To determine which ion is formed by providing the second ionization energy to remove an electron, let's carefully consider what second ionization energy entails and analyze each of the options given.
Second Ionization Energy:
The second ionization energy is the amount of energy required to remove a second electron from an atom that has already lost one electron. This means that initially the atom must be in a singly ionized state (positive ion, [tex]\(X^+\)[/tex]) before removing another electron to form a doubly ionized ion ( [tex]\(X^{2+}\)[/tex]).
Now let's evaluate each option:
1. [tex]\( \mathbf{Ca^{2+}} \)[/tex]:
- Calcium ( [tex]\(Ca\)[/tex] ) initially has a neutral charge.
- The first ionization energy would remove one electron to form [tex]\(Ca^+\)[/tex].
- Applying the second ionization energy to [tex]\(Ca^+\)[/tex] would remove another electron, resulting in [tex]\(Ca^{2+}\)[/tex].
2. [tex]\( \mathbf{N^{3-}} \)[/tex]:
- Nitrogen ( [tex]\(N\)[/tex] ) is initially neutral.
- This ion ([tex]\(N^{3-}\)[/tex]) is formed by gaining three electrons, rather than losing them. Therefore, ionization energies are not relevant here as we're discussing electron gain (not loss).
3. [tex]\( \mathbf{Fe^{3+}} \)[/tex]:
- Iron ( [tex]\(Fe\)[/tex] ) initially has a neutral charge.
- The first ionization energy would remove one electron to form [tex]\(Fe^+\)[/tex].
- The second ionization energy would remove another electron to form [tex]\(Fe^{2+}\)[/tex].
- A third ionization energy would be required to reach [tex]\(Fe^{3+}\)[/tex], meaning the formation of [tex]\(Fe^{3+}\)[/tex] involves removing three electrons in total.
4. [tex]\( \mathbf{S^{2-}} \)[/tex]:
- Sulfur ( [tex]\(S\)[/tex] ) is initially neutral.
- [tex]\(S^{2-}\)[/tex] is formed by gaining two electrons. Similar to nitrogen, ionization energies are not relevant here since it involves electron gain, not loss.
From the analysis, the only ion that matches the condition (where the ion was formed by removing the second electron given the second ionization energy) is [tex]\(\mathbf{Ca^{2+}}\)[/tex].
Thus, the ion formed by providing the second ionization energy to remove an electron is [tex]\(\mathbf{Ca^{2+}}\)[/tex].
