In nuclear chemistry, what are isobars with respect to the atomic number and mass number of elements or nuclides?

Introduction / Context:
This question belongs to the area of nuclear chemistry and atomic structure, where terms such as isotopes, isobars, isotones and isoelectronic species are used to describe relationships between nuclides. The term isobar is often tested in examinations because it reflects how elements can share the same mass number while having different atomic numbers and therefore belong to different chemical elements. Understanding these definitions helps in interpreting nuclear reactions, decay schemes and stability patterns in the periodic table.

Given Data / Assumptions:
Atomic number is the number of protons in the nucleus and defines the chemical identity of an element.
Mass number is the total number of protons and neutrons in the nucleus of a given nuclide.
Examples of nuclides often used include 40Ar, 40Ca and 40K, which can be compared by atomic number and mass number.
We assume standard definitions used in introductory chemistry and physics texts.

Concept / Approach:
The key concept is to recall and differentiate the various related terms. Isotopes are nuclides with the same atomic number but different mass numbers. Isobars are nuclides with different atomic numbers but the same mass number. Isotones share the same number of neutrons but have different atomic numbers. Isoelectronic species have the same number of electrons. The question specifically asks about isobars, so we must focus on the relationship involving the mass number being the same while the atomic number differs, meaning the elements are chemically distinct but have nuclei with the same total number of nucleons.

Step-by-Step Solution:
Step 1: Recall that atomic number (Z) is the number of protons, and mass number (A) is the total of protons plus neutrons. Step 2: For isotopes, Z is the same but A is different, for example 1H, 2H and 3H for hydrogen. This does not match the definition of isobars. Step 3: For isobars, the mass number A is the same for two or more nuclides, but the atomic number Z is different. A classic example is 40Ar (Z = 18), 40Ca (Z = 20) and 40K (Z = 19). Each has mass number 40 but different atomic numbers. Step 4: Thus, the correct description of isobars is that they are elements or nuclides with different atomic numbers but the same mass number. Step 5: Compare this with the options given to find the statement that exactly matches this definition.

Verification / Alternative check:
To verify, you can use any pair of well known isobars from nuclear data tables. For example, 14C (atomic number 6, mass number 14) and 14N (atomic number 7, mass number 14) are isobars. They clearly have different atomic numbers, they belong to different chemical elements (carbon and nitrogen), but they share the same mass number 14. This is consistent with the standard definition of isobars presented in most textbooks. None of the other definitions, such as isotopes, fits this pair, confirming that isobars must have the same mass number and different atomic numbers.

Why Other Options Are Wrong:
Elements with the same atomic number but different mass number describe isotopes, not isobars, so option A is incorrect.
Elements with different atomic number and different mass number do not define any special relationship and therefore do not correspond to isobars, making option C wrong.
Elements with the same atomic number and the same mass number represent identical nuclides and are not given any special relational name in this context, so option D is also incorrect.

Common Pitfalls:
Students often mix up isotopes and isobars because both terms involve comparisons of atomic and mass numbers. A useful memory aid is that iso in both terms means same, but the second part of the word tells what is the same: in isotopes, tope relates to place in the periodic table, so atomic number is the same; in isobars, bar suggests weight or mass, so mass number is the same. Confusing mass number and atomic number or forgetting which quantity defines the element can also lead to incorrect answers. Keeping examples like 14C and 14N in mind helps to avoid this confusion.

Final Answer:
Isobars are defined as elements with different atomic number but the same mass number.