Problem 22 - Chemistry The Central Science In Si Units

Question

One nuclide in each of these pairs is radioactive. Predict which is radioactive and which is stable: \((\mathbf{a}){ }_{20}^{40} \mathrm{Ca}\) and \({ }_{20}^{45} \mathrm{Ca},\) (b) \(^{12} \mathrm{C}\) and \({ }^{14} \mathrm{C}\) (c) lead-206 and thorium-230. Explain your choice in each case.

Step-by-Step Solution

Answer

In each pair, the radioactive nuclides are (a) \( _{20}^{45} \mathrm{Ca}\), (b) \(^{14} \mathrm{C}\), (c) Thorium-230.

Step 1: Understanding Radioactive vs. Stable Nuclides

Nuclides are characterized by their number of protons and neutrons. Radioactive nuclides typically have an imbalanced ratio of protons to neutrons or an atomic number higher than lead. Stable nuclides have a balanced proton-neutron ratio or are among specific known stable isotopes.

Step 2: Analyzing Calcium Isotopes

Calcium isotopes: - \( _{20}^{40}\text{Ca} \) and \( _{20}^{45}\text{Ca} \).- \( _{20}^{40}\text{Ca} \) has a balanced ratio, it is stable.- \( _{20}^{45}\text{Ca} \) has 5 additional neutrons, causing imbalance, making it radioactive.

Step 3: Comparing Carbon Isotopes

Carbon isotopes: - \( ^{12}\text{C} \) is a common stable isotope with equal protons and neutrons.- \( ^{14}\text{C} \) has 2 extra neutrons compared to the stable \( ^{12}\text{C} \), making it radioactive, known for use in radiocarbon dating.

Step 4: Examining Lead and Thorium

Lead and thorium: - Lead-206 is a stable isotope, a common end-product of radioactive decay chains. - Thorium-230 has a long decay chain, part of the uranium-238 decay series and is radioactive because thorium naturally undergoes radioactive decay.

Key Concepts

Nuclides

A nuclide is any distinct atom or nucleus characterized by a specific number of protons and neutrons. The nucleus is the core of an atom, where protons and neutrons are packed together. Nuclides can vary in terms of these numbers, giving them different properties. Each nuclide has a specific atomic number, which is the count of protons in its nucleus, and a mass number, the sum of protons and neutrons. Studying these differences in nuclides helps us understand why some are stable while others are radioactive.

• Proton count determines the element's chemical identity.
• Neutron count affects the stability of the nuclide.

Often, small variations in neutron numbers result in isotopes of an element, leading some nuclides to natural radioactivity. A radioactive nuclide will eventually decay, releasing particles and energy, until it reaches a more stable form. This transformation underlies many natural phenomena, such as radiocarbon dating and decay chains in heavier elements.

Isotopes

Isotopes are variations of the same element that have the same number of protons but differ in numbers of neutrons. This means they share the same atomic number but have different mass numbers. Every element can have multiple isotopes, and these isotopes can be either stable or radioactive.

• Stable isotopes have a balanced proton-neutron ratio.
• Radioactive isotopes have an imbalance in this ratio, leading them to decay over time.

For example, carbon has several isotopes, including the stable

Understanding Carbon Isotopes

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Proton-neutron ratio

The proton-neutron ratio is a crucial factor in determining the stability of a nuclide.

Importance of the Ratio

A balanced ratio tends to make a nuclide stable, as it ensures a good interaction between the forces within the nucleus. Instability often arises when this balance is lost, leading to various forms of decay to achieve a more stable state.

• Balanced proton-neutron ratios are often found in lighter elements, typically around 1:1.
• Heavier elements tend to have more neutrons than protons to maintain stability, often exceeding a ratio of 1:1.

Case Studies: Calcium and Carbon

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