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Complete the following decay processes by stating what the symbol \(X\) represents \(\left(X=\alpha, \beta^{-}, \beta^{+},\right.\) or \(\left.\gamma\right)\): (a) \({ }_{82}^{211} \mathrm{Pb} \rightarrow{ }_{83}^{211} \mathrm{Bi}+\mathrm{X}\) (b) \({ }_{6}^{11} \mathrm{C} \rightarrow{ }_{5}^{11} \mathrm{B}+\mathrm{X}\) (c) \(_{90 }^{231} \mathrm{Th}^{*} \rightarrow{ }_{90}^{231} \mathrm{Th}+\mathrm{X}\) (d) \(^{210}_{84}\mathrm{Po} \rightarrow{ }_{82}^{206} \mathrm{Pb}+\mathrm{X}\)

Short Answer

Expert verified
(a) \( \beta^{+} \); (b) \( \beta^{-} \); (c) \( \gamma \); (d) \( \alpha \).

Step by step solution

01

Analyze Decay Process (a)

The process is given by \( {}_{82}^{211} \mathrm{Pb} \rightarrow {}_{83}^{211} \mathrm{Bi} + \mathrm{X} \). The atomic number increases by 1, while the mass number stays the same. This type of process corresponds to \( \beta^{+} \) decay (positron emission), where a neutron is converted into a proton.
02

Analyze Decay Process (b)

The process is given by \( {}_{6}^{11} \mathrm{C} \rightarrow {}_{5}^{11} \mathrm{B} + \mathrm{X} \). The atomic number decreases by 1, with the mass number remaining constant. This indicates \( \beta^{-} \) decay (beta decay), where a proton turns into a neutron.
03

Analyze Decay Process (c)

The process is given by \( {}_{90}^{231} \mathrm{Th}^{*} \rightarrow {}_{90}^{231} \mathrm{Th} + \mathrm{X} \). The '*' denotes an excited state, and the decay does not change either the atomic number or the mass number, which suggests emission of a \( \gamma \) ray (gamma decay).
04

Analyze Decay Process (d)

The process is given by \( {}_{84}^{210} \mathrm{Po} \rightarrow {}_{82}^{206} \mathrm{Pb} + \mathrm{X} \). The atomic number decreases by 2 and the mass number decreases by 4, which signifies \( \alpha \) decay, where an \( \alpha \) particle (helium nucleus, \( {}_{2}^{4}\mathrm{He} \)) is emitted.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Beta Decay
Beta decay is a type of radioactive decay in which a nucleus emits a beta particle. This can occur in two forms: beta-minus (\( \beta^- \)) decay and beta-plus (\( \beta^+ \)) decay.

- **Beta-minus decay (\( \beta^- \) decay):** In this process, a neutron is converted into a proton within the nucleus. - As a result, an electron, designated as \( \beta^- \), and an antineutrino are emitted. - The atomic number of the element increases by one, while the mass number remains unchanged. - A classic example is the decay of carbon-11 to boron-11, as seen in the original exercise. - **Beta-plus decay (\( \beta^+ \) decay):** This type of decay involves the conversion of a proton into a neutron. - It's accompanied by the emission of a positron, - which is the electron's antimatter counterpart, and a neutrino. - In this process, the atomic number decreases by one, and the mass number stays constant. - The conversion of lead-211 into bismuth-211 is an example of \( \beta^+ \) decay.
Gamma Decay
Gamma decay occurs when an excited nucleus releases energy in the form of gamma rays, which are high-energy photons. Unlike other forms of decay, gamma decay does not result in a change of mass number or atomic number.

  • When a nucleus is in an excited state, it has excess energy.
  • To return to its ground state, it may release this excess energy as gamma radiation.
  • This process can often follow other types of decay like alpha or beta decay.
  • Gamma rays have no mass or charge, but they are very penetrating.
Gamma decay is observed in the decay of excited thorium-231 atoms into their stable form, with the emission of a gamma photon.
Alpha Decay
Alpha decay is a radioactive process where an unstable nucleus emits an alpha particle. An alpha particle consists of two protons and two neutrons, equivalent to a helium nucleus (\( ^4_2\mathrm{He} \)).

  • Alpha decay reduces the atomic number by 2 and the mass number by 4.
  • This loss effectively transforms the original element into another with lower atomic mass.
  • It typically occurs in heavy elements such as uranium or polonium.
In the exercise above, the conversion of polonium-210 to lead-206 is an instance of alpha decay.This type of decay is significant because it leads to a substantial change in the mass of the nucleus.
Nuclear Reactions
Nuclear reactions involve changes in an atom's nucleus and differ from chemical reactions. They can include a variety of processes, including fusion, fission, and decay.

  • In **fusion** reactions, smaller nuclei combine to form a larger nucleus, releasing energy in the process.
  • **Fission** reactions involve splitting a large nucleus into smaller fragments, also releasing energy.
  • Both of these types of reactions are central to nuclear energy production and atomic theory.
Radioactive decay processes such as beta, gamma, and alpha decay represent a subset of nuclear reactions where unstable nuclei transform into more stabilized forms. Understanding these reactions allows scientists to harness energy and appreciate the life cycles of stars, as well as various applications in medicine and industry.

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Most popular questions from this chapter

When uranium \({ }_{92}^{235}\) U decays, it emits (among other things) a \(\gamma\) ray that has a wavelength of \(1.14 \times 10^{-11} \mathrm{m} .\) Determine the energy (in \(\mathrm{MeV}\) ) of this \(\gamma\) ray.

The \(\beta^{-}\) decay of phosphorus \({ }_{15}^{32} \mathrm{P}\) (atomic mass \(=31.973907 \mathrm{u}\) ) pro-duces a daughter nucleus that is sulfur \(\frac{32}{16} \mathrm{S}\) (atomic mass \(=31.972070 \mathrm{u}\) ),\(\mathrm{a} \beta^{-}\) particle, and an antineutrino. The kinetic energy of the \(\beta^{-}\) particle is \(0.90 \mathrm{MeV}\). Find the maximum possible energy (in \(\mathrm{MeV}\) ) that the antineutrino could carry away.

In the form \({ }_{Z}^{A} \mathrm{X}\), identify the daughter nucleus that results when (a) plutonium \({ }_{94}^{244}\) Pu undergoes \(\alpha\) decay, (b) sodium \({ }_{11}^{24}\) Na undergoes \(\beta^{-}\) decay, and (c) nitrogen \({ }_{7}^{13} \mathrm{N}\) undergoes \(\beta^{+}\) decay.

Determine the symbol \({ }_{Z}^{A} \mathrm{X}\) for the parent nucleus whose \(\alpha\) decay produces the same daughter as the \(\beta^{-}\) decay of thallium \({ }_{81}^{208} \mathrm{Tl}\).

Thorium \({ }_{90}^{228}\) Th produces a daughter nucleus that is radioactive. The daughter, in turn, produces its own radioactive daughter, and so on. This process continues until bismuth \({ }_{83}^{21} \mathrm{Bi}\) is reached. Concepts: (i) How many of the 90 protons in the thorium nucleus are carried off by the \(\alpha\) particles? (ii) How many protons are left behind when the \(\beta^{-}\) particles are emitted? (iii) How many of the 228 nucleons in the thorium nucleus are carried off by the \(\alpha\) particles? (iv) Does the departure of a \(\beta^{-}\) particle alter the number of nucleons? Calculations: What are the total number \(N_{\alpha}\) of \(\alpha\) particles and the total number \(N_{\beta}\) of \(\beta^{-}\) particles that are generated in this series of radioactive decays?

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