Let's carefully examine whether the given atoms are isotopes of each other.
Isotopes are atoms that have the same atomic number but different mass numbers.
1. Comparing atoms [tex]\(X\)[/tex] and [tex]\(Y\)[/tex]:
- Atomic number of [tex]\(X\)[/tex] is 10.
- Atomic number of [tex]\(Y\)[/tex] is also 10.
- Both [tex]\(X\)[/tex] and [tex]\(Y\)[/tex] have different mass numbers (20 and 21, respectively).
Since [tex]\(X\)[/tex] and [tex]\(Y\)[/tex] have the same atomic number but different mass numbers, they are isotopes of each other.
2. Comparing atoms [tex]\(X\)[/tex] and [tex]\(Z\)[/tex]:
- Atomic number of [tex]\(X\)[/tex] is 10.
- Atomic number of [tex]\(Z\)[/tex] is 11.
Since [tex]\(X\)[/tex] and [tex]\(Z\)[/tex] have different atomic numbers, they are not isotopes of each other.
3. Comparing atoms [tex]\(Y\)[/tex] and [tex]\(Z\)[/tex]:
- Atomic number of [tex]\(Y\)[/tex] is 10.
- Atomic number of [tex]\(Z\)[/tex] is 11.
Since [tex]\(Y\)[/tex] and [tex]\(Z\)[/tex] have different atomic numbers, they are not isotopes of each other.
To summarize, from the given information:
- [tex]\(X\)[/tex] and [tex]\(Y\)[/tex] are isotopes of each other.
- [tex]\(X\)[/tex] and [tex]\(Z\)[/tex] are not isotopes.
- [tex]\(Y\)[/tex] and [tex]\(Z\)[/tex] are not isotopes.
Therefore, the correct answer is:
A. [tex]\(X\)[/tex] and [tex]\(Y\)[/tex]
