Q.Two atoms are said to be isobars if.

The key idea here is Atomic Notation and Classification of Nuclides.

Atoms are characterized by their atomic number ($Z$) and mass number ($A$).

1. The atomic number ($Z$) represents the number of protons in the nucleus. It defines the element.
2. The mass number ($A$) represents the total number of protons and neutrons in the nucleus ($A = \text{protons} + \text{neutrons}$).
3. Isobars are defined as atoms of different elements that have the same mass number ($A$) but different atomic numbers ($Z$). …

When we talk about different types of atoms, we use specific terms to classify them based on their composition of protons, neutrons, and electrons. Understanding these terms requires a clear grasp of atomic notation.

Every atom can be represented using the notation $_Z^A X$, where:

• $X$ is the chemical symbol of the element.
• $Z$ is the atomic number, which represents the number of protons in the nucleus. This number uniquely identifies an element. For a neutral atom, $Z$ also equals the number of electrons.
• $A$ is the mass number, which represents the total number of protons and neutrons in the nucleus. It's essentially the total number of nucleons (particles in the nucleus).

From this, we can also determine the number of neutrons ($N$) in an atom:

Now, let's define isobars and related terms to understand the distinctions.

1. Understand the definition of Isobars.

   Isobars are atoms of different chemical elements that have the same mass number ($A$) but different atomic numbers ($Z$). Since they have different atomic numbers, they are different elements and thus have different numbers of protons. Because their mass numbers are the same, the sum of their protons and neutrons is identical.

   Important

   For isobars:

   • Same mass number ($A$).
   • Different atomic number ($Z$).
   • Different number of protons.
   • Different number of neutrons (since $N = A - Z$ and $Z$ is different while $A$ is same).
   • Different chemical properties (due to different $Z$).

   Let's consider an example: Carbon-14 ($_{6}^{14}\text{C}$) and Nitrogen-14 ($_{7}^{14}\text{N}$).

   • For Carbon-14: $A = 14$, $Z = 6$. Number of protons $= 6$, Number of neutrons $= 14 - 6 = 8$.
   • For Nitrogen-14: $A = 14$, $Z = 7$. Number of protons $= 7$, Number of neutrons $= 14 - 7 = 7$. They both have a mass number of $14$, but different atomic numbers ($6$ and $7$). Therefore, they are isobars.

2. Analyze the given options.

   • (A) they have same atomic number but different mass number.

     This describes isotopes. Isotopes are atoms of the same element (same $Z$) but with different numbers of neutrons, leading to different mass numbers ($A$). For example, Carbon-12 ($_{6}^{12}\text{C}$) and Carbon-14 ($_{6}^{14}\text{C}$) are isotopes. This option is incorrect for isobars.

   • (B) they have same number of electrons but different number of neutrons. …