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Chapter 21: Problem 32

Write a nuclear equation for the indicated decay of each nuclide. $$ \begin{array}{l}{\text { a. } \mathrm{Po}-210 \text { (alpha) }} \\ {\text { b. } \mathrm{Ac}-227 \text { (beta) }} \\ {\text { c. } \mathrm{Tl}-207 \text { (beta) }} \\ {\text { d. } \mathrm{O}-207 \text { (beta) }} \\ {\text { e. } \mathrm{Pd}-103 \text { (electron capture) }}\end{array} $$

Short Answer

Expert verified
\(_{84}^{210}\text{Po} \rightarrow _{82}^{206}\text{Pb} + _{2}^{4}\text{He} \quad ; \quad _{89}^{227}\text{Ac} \rightarrow _{90}^{227}\text{Th} + _{-1}^{0}\text{e} \quad ; \quad _{81}^{207}\text{Tl} \rightarrow _{82}^{207}\text{Pb} + _{-1}^{0}\text{e} \quad ; \quad \text{Cannot solve for O-207 (no such isotope)} \quad ; \quad _{46}^{103}\text{Pd} + _{-1}^{0}\text{e} \rightarrow _{45}^{103}\text{Rh.}

Step by step solution

01

Identify the Type of Decay for Po-210

Understand that Po-210 undergoes alpha decay. In alpha decay, the parent nucleus emits an alpha particle, which consists of 2 protons and 2 neutrons.
02

Write the Nuclear Equation for Po-210 Decay

Write the equation by subtracting 2 from the atomic number (Z) and 4 from the mass number (A) of the parent nucleus. The alpha particle is represented as _{2}^4He.
03

Identify the Type of Decay for Ac-227

Recognize that Ac-227 undergoes beta decay. In beta decay, a neutron in the nucleus is converted into a proton, and a beta particle (electron) is emitted.
04

Write the Nuclear Equation for Ac-227 Decay

For beta decay, add 1 to the atomic number (Z) while the mass number (A) remains the same. The beta particle is represented as _{-1}^0e.
05

Identify the Type of Decay for Tl-207

Tl-207 also undergoes beta decay. Follow the understanding from the previous beta decay example.
06

Write the Nuclear Equation for Tl-207 Decay

Use the same method as Ac-227 because they both experience beta decay.
07

Identify the Type of Decay for O-15

There seems to be a typo in the provided nuclide, Oxygen (O) does not have a mass number of 207. Since this cannot be accurately addressed without the correct nuclide, the response for O-207 decay cannot be provided. This step should be skipped.
08

Identify the Type of Decay for Pd-103

Acknowledge that Pd-103 undergoes electron capture. In electron capture, an electron is captured by the nucleus, which results in converting a proton into a neutron.
09

Write the Nuclear Equation for Pd-103 Decay

Since electron capture reduces the atomic number (Z) by 1 while the mass number (A) remains the same, represent the captured electron as _{-1}^0e on the reactant side.

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Key Concepts

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

Alpha Decay
One of the primary processes in nuclear physics is alpha decay, an event where an unstable atom releases an alpha particle to become more stable. An alpha particle consists of two protons and two neutrons, which is essentially a helium-4 nucleus.
Alpha decay results in a decrease in both the mass number (A) and the atomic number (Z) of the original nuclide. If we take polonium-210 (Po-210) as an example, it will emit an alpha particle to transform into lead-206 (Pb-206) with the equation:
\[_{84}^{210}Po \rightarrow _{82}^{206}Pb + _{2}^{4}He\].
The mass number decreases by 4 units and the atomic number by 2, indicating the emission of an alpha particle.
Beta Decay
Another common type of radioactive decay is beta decay, where a neutron in the nucleus of an atom is converted into a proton, and as a result, a beta particle, which is an electron, is emitted. This process causes the atomic number (Z) to increase by 1 while the mass number (A) stays constant.
Take, for example, actinium-227 (Ac-227), which undergoes beta decay to become thorium-227 (Th-227), as represented in the nuclear equation:
\[_{89}^{227}Ac \rightarrow _{90}^{227}Th + _{-1}^{0}e\].
Similarly, thallium-207 (Tl-207) decays into lead-207 (Pb-207) through beta decay, and is represented as:
\[_{81}^{207}Tl \rightarrow _{82}^{207}Pb + _{-1}^{0}e\].
Electron Capture
Electron capture is a process where an inner orbital electron is captured by the nucleus of its own atom, leading to a transformation wherein a proton becomes a neutron. This process decreases the atomic number (Z) by 1, without changing the mass number (A).
For instance, palladium-103 (Pd-103) experiences electron capture and transmutes into rhodium-103 (Rh-103):
\[_{46}^{103}Pd + _{-1}^0e \rightarrow _{45}^{103}Rh\].
In this equation, the captured electron appears on the left side to reflect its role in the nuclear change.
Nuclear Reactions
Nuclear reactions involve changes in an atom's nucleus and result in different isotopes or elements. These changes can occur naturally, as in the case of radioactive decay, or can be induced in a laboratory or nuclear reactor. Nuclear reactions are governed by conservation laws, including conservation of mass-energy, momentum, and charge.
Reactions such as alpha decay, beta decay, and electron capture are all examples of nuclear reactions that change the composition of a nucleus. The balanced nuclear equations represent these changes and help scientists understand the behavior of nuclear material.
Radioactive Isotopes
Radioactive isotopes, or radioisotopes, are variants of chemical elements that have unstable nuclei and exhibit radioactivity. The instability arises from an imbalance in neutrons and protons, which results in the atom seeking a more stable configuration through radioactive decay processes such as alpha decay, beta decay, and electron capture.
Radioisotopes have a wide range of applications, including medical imaging, cancer treatment, dating archaeological findings, and as tracers in biochemical research. The study of these isotopes provides valuable insights into nuclear reactions and the nature of atomic structure.

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