To determine which pair of atoms are isotopes of the same element, we need to understand the concept of isotopes. Isotopes are atoms of the same element (same atomic number) that have different numbers of neutrons, which means they have different mass numbers.
Step-by-Step Solution:
1. Identify Atomic Numbers and Mass Numbers:
- Atomic number (Z): The number of protons in the nucleus of an atom. It determines the element.
- Mass number (A): The sum of the number of protons and neutrons in the nucleus.
2. Analyze the Given Pairs:
- Option (A) [tex]\( {}_2^3 X \)[/tex] and [tex]\( {}_2^4 X \)[/tex]
- Both atoms have the atomic number [tex]\( Z = 2 \)[/tex], meaning they have the same number of protons.
- The mass numbers are different: 3 and 4 respectively.
- Since they have the same atomic number and different mass numbers, they are isotopes of the same element.
- Option (B) [tex]\( {}_2^3 X \)[/tex] and [tex]\( {}_3^4 X \)[/tex]
- The first atom has an atomic number [tex]\( Z = 2 \)[/tex].
- The second atom has an atomic number [tex]\( Z = 3 \)[/tex].
- The atomic numbers are different, which means they are not the same element and, therefore, cannot be isotopes of the same element.
- Option (C) [tex]\( {}_2^4 X \)[/tex] and [tex]\( {}_3^4 X \)[/tex]
- The first atom has an atomic number [tex]\( Z = 2 \)[/tex].
- The second atom has an atomic number [tex]\( Z = 3 \)[/tex].
- Again, the atomic numbers are different, so these atoms are not the same element and cannot be isotopes of the same element.
3. Conclusion:
- The pair in Option (A) [tex]\( {}_2^3 X \)[/tex] and [tex]\( {}_2^4 X \)[/tex] are isotopes of the same element because they share the same atomic number (2) but have different mass numbers (3 and 4).
Therefore, the correct answer is:
(A) [tex]\( {}_2^3 X \)[/tex] and [tex]\( {}_2^4 X \)[/tex]
