To determine which of the given options could be an isotope of indium (In), we need to verify if they meet the criteria for isotopes: having the same atomic number (Z) but different mass numbers (A).
Option 1: [tex]\( Z = 49, A = 113 \)[/tex]
- Atomic number (Z) is 49, which matches the atomic number of indium.
- Mass number (A) is 113.
- Since the atomic number matches and indium's atomic number is 49, this is an isotope of indium.
- Conclusion: This option is correct.
Option 2: [tex]\( N = 64, Z = 49 \)[/tex]
- Atomic number (Z) is 49, which matches the atomic number of indium.
- Number of neutrons (N) is 64.
- Mass number [tex]\( A \)[/tex] is determined by the formula [tex]\( A = Z + N \)[/tex].
[tex]\[
A = 49 + 64 = 113
\][/tex]
- Since the atomic number matches and the mass number calculated is 113, this is an isotope of indium.
- Conclusion: This option is correct.
Option 3: [tex]\( N = 61, A = 113 \)[/tex]
- Mass number (A) is 113.
- Number of neutrons (N) is 61.
- The atomic number [tex]\( Z \)[/tex] is determined by the formula [tex]\( Z = A - N \)[/tex].
[tex]\[
Z = 113 - 61 = 52
\][/tex]
- Since the atomic number calculated is 52, which does not match the atomic number of indium (49), this option is not an isotope of indium.
- Conclusion: This option is incorrect.
Option 4: [tex]\( A = 110, N = 49 \)[/tex]
- Mass number (A) is 110.
- Number of neutrons (N) is 49.
- The atomic number [tex]\( Z \)[/tex] is determined by the formula [tex]\( Z = A - N \)[/tex].
[tex]\[
Z = 110 - 49 = 61
\][/tex]
- Since the atomic number calculated is 61, which does not match the atomic number of indium (49), this option is not an isotope of indium.
- Conclusion: This option is incorrect.
Summary:
- The correct isotopes of indium (In) based on the given options are:
- [tex]\( Z = 49, A = 113 \)[/tex]
- [tex]\( N = 64, Z = 49 \)[/tex]
- The following options are not isotopes of indium:
- [tex]\( N = 61, A = 113 \)[/tex]
- [tex]\( A = 110, N = 49 \)[/tex]
