To determine which pair of nuclei are isobars, we need to understand the concept of isobars in nuclear physics. Isobars are atoms (nuclei) of different chemical elements that have the same mass number (\(A\)) but a different atomic number (\(Z\)).
The mass number is given by the sum of the number of protons and neutrons in the nucleus. Thus, for two nuclei to be isobars, they must have the same mass number.
Let's evaluate the given options:
$^{236}_{92}U$ and $^{238}_{92}U$
Mass numbers: 236 and 238
Different mass numbers, therefore not isobars.
$^2_1H$ and $^3_1H$
Mass numbers: 2 and 3
Different mass numbers, therefore not isobars.
$^3_1H$ and $^3_2He$
Mass numbers: 3 and 3
Same mass number but different atomic numbers, therefore they are isobars.
$^{198}_{80}Hg$ and $^{197}_{79}Au$
Mass numbers: 198 and 197
Different mass numbers, therefore not isobars.
Therefore, the correct pair of isobars is $^3_1H$ and $^3_2He$.
