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Chapter 21: Problem 16

Compare and contrast positron-emission and electron-capture processes.

Short Answer

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Question: Compare and contrast positron emission and electron capture processes in nuclear reactions, mentioning their similarities and differences. Answer: Both positron emission and electron capture are nuclear processes that involve changes in the atomic nucleus and are governed by the weak nuclear force. In both processes, the atomic number of the atom decreases by 1, resulting in the formation of a new element, and a neutrino is produced and released. The differences include the particles involved, with positron emission converting a proton into a neutron by emitting a positron, while electron capture converts a proton into a neutron by capturing an electron. Additionally, positron emission occurs in elements with a high proton-to-neutron ratio and is exothermic, whereas electron capture occurs in elements with a low proton-to-neutron ratio and is endothermic.

Step by step solution

01

Brief Introduction to the Processes

Positron-emission and electron-capture are two nuclear processes that involve changes in the atomic nucleus. They are involved in nuclear reactions that result in changes to the structure of the nucleus, leading to the formation of different atoms. Both processes involve the weak nuclear force and are responsible for the transformation of a neutron into a proton, or vice versa, which changes the atomic number (number of protons) of the atom.
02

Positron Emission

In positron emission, a proton inside the atomic nucleus is converted into a neutron, releasing a positron (the antiparticle of an electron) and a neutrino. The emission of a positron decreases the atomic number of the atom by 1, forming a new element. Positron emission is usually observed for elements with a high proton-neutron ratio.
03

Electron Capture

In electron capture, a proton in the nucleus captures an electron from an inner electron shell, usually the K-shell, and is transformed into a neutron. A neutrino is produced and released in this process as well. This also decreases the atomic number of the atom by 1, resulting in the formation of a new element. Electron capture normally occurs in elements with a low proton-to-neutron ratio.
04

Similarities between Positron Emission and Electron Capture

1. Both processes involve the weak nuclear force, which is responsible for the transformation of subatomic particles inside the nucleus. 2. In both processes, the atomic number of the atom decreases by 1, which results in the formation of a new element. 3. Both processes involve the production and release of a neutrino, which is a nearly massless and neutral subatomic particle.
05

Differences between Positron Emission and Electron Capture

1. In positron emission, a proton is converted into a neutron by emitting a positron, while in electron capture, a proton captures an electron and is converted into a neutron. 2. Positron emission occurs in elements with a high proton-to-neutron ratio, while electron capture occurs in elements with a low proton-to-neutron ratio. 3. Positron emission is an exothermic reaction, releasing energy in the form of a positron, while electron capture is an endothermic process, absorbing energy in the form of the captured electron. By understanding these similarities and differences, students will gain a better understanding of the processes of positron emission and electron capture, as well as their respective roles in nuclear reactions.

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Key Concepts

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

Positron Emission
Positron emission is a fascinating nuclear process where a proton within an atomic nucleus is transformed into a neutron. This transformation releases a positron, which is essentially an electron's antiparticle, along with a neutrino. The key outcome of this process is the reduction of the atomic number by 1, yielding a new element.

A critical factor influencing positron emission is the proton-to-neutron ratio. When an atom has a relatively high number of protons compared to neutrons, this process is more likely to occur.

Here are some important characteristics of positron emission:
  • It is an exothermic process, which means it releases energy in the form of a positron.
  • It enables the nucleus to achieve a more stable state by reducing the proton count.
  • Positron emission is observed in radioisotopes used in numerous applications, including medical imaging techniques like PET scans.
Electron Capture
Electron capture is another intriguing nuclear process where a proton-rich nucleus can reduce its atomic number. Here, an electron from the innermost shell of an atom is captured by the nucleus. This results in the conversion of a proton into a neutron, accompanied by the emission of a neutrino.

Unlike positron emission, electron capture usually happens in atoms with a low proton-to-neutron ratio. The captured electron allows the nucleus to maintain a balance by reducing excess protons.

Some distinguished points about electron capture include:
  • It is an endothermic process, implying that energy is absorbed during the capturing of an electron.
  • Electron capture is vital in certain isotopes and is a key mechanism in the decay of heavy elements to lighter ones.
  • Due to the absence of positron emission, this process is silent and doesn't involve the emission of detectable particles apart from neutrinos.
Weak Nuclear Force
The weak nuclear force is one of the four fundamental forces in the universe and plays a crucial role in nuclear processes like positron emission and electron capture.

This force is essential for the transformation that occurs at the subatomic level, such as changing a proton to a neutron or vice versa. Despite its name, the weak nuclear force is incredibly powerful in its designated role, enabling various transformations that are vital for nuclear stability.

