Which of these are pairs of isobars?

The correct answer is option 3. ²⁰C₄₀,¹⁸Ar₄₀.

Isobars are atoms of different chemical elements that have the same mass number, meaning they have the same total number of protons and neutrons in their nuclei, but different atomic numbers.

Let's examine the pairs provided:

1. \(^6C_{12},\, \ ^8O_{16}\): These are not isobars because they have different mass numbers. Carbon-12 \((^6C_{12})\) has a mass number of 12, while oxygen-16 \((^8O_{16})\) has a mass number of 16.

2. \(^6C_{13},\, \  ^6C_{14}\): These are not isobars because they have the same atomic number (6), indicating they are isotopes of carbon. Isotopes have the same number of protons but different numbers of neutrons, resulting in different mass numbers.

3. \(^{20}C_{40},\, \ ^{18}Ar_{40}\): This pair represents isobars because they have the same mass number (40) but belong to different elements with different atomic numbers. Carbon-40 \((^{20}C_{40})\) has an atomic number of 20, while argon-40 \((^{18}Ar_{40})\) has an atomic number of 18.

Therefore, the pair \(^{20}C_{40},\, \ ^{18}Ar_{40}\) represents isobars because they have the same mass number but belong to different elements. This distinction highlights the importance of considering both the atomic number and mass number when identifying isotopes, isobars, and other nuclear properties.