Step 1: Understanding the Concept:
Isobars are atoms of different elements with the same mass number \(A\). Isotopes have the same atomic number \(Z\) but different \(A\).
Step 2: Check each pair:
A: \(^3\text{He}_2\) and \(^4\text{He}_2\): same \(Z\), different \(A\), so they are isotopes.
B: \(^{24}\text{Mg}_{12}\) and \(^{25}\text{Mg}_{12}\): same \(Z\), different \(A\), isotopes.
C: \(^{40}\text{K}_{19}\) and \(^{40}\text{Ca}_{20}\): same \(A = 40\), different \(Z\). These are isobars.
D: \(^{40}\text{K}_{19}\) and \(^{39}\text{K}_{19}\): isotopes.
Final Answer:
The isobars are \(^{40}\text{K}_{19}\) and \(^{40}\text{Ca}_{20}\), option (C).
\[ \boxed{^{40}\text{K}_{19}\ \text{and}\ ^{40}\text{Ca}_{20}} \]