Explanation

Isobars are nuclei which have the same mass number but different atomic numbers.

Let us analyze each option step by step.

Option A:

$$ {}^{3}_{1}\text{H} \quad \text{and} \quad {}^{3}_{2}\text{He} $$

Both nuclei have the same mass number $A = 3$ but different atomic numbers ($Z = 1$ and $Z = 2$). Hence, they are isobars.

Option B:

$$ {}^{198}_{80}\text{Hg} \quad \text{and} \quad {}^{197}_{79}\text{Au} $$

Mass numbers are different ($198 \neq 197$), so these are not isobars.

Option C:

$$ {}^{2}_{1}\text{H} \quad \text{and} \quad {}^{3}_{1}\text{H} $$

Atomic number is the same but mass number is different, so these are isotopes, not isobars.

Option D:

$$ {}^{236}_{92}\text{U} \quad \text{and} \quad {}^{238}_{92}\text{U} $$

Again, same atomic number but different mass numbers, hence these are isotopes.

Therefore, the correct pair of isobars is

$$ {}^{3}_{1}\text{H} \;\text{and}\; {}^{3}_{2}\text{He} $$

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