The correct option is Option 4: \(_{18}^{40}\text{Ar}\) and \(_{20}^{40}\text{Ca}\).

Understanding Isobars

In nuclear chemistry, isobars are atoms of different chemical elements that have the same mass number (\(A\)) but different atomic numbers (\(Z\)).

When looking at chemical notation represented as:

\(_{Z}^{A}\text{X}\)

\(A\) (Top Number): Mass number (Total number of protons + neutrons).

\(Z\) (Bottom Number): Atomic number (Number of protons).

For Argon (\(_{18}^{40}\text{Ar}\)) and Calcium (\(_{20}^{40}\text{Ca}\)):

Both have the exact same mass number, \(A = 40\).

They have different atomic numbers (\(Z = 18\) for Argon, \(Z = 20\) for Calcium), which means they are completely different chemical elements with different physical and chemical properties.

Why the Other Options are Incorrect (They are Isotopes):

Options 1, 2, and 3 represent pairs of isotopes, not isobars. Isotopes are atoms of the same element that have the same atomic number (\(Z\)) but different mass numbers (\(A\)).

Option 1 (\(_{1}^{1}\text{H}\) and \(_{1}^{3}\text{H}\)): Protium and Tritium. They share the same atomic number (1) but have different mass numbers (1 and 3).

Option 2 (\(_{1}^{1}\text{H}\) and \(_{1}^{2}\text{H}\)): Protium and Deuterium. They share the same atomic number (1) but have different mass numbers (1 and 2).

Option 3 (\(_{6}^{12}\text{C}\) and \(_{6}^{14}\text{C}\)): Carbon-12 and Carbon-14. They share the same atomic number (6) but have different mass numbers (12 and 14).