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Chapter 21: Problem 15

How can the belt of stability be used to predict the probable decay mode of an unstable nuclide?

Short Answer

Expert verified
Answer: The Belt of Stability is a graphical representation of stable nuclides on a plot of neutron number (N) versus proton number (Z). It represents the region where stable nuclides exist, and when a nuclide falls outside of this belt, it becomes unstable and undergoes radioactive decay to reach a stable state. By determining where the unstable nuclide falls with respect to the Belt of Stability, we can predict its most probable decay mode, such as beta-minus decay if it has too many neutrons, beta-plus decay or electron capture if it has too few neutrons, or alpha decay if it has too many nucleons in total.

Step by step solution

01

Understand the Belt of Stability

The Belt of Stability is a graphical representation of stable nuclides on a plot of neutron number (N) versus proton number (Z). It represents the region where the stable nuclides exist, and when a nuclide falls outside of this belt, it becomes unstable and undergoes radioactive decay to eventually reach a state within the belt. Stable nuclides follow a linear trend, where the ratio of neutrons to protons is approximately 1 for low atomic numbers and increases for heavier nuclei. The reason behind this trend is the balance between the attractive strong nuclear force and the repulsive electrostatic force that exists within an atomic nucleus.
02

Learn about Decay Modes

Unstable nuclides can undergo various types of radioactive decay modes to reach a more stable state within the Belt of Stability. These decay modes are: 1. Alpha Decay: In this decay mode, a nucleus emits an alpha particle, which consists of two protons and two neutrons. 2. Beta Decay: There are two types of beta decay: Beta-minus (尾-) and Beta-plus (尾+). In beta-minus decay, a neutron within the nucleus is transformed into a proton, and an electron (尾- particle) is emitted. In beta-plus decay, a proton within the nucleus is transformed into a neutron, and a positron (尾+ particle) is emitted. 3. Electron Capture: This process involves a proton capturing an electron from the innermost shell of the atom and converting into a neutron.
03

Predict the Decay Mode

To predict the probable decay mode of an unstable nuclide, you need to determine where it falls with respect to the Belt of Stability. There are three possible scenarios: 1. If the nuclide has too many neutrons for stable nuclei with the same atomic number, it tends to undergo 尾- decay to reach the Belt of Stability. 2. If the nuclide has too few neutrons for stable nuclei with the same atomic number, it tends to undergo 尾+ decay or electron capture to reach the Belt of Stability. 3. If the nuclide has too many nucleons in total, it tends to undergo alpha decay to reach the Belt of Stability. Knowing where the nuclide stands concerning the Belt of Stability helps in predicting its most probable decay mode, and thus its pathway towards becoming a stable nuclide.

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Most popular questions from this chapter

Explain how the product of \(\beta\) decay has a higher atomic number than the radio nuclide from which the product forms

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?

What nuclide is produced in the core of a collapsing giant star by each of the following reactions? a. \({ }_{29}^{65} \mathrm{Cu}+3{ }_{0}^{1} \mathrm{n} \rightarrow ?+{ }_{-1}^{0} \boldsymbol{\beta}\) b. \({ }_{30}^{68} \mathrm{Zn}+2{ }_{0}^{1} \mathrm{n} \rightarrow ?+{ }_{-1}^{0} \beta\) c. \({ }_{38}^{88} \mathrm{Sr}+{ }_{0}^{1} \mathrm{n} \rightarrow ?+{ }_{-1}^{0} \beta\)

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. $$\begin{aligned} &t_{1 / 2}=^{233} \mathrm{U} \quad 7.04 \times 10^{8} \mathrm{yr} \quad^{231} \mathrm{Th} \quad \rightarrow \quad^{231} \mathrm{p}_{2} \quad 3 \quad \rightarrow \quad\\\ &t_{1 / 2}=^{234} \mathrm{U} \quad \begin{array}{rl}\rightarrow & ^{230} \mathrm{Th} \\ 2.44 \times 10^{5} \mathrm{yr} & 7.7 \times 10^{4} \mathrm{hr}\end{array} \quad \begin{array}{rl} 226 \mathrm{p}_{2} & \rightarrow \\\1600 & \mathrm{yr}\end{array}\end{aligned}$$

Strontium-90 in Milk In the years immediately following the explosion at the Chernobyl nuclear power plant, the concentration of \({ }^{90} \mathrm{Sr}\) in cow's milk in southern Europe was slightly elevated. Some samples contained as much as \(1.25 \mathrm{~Bq} / \mathrm{L}\) of \({ }^{90} \mathrm{Sr}\) radioactivity. The half-life of strontium-90 is 28.8 years. a. Write a balanced nuclear equation describing the decay of \({ }^{90} \mathrm{Sr}\). b. How many atoms of \({ }^{90} \mathrm{Sr}\) are in a \(200 \mathrm{~mL}\) glass of milk with \(1.25 \mathrm{~Bq} / \mathrm{L}\) of \({ }^{90} \mathrm{Sr}\) radioactivity? c. Why would strontium-90 be more concentrated in milk than other foods, such as grains, fruits, or vegetables?
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