The size of isoelectronic species `O^(-2) F^(-)` and `Na^(+)` is affected by:

Options

A. nuclear charge `(Z)`
B. valence principal quantum number `(n)`
C. electron-electron interaction in the outer orbitals.
D. none of the factors because their size is the same.

Answer

To determine how the size of the isoelectronic species \( O^{2-}, F^{-}, \) and \( Na^{+} \) is affected, we can follow these steps:

### Step 1: Identify the isoelectronic species
The species \( O^{2-}, F^{-}, \) and \( Na^{+} \) are