Question

Which of these unidentified nuclides are isotopes of each other? $$ { }_{71}^{175}(?) $$ $$ \frac{71}{32}(?) $$ $$ \frac{175}{74}(?) $$ $$ { }_{71}^{167}(?) $$ $$ \frac{71}{30}(?) $$ $$ { }_{74}^{180}(?) $$

Short answer

Nuclides: 1. ${}_{71}^{175}(?)$ 2. $\frac{71}{32}(?)$ 3. $\frac{175}{74}(?)$ 4. ${}_{71}^{167}(?)$ 5. $\frac{71}{30}(?)$ 6. ${}_{74}^{180}(?)$ Answer: The isotopes among the given unidentified nuclides are nuclides 1 and 4, 1 and 2, 1 and 5, 4 and 2, and 4 and 5.

Step-by-step solution

Identify the atomic numbers and mass numbers of each nuclide

For each nuclide, we need to identify the atomic number (Z) and the mass number (A). The atomic number is represented by the subscript and the mass number is represented by the superscript. $$ { }_{71}^{175}(?) \Longrightarrow Z = 71, A = 175 $$ $$ \frac{71}{32}(?) \Longrightarrow Z = 71, A = 32 $$ $$ \frac{175}{74}(?) \Longrightarrow Z = 175, A = 74 $$ $$ { }_{71}^{167}(?) \Longrightarrow Z = 71, A = 167 $$ $$ \frac{71}{30}(?) \Longrightarrow Z = 71, A = 30 $$ $$ { }_{74}^{180}(?) \Longrightarrow Z = 74, A = 180 $$

Determine which nuclides have the same atomic number but different mass numbers

By comparing the atomic numbers and mass numbers of the nuclides, we can identify isotopes. Isotopes will have the same atomic number (Z) but different mass numbers (A). $$ { }_{71}^{175}(?) \; \text{and} \; { }_{71}^{167}(?) \Longrightarrow \text{Isotopes} $$ $$ { }_{71}^{175}(?) \; \text{and} \; \frac{71}{32}(?) \Longrightarrow \text{Isotopes} $$ $$ { }_{71}^{175}(?) \; \text{and} \; \frac{71}{30}(?) \Longrightarrow \text{Isotopes} $$ $$ { }_{71}^{167}(?) \; \text{and} \; \frac{71}{32}(?) \Longrightarrow \text{Isotopes} $$ $$ { }_{71}^{167}(?) \; \text{and} \; \frac{71}{30}(?) \Longrightarrow \text{Isotopes} $$ Other pairs of nuclides are not isotopes because their atomic numbers are different.

Conclusion

The isotopes among the given unidentified nuclides are: - \({ }_{71}^{175}(?)\) and \({ }_{71}^{167}(?)\) - \({ }_{71}^{175}(?)\) and \(\frac{71}{32}(?)\) - \({ }_{71}^{175}(?)\) and \(\frac{71}{30}(?)\) - \({ }_{71}^{167}(?)\) and \(\frac{71}{32}(?)\) - \({ }_{71}^{167}(?)\) and \(\frac{71}{30}(?)\)