Question

The radioactive series to which \({ }_{88} \mathrm{Ra}^{224}\) belongs is (a) Actinium series (b) Thorium series (c) Uranium series (d) Neptunium series

Short answer

Radium-224 ({ }_{88}Ra^{224}) belongs to the Thorium series.

Step-by-step solution

Identify the Radioactive Series

The radioactive series are identified based on the final stable nucleus they lead to after undergoing radioactive decay. There are four such series: Uranium, Actinium, Thorium, and Neptunium. Each series ends with a stable isotope of lead. For an isotope to be a part of a particular decay series, its atomic mass (A) must satisfy the relation A = 4n + r, where n is a positive integer and r is the series-specific remainder when A is divided by 4.

Calculate the Remainder for Ra-224

For Radium-224 ({ }_{88}Ra^{224}), calculate the remainder when the mass number 224 is divided by 4. If the remainder matches the specific remainder for any of the radioactive series, it belongs to that series.

Determine the Series for Radium-224

For the mass number 224, dividing by 4 gives a remainder of 0 (224 = 4 * 56). The Thorium series is characterized by having a remainder of 0 (A = 4n). Therefore, Radium-224 belongs to the Thorium series.

Key concepts

Radioactive Series

Understanding the concept of radioactive series is critical in nuclear chemistry, as it explains the sequential transformations a radioactive isotope undergoes until it becomes stable. A radioactive series begins with a parent nuclide and progresses through several radioactive daughter nuclides, which are the products of various types of decay such as alpha and beta decay. The series ends when a stable non-radioactive nuclide is formed.

For instance, taking the case of Radium-224, we classify it based on the atomic mass and the sequence of isotopes it produces upon decay. The key to identifying to which series a certain isotope belongs is by looking at the atomic mass number (A) and applying the formula: \( A = 4n + r \), where \( n \) is any positive integer and \( r \) is the series-specific remainder upon division by 4. The radioactivity chain ends with a stable isotope of lead, and since Radium-224 falls under the Thorium series, which is characterized by the remainder \( r = 0 \), we can anticipate the sequence of decays that lead to a stable Lead isotope.

Nuclear Chemistry

Nuclear chemistry is a fascinating branch of chemistry that studies atomic nuclei, their reactions, and the changes they undergo. This area of chemistry answers questions about how and why elements undergo radioactive decay, how to harness energy from these processes, and the implications for both practical applications and the environment. At its core, nuclear chemistry helps to develop medical isotopes for diagnosis and treatment, understand cosmic phenomena, and create energy through nuclear power.

In the context of our problem, applying principles of nuclear chemistry allows us to predict the behavior of a radioactive element like Radium-224 within the Thorium decay series. We can further understand how nuclear reactions drive the transformation of one element to another, shedding light on the powerful forces within an atom's nucleus.

Radioactive Isotopes

Radioactive isotopes, or radioisotopes, are variants of chemical elements that have unstable nuclei and release radiation as they decay to a more stable form. This decay can happen in several ways, including alpha decay (emission of helium nuclei), beta decay (conversion of a neutron to a proton or vice versa), or gamma emission (release of high-energy photons).

Radium-224, the specific isotope in our exercise, is just one example of a radioisotope that undergoes such decay, eventually leading to a stable isotope after a series of transformations. Understanding these isotopes is vital in various fields such as medicine for cancer treatment, archaeology for dating artifacts, and space exploration. In studying the decay series to which Radium-224 belongs, we gain insight into the predictable pattern of its decay and the properties of the isotopes that form as intermediates in the radioactive series.