To identify which ion was formed by providing the second ionization energy to remove an electron, let’s examine each of the given ions: [tex]\( Ca^{2+} \)[/tex], [tex]\( N^{3-} \)[/tex], [tex]\( Fe^{3+} \)[/tex], and [tex]\( S^{2-} \)[/tex].
1. Second Ionization Energy: This term refers to the energy required to remove an electron from a singly charged positive ion (X^+), resulting in the formation of a doubly charged positive ion (X^{2+}).
Let’s analyze each option individually:
1. [tex]\( Ca^{2+} \)[/tex]:
- A calcium atom (Ca) has an atomic number of 20. Removing the first electron results in [tex]\( Ca^{+} \)[/tex].
- Removing the second electron from [tex]\( Ca^{+} \)[/tex] (the second ionization energy) forms [tex]\( Ca^{2+} \)[/tex].
2. [tex]\( N^{3-} \)[/tex]:
- A nitrogen atom (N) has an atomic number of 7. Gaining three electrons results in [tex]\( N^{3-} \)[/tex].
- This is not relevant to the removal of electrons needed for second ionization energy.
3. [tex]\( Fe^{3+} \)[/tex]:
- An iron atom (Fe) has an atomic number of 26. If we start with an iron ion [tex]\( Fe^{2+} \)[/tex], further removal of one electron forms [tex]\( Fe^{3+} \)[/tex].
- This involves the third ionization energy, not the second.
4. [tex]\( S^{2-} \)[/tex]:
- A sulfur atom (S) has an atomic number of 16. Gaining two electrons results in [tex]\( S^{2-} \)[/tex].
- This is also irrelevant to the process of removing electrons as required by the second ionization energy.
From the above analysis, we see that the [tex]\( Ca^{2+} \)[/tex] ion is formed by providing the second ionization energy to remove an electron from [tex]\( Ca^{+} \)[/tex].
Thus, the correct answer is [tex]\( Ca^{2+} \)[/tex].
