Problem 47 - Advanced Problems in Physical Chemistry for Competitive Examinations

Question

Actinium series starts with \(\mathrm{A}\) and ends at Z. \(\mathrm{A}\) and \(\mathrm{Z}\) are (a) \({ }_{90} \mathrm{Th}^{232},{ }_{82} \mathrm{~Pb}^{206}\) (b) \({ }_{90} \mathrm{Th}^{235},{ }_{82} \mathrm{~Pb}^{207}\) (c) \({ }_{92} \mathrm{U}^{235},{ }_{82} \mathrm{~Pb}^{207}\) (d) \({ }_{90} \mathrm{Ac}^{227},{ }_{82} \mathrm{~B} \mathrm{i}^{209}\)

Step-by-Step Solution

Answer

(c) { }_{92} {U}^{235},{ }_{82} {Pb}^{207}

Step 1: Identify the Actinium Series

Recognize that the Actinium series is one of the naturally occurring decay series. It starts with the parent nuclide with atomic number 89 (Actinium) and ends with a stable nuclide, Lead (Pb) with atomic number 82.

Step 2: Find the Parent Nuclide of the Actinium Series

The Actinium series originates with Actinium, but the parent isotope in this series is actually Uranium-235 ({ }_{92} {U}^{235}).

Step 3: Compare the Given Options

Analyze all options given to find which match starts with Uranium-235 and ends with Lead.

Step 4: Choose the Correct Match

The Actinium series traditionally ends with Lead-207 ({ }_{82} {Pb}^{207}). Thus, the starting and ending nuclides are { }_{92} {U}^{235} and { }_{82} {Pb}^{207}, respectively.

Key Concepts

Decay Series

Radioactive elements can transform into other elements through a chain of decays known as a decay series. This sequential process involves a parent nuclide undergoing radioactive decay to produce a daughter nuclide, which may itself be unstable and decay further. This chain continues until a stable, non-radioactive element emerges. There are four natural decay series, and the Actinium series is one of them. It begins with an unstable, radioactive element and, over time, decays down to lead, a stable element. Understanding the start and end points of a decay series is critical in nuclear chemistry.

For example, the Actinium series begins with Uranium-235 ({ }_{92}{U}^{235}) and ends with Lead-207 ({ }_{82}{Pb}^{207}), signifying a chain of decays where each step is characterized by the emission of alpha or beta particles. As a student, identifying the parent nuclide and following the sequence to its last stable nuclide helps you grasp the concept of decay series and the natural transmutation of elements.

Parent Nuclide

In a decay series, the parent nuclide is the original radioactive atom that begins the sequence of decay. It's essential to accurately identify the parent nuclide to understand the progression of transformations that lead to the final stable element. The parent nuclide possesses a significant amount of nuclear energy that it loses through a series of radioactive decays. The case of the Actinium series identifies Uranium-235 as the parent nuclide, even though the series is named after Actinium. This is because Uranium-235 decays into Actinium, which then continues to decay further down the series.

By recognizing Uranium-235 ({ }_{92}{U}^{235}) as the parent, the complex series of transformations becomes more transparent, enabling students to trace the stepwise decay process until it culminates in a stable nuclide, in this case, Lead-207 ({ }_{82}{Pb}^{207}). Understanding the role of the parent nuclide is pivotal in nuclear physics and chemistry, linking it directly to the stability, transmutation, and radioactivity of elements.

Radioactive Decay

Radioactive decay is a natural, spontaneous process in which an unstable atomic nucleus loses energy by emitting radiation, such as alpha particles, beta particles, or gamma rays. This process plays a crucial role in the transformation of elements in a decay series. Each emitted particle signifies a decay event, leading the original unstable nucleus, the parent nuclide, closer to a stable form.

The Actinium series showcases radioactive decay through a cascade of alpha and beta decays, starting with Uranium-235 and ending with stable Lead-207. The concept of radioactive decay is fundamental in understanding not only the mechanics of how elements alter over time but also the potential hazards and applications of radioactive materials. For instance, radioactive decay is utilized in medical treatments, power generation, and understanding the age of geological formations through radiometric dating. As students learn about the Actinium series, they come to appreciate the intricate balance between stability and instability that governs the very fabric of our universe.