Key aspects of the weak nuclear force include:
  • It governs beta decay processes, including both positron emission and electron capture.
  • Contrary to the strong nuclear force, which binds protons and neutrons in a nucleus, the weak force facilitates changes in their identity.
  • Though not exerting force over macroscopic distances, it is indispensable on an atomic scale for the balance of nuclei.
Proton-to-Neutron Ratio
The proton-to-neutron ratio is an essential parameter in understanding nuclear stability and the likelihood of certain nuclear reactions, such as positron emission and electron capture. This ratio indicates the relative numbers of protons and neutrons within an atomic nucleus.

This balance is vital because:
  • A high proton-to-neutron ratio can make a nucleus unstable, favoring positron emission to convert protons to neutrons.
  • A low proton-to-neutron ratio prompts nuclear stability through processes like electron capture, where excess protons are converted to neutrons.
  • The ratio helps predict the type of decay or transformation that an isotope may undergo to achieve a more stable configuration.
Understanding this ratio assists in predicting behaviors and energy emissions of isotopes, which is important in fields like nuclear physics and radiometric dating.

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Most popular questions from this chapter

Potassium- 40 is a radioactive isotope of potassium, a very common element in terrestrial rocks, which decays to \(^{40}\) Ar with a half-life of \(1.28 \times 10^{9}\) years. By measuring the ratio of \(^{40} \mathrm{Ar}\) to \(^{40} \mathrm{K},\) geologists can to determine the age of ancient rocks. a. Balance the nuclear equations for the decay of \(^{40} \mathrm{K}\) by identifying the missing isotope or particle.$$\begin{array}{l}^{40} \mathrm{K} \rightarrow^{40} \mathrm{Ar}+? \\\^{40} \mathrm{K} \rightarrow +_{-1}^{0} \beta\end{array}$$.b. Why might \(^{40} \mathrm{K}\) decay by two different pathways? c. Only about \(11 \%\) of the \(^{40} \mathrm{K}\) decays to \(^{40} \mathrm{Ar}\). If the ratio of \(^{40} \mathrm{Ar}\) to \(^{40} \mathrm{K}\) in a rock is found to be \(0.435,\) how old is the rock? d. Why don't geologists measure the \(^{40} \mathrm{Ca}:^{40} \mathrm{K}\) ratio instead?

Calculate the neutron-to-proton ratios for each of the following and predict the decay pathways of the following radioactive isotopes: \((\mathrm{a})^{238} \mathrm{U} ;(\mathrm{b})^{186} \mathrm{Re} ;(\mathrm{c})^{86} \mathrm{Y}\).

Describe the dangers of exposure to radon-222.

What nuclide is produced in the core of a giant star by each of the following fusion reactions? Assume there is only one product in each reaction. a. \(28 \mathrm{Si}+^{4} \mathrm{He} \rightarrow\) b. \(^{40} \mathrm{Ca}+^{4} \mathrm{He} \rightarrow\) c. \(^{24} \mathrm{Mg}+^{4} \mathrm{Hc} \rightarrow\)

Dating Cave Paintings Cave paintings in Gua Saleh Cave in Borneo have been dated by measuring the amount of \(^{14} \mathrm{C}\) in calcium carbonate deposits that formed over the pigments used in the paint. The source of the carbonate ion was atmospheric \(\mathrm{CO}_{2}\).a. What is the ratio of the \(^{14} \mathrm{C}\) radioactivity in calcium carbonate that formed 9900 years ago to that in calcium carbonate formed today? b. The archaeologists also used a second method, uranium-thorium dating, to confirm the age of the paintings by measuring trace quantities of these elements present as contaminants in the calcium carbonate. Shown below are two candidates for the U-Th dating method. Which isotope of uranium do you suppose was chosen? Explain your answer. $$\begin{aligned} &t_{1 / 2}=^{233} \mathrm{U} \quad 7.04 \times 10^{8} \mathrm{yr} \quad^{231} \mathrm{Th} \quad \rightarrow \quad^{231} \mathrm{p}_{2} \quad 3 \quad \rightarrow \quad\\\ &t_{1 / 2}=^{234} \mathrm{U} \quad \begin{array}{rl}\rightarrow & ^{230} \mathrm{Th} \\ 2.44 \times 10^{5} \mathrm{yr} & 7.7 \times 10^{4} \mathrm{hr}\end{array} \quad \begin{array}{rl} 226 \mathrm{p}_{2} & \rightarrow \\\1600 & \mathrm{yr}\end{array}\end{aligned}$$
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