Step 1: Understanding the Concept:
Isoelectronic species are atoms, ions, or molecules that possess the same total number of electrons. To determine which pair is not isoelectronic, we must calculate the electron count for each ion presented in the options.
Step 2: Key Formula or Approach:
The number of electrons in an ion can be calculated using the formula:
Number of electrons = Atomic number (\(Z\)) \(-\) Charge of the ion.
{Note: The options provided in the original text contain typographical errors, lacking standard '+' and '-' charge indicators. To solve the problem logically, we must interpret them as common, stable ions: \(\text{Na}^+, \text{Mg}^{2+}\), \(\text{Mn}^{2+}, \text{Fe}^{3+}\), \(\text{Fe}^{2+}, \text{Mn}^{3+}\), and \(\text{O}^{2-}, \text{F}^-\).}
Step 3: Detailed Explanation:
Let's analyze each pair based on their standard ionic forms:
- Pair (a) interpreted as \(\text{Na}^+, \text{Mg}^{2+}\):
Sodium (Na) has \(Z = 11\). The number of electrons in \(\text{Na}^+ = 11 - 1 = 10\).
Magnesium (Mg) has \(Z = 12\). The number of electrons in \(\text{Mg}^{2+} = 12 - 2 = 10\).
Both have 10 electrons, making them an isoelectronic pair.
- Pair (b) interpreted as \(\text{Mn}^{2+}, \text{Fe}^{3+}\):
Manganese (Mn) has \(Z = 25\). The number of electrons in \(\text{Mn}^{2+} = 25 - 2 = 23\).
Iron (Fe) has \(Z = 26\). The number of electrons in \(\text{Fe}^{3+} = 26 - 3 = 23\).
Both have 23 electrons, making them an isoelectronic pair.
- Pair (c) interpreted as \(\text{Fe}^{2+}, \text{Mn}^{3+}\):
Iron (Fe) has \(Z = 26\). The number of electrons in \(\text{Fe}^{2+} = 26 - 2 = 24\).
Manganese (Mn) has \(Z = 25\). The number of electrons in \(\text{Mn}^{3+} = 25 - 3 = 22\).
They have different numbers of electrons (24 and 22 respectively), so they are not an isoelectronic pair.
- Pair (d) interpreted as \(\text{O}^{2-}, \text{F}^-\):
Oxygen (O) has \(Z = 8\). The number of electrons in \(\text{O}^{2-} = 8 - (-2) = 10\).
Fluorine (F) has \(Z = 9\). The number of electrons in \(\text{F}^- = 9 - (-1) = 10\).
Both have 10 electrons, making them an isoelectronic pair.
Step 4: Final Answer:
The pair consisting of iron(II) and manganese(III) ions is not isoelectronic. Therefore, option (c) is the correct choice.