Which of the following pair of nuclei are isobars of the element?

We need to identify which pair of nuclei are isobars.

First, we recall that isobars are nuclides with the same mass number (A) but different atomic numbers (Z), meaning they have the same total number of nucleons (protons + neutrons) yet represent different elements.

Next, we examine each option in turn.

In the first case, $$^{198}_{80}Hg$$ and $$^{197}_{79}Au$$ have mass numbers 198 and 197, respectively, so they are different and thus not isobars.

Then, $$^{3}_{1}H$$ (tritium) and $$^{3}_{2}He$$ (helium-3) both possess mass number 3 but differ in atomic number, so they share the same mass number while representing different elements; these are isobars.

By contrast, $$^{236}_{92}U$$ and $$^{238}_{92}U$$ both have atomic number 92 but mass numbers 236 and 238, making them isotopes rather than isobars.

Similarly, $$^{2}_{1}H$$ (deuterium) and $$^{3}_{1}H$$ (tritium) share atomic number 1 yet differ in mass numbers 2 and 3, so they too are isotopes, not isobars.

The correct answer is Option (2): $$^{3}_{1}H$$ and $$^{3}_{2}He$$.