability among nuclides, there is a very wide range of half-lives of radioactive substances. Many of these substances have found useful applications in medical diagnosis and treatment, determining the age of archaeological and geological objects, and more.

Key equations

  • decay rate = λN
  • t 1 / 2 = ln 2 λ = 0.693 λ

Chemistry end of chapter exercises

What are the types of radiation emitted by the nuclei of radioactive elements?

α (helium nuclei), β (electrons), β + (positrons), and η (neutrons) may be emitted from a radioactive element, all of which are particles; γ rays also may be emitted.

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What changes occur to the atomic number and mass of a nucleus during each of the following decay scenarios?

(a) an α particle is emitted

(b) a β particle is emitted

(c) γ radiation is emitted

(d) a positron is emitted

(e) an electron is captured

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What is the change in the nucleus that results from the following decay scenarios?

(a) emission of a β particle

(b) emission of a β + particle

(c) capture of an electron

(a) conversion of a neutron to a proton: 0 1 n 1 1 p + +1 0 e ; (b) conversion of a proton to a neutron; the positron has the same mass as an electron and the same magnitude of positive charge as the electron has negative charge; when the n:p ratio of a nucleus is too low, a proton is converted into a neutron with the emission of a positron: 1 1 p 0 1 n + +1 0 e ; (c) In a proton-rich nucleus, an inner atomic electron can be absorbed. In simplest form, this changes a proton into a neutron: 1 1 p + -1 0 e 0 1 p

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Many nuclides with atomic numbers greater than 83 decay by processes such as electron emission. Explain the observation that the emissions from these unstable nuclides also normally include α particles.

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Why is electron capture accompanied by the emission of an X-ray?

The electron pulled into the nucleus was most likely found in the 1 s orbital. As an electron falls from a higher energy level to replace it, the difference in the energy of the replacement electron in its two energy levels is given off as an X-ray.

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Explain, in terms of [link] , how unstable heavy nuclides (atomic number>83) may decompose to form nuclides of greater stability (a) if they are below the band of stability and (b) if they are above the band of stability.

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Which of the following nuclei is most likely to decay by positron emission? Explain your choice.

(a) chromium-53

(b) manganese-51

(c) iron-59

Manganese-51 is most likely to decay by positron emission. The n:p ratio for Cr-53 is 29 24 = 1.21; for Mn-51, it is 26 25 = 1.04; for Fe-59, it is 33 26 = 1.27. Positron decay occurs when the n:p ratio is low. Mn-51 has the lowest n:p ratio and therefore is most likely to decay by positron emission. Besides, 24 53 Cr is a stable isotope, and 26 59 Fe decays by beta emission.

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Source:  OpenStax, Chemistry. OpenStax CNX. May 20, 2015 Download for free at http://legacy.cnx.org/content/col11760/1.9
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