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

Question

Accepted Answer

Given: We need to identify the pair of nuclei that are isobars.

Find: Which option contains nuclei with the same mass number $A$ but different atomic number $Z$ .

Isobars are nuclei having the same mass number $A$ and different atomic numbers $Z$ .

Checking the options:

Option A: $^{236}_{92}U$ and $^{238}_{92}U$ have the same $Z = 92$ but different $A$ , so they are not isobars.
Option B: $^2_1H$ and $^3_1H$ have the same $Z = 1$ but different $A$ , so they are not isobars.
Option C: $^3_1H$ and $^3_2He$ have the same mass number $A = 3$ but different atomic numbers $Z = 1$ and $Z = 2$ , so they are isobars.
Option D: $^{198}_{80}Hg$ and $^{197}_{79}Au$ have different $A$ and different $Z$ , so they are not isobars.

Therefore, the correct option is C.

Given: The options list four pairs of nuclei.

Find: The pair that satisfies the definition of isobars.

Use the definition:

\text{Isobars} \Rightarrow \text{same } A \text{ and different } Z

Now compare each pair:

\begin{aligned} \text{A: } & ^{236}_{92}U,\ ^{238}_{92}U && \Rightarrow A \text{ different, } Z \text{ same} \\ \text{B: } & ^2_1H,\ ^3_1H && \Rightarrow A \text{ different, } Z \text{ same} \\ \text{C: } & ^3_1H,\ ^3_2He && \Rightarrow A = 3 \text{ same, } Z = 1,2 \text{ different} \\ \text{D: } & ^{198}_{80}Hg,\ ^{197}_{79}Au && \Rightarrow A \text{ different, } Z \text{ different} \end{aligned}

Only option C matches the condition for isobars.

Therefore, the correct answer is C.

Answer