Problem 144 - A Complete Resource Book in Chemistry for JEE Main

Question

A photon of hard \(\gamma\) radiation knocks a proton out of \({ }_{12} \mathrm{Mg}^{44}\) nucleus to form (a) the isotope of parent nucleus (b) the isobar of parent nucleus (c) the nuclide of \({ }_{14} \mathrm{Na}^{23}\) (d) the isobar of \(_{11} \mathrm{Na}^{23}\)

Step-by-Step Solution

Answer

(a) No isotope post-proton removal, sodium remains. (b) Example isobar: \(^{44}_{20}\text{Ca} \). (c) After reaction \(^{23}_{14}\text{Si} \). (d) \(^{23}_{12}\text{Mg} \).

Step 1: Define Terms Involved

To solve the exercise, we need to clarify the terms 'isotope', 'isobar', and 'nuclide'. An 'isotope' refers to different forms of the same element, having the same number of protons but different numbers of neutrons. An 'isobar' denotes nuclides of different elements with the same mass number. A 'nuclide' is characterized by a specific composition of protons and neutrons.

Step 2: Analyze the Reaction

When a photon knocks a proton out, the atomic number of the nucleus decreases by one, as it loses a proton. Thus, \(^{44}_{12}\text{Mg} \) becomes \(^{43}_{11}\text{Na} \).

Step 3: Identify the Isotope

For part (a), the resulting isotope will have the same number of protons as the original magnesium nucleus but will be lighter by one proton. Since it's now sodium, there is no direct isotope within the same elemental family for magnesium; we explore properties of sodium.

Step 4: Identify the Isobar of Parent Nucleus

Part (b) asks for an isobar of the original magnesium nucleus, which has a mass number of 44. An isobar could be \(^{44}_{20}\text{Ca} \), which shares the same mass number.

Step 5: Identify the Nuclide of \(^{23}_{14}\text{Si} \)

For part (c), the nuclide that relates to \(^{23}_{14}\text{Si} \) in terms of its atomic composition, but after transformation by gaining 1 neutron (adding proton) becomes \(^{23}_{14}\text{Si} \).

Step 6: Identify the Isobar of \(^{23}_{11}\text{Na} \)

Part (d) requires the isobar for the nucleus \(^{23}_{11}\text{Na} \). An isobar here would also have mass number 23. An example would be \(^{23}_{12}\text{Mg} \).

Key Concepts

Isotopes

Isotopes are fascinating variants of a particular chemical element. They have the same number of protons, which means they share the same atomic number, but they differ in the number of neutrons, leading to different mass numbers.
This variance results in isotopes having nearly identical chemical behavior, as chemical properties are dictated by the electron configuration, which is influenced by the number of protons. For instance, suppose we look at hydrogen. It has three primary isotopes: protium (with no neutrons), deuterium (one neutron), and tritium (two neutrons). Despite these differences, all isotopes of hydrogen behave similarly in chemical reactions. Isotopes are crucial in many scientific fields:

• In medicine: Isotopes like Carbon-14 are used in radiocarbon dating, pivotal for understanding historical timelines.
• In industry: Isotopes play roles in power generation, such as Uranium-235 in nuclear reactors.
• In research: Stable isotopes help study plant metabolism or track climate patterns through ice cores.

Recognizing isotopes allows us to unlock a deeper understanding of both fundamental science and practical applications.

Isobars

Isobars are intriguing counterparts to isotopes, yet they differ fundamentally. While isotopes pertain to the same element, isobars pertain to nuclides of different elements but with the same mass number.
This similarity in mass number means isobars can be different elements entirely, like calcium-40 and argon-40. Here's what makes isobars special:

• Mass Conservation: Isobars have the same total number of neutrons and protons combined, meaning the mass number remains constant, even though the atomic structure is different.
• Nuclear Stability: Isobars can exhibit varied nuclear properties like differing half-lives or decay modes, often influencing their stability.
• Mass Number & Chemical Behavior: Unlike isotopes, isobars often exhibit different chemical behaviors due to different numbers of protons (which define the element).

Understanding isobars is critical, particularly when assessing nuclear reactions or decay processes, often influencing studies in nuclear physics and chemistry.

Nuclides

A nuclide is a term that defines a species of an atom, characterized by its number of protons and neutrons. It's a more specific term that encompasses both the concepts of isotopes and isobars.
This specificity in description highlights the unique aspects of a given atomic species. Essential features of nuclides include:

• Atomic Identity: A nuclide is identified by its atomic number (protons) and its mass number (protons + neutrons). Every distinct atomic configuration is a distinct nuclide.
• Nuclide Chart: Scientists use charts to map out all known nuclides, each point on the graph representing a unique configuration.
• Radioactivity: Many nuclides are unstable and exhibit radioactivity. Their study is crucial for understanding nuclear stability, decay, and transformations.

Understanding nuclides allows us to explore the entirety of atomic composition, from stable atoms we encounter daily to radioactive species with important applications in medicine and beyond.