To determine which of the given candidates could be an isotope of indium (In), we need to understand a few key concepts from chemistry, specifically concerning isotopes.
An isotope is an atom of the same element (same number of protons, denoted as [tex]\( Z \)[/tex]), but with a different number of neutrons. The number of protons [tex]\( Z \)[/tex] determines the element. The mass number [tex]\( A \)[/tex] is the total number of protons and neutrons in the nucleus and is given by [tex]\( A = Z + N \)[/tex], where [tex]\( N \)[/tex] is the number of neutrons.
Indium (In) has an atomic number [tex]\( Z \)[/tex] of 49. Therefore, any isotope of indium must have [tex]\( Z = 49 \)[/tex].
Let's evaluate each candidate:
1. Candidate: [tex]\( Z = 49, A = 113 \)[/tex]
- Here, the atomic number [tex]\( Z = 49 \)[/tex] matches indium.
- Given the mass number [tex]\( A = 113 \)[/tex],
[tex]\[
N = A - Z = 113 - 49 = 64
\][/tex]
- This means the number of neutrons [tex]\( N = 64 \)[/tex].
- Since for indium, [tex]\( Z = 49 \)[/tex] and we have a valid mass number, this candidate is an isotope of indium.
2. Candidate: [tex]\( N = 64, Z = 49 \)[/tex]
- Here, the atomic number [tex]\( Z = 49 \)[/tex] matches indium.
- Given [tex]\( N = 64 \)[/tex],
[tex]\[
A = Z + N = 49 + 64 = 113
\][/tex]
- This gives a mass number [tex]\( A = 113 \)[/tex].
- Since for indium, [tex]\( Z = 49 \)[/tex] and we have a valid mass number, this candidate is also an isotope of indium.
3. Candidate: [tex]\( N = 61, A = 113 \)[/tex]
- Here, the mass number [tex]\( A = 113 \)[/tex] is provided directly.
- To find [tex]\( Z \)[/tex], we use the relationship:
[tex]\[
Z = A - N = 113 - 61 = 52
\][/tex]
- The atomic number [tex]\( Z = 52 \)[/tex] does not match that of indium (which is [tex]\( Z = 49 \)[/tex]).
- Therefore, this candidate cannot be an isotope of indium.
4. Candidate: [tex]\( A = 110, N = 49 \)[/tex]
- Here, the mass number [tex]\( A = 110 \)[/tex] is provided directly.
- To find [tex]\( Z \)[/tex], we use the relationship:
[tex]\[
Z = A - N = 110 - 49 = 61
\][/tex]
- The atomic number [tex]\( Z = 61 \)[/tex] does not match that of indium (which is [tex]\( Z = 49 \)[/tex]).
- Therefore, this candidate cannot be an isotope of indium.
In summary, the candidates that could be isotopes of indium (In) are:
- [tex]\( Z = 49, A = 113 \)[/tex]
- [tex]\( N = 64, Z = 49 \)[/tex]
These two candidates meet the criteria for being isotopes of indium because they have the correct atomic number [tex]\( Z = 49 \)[/tex].
