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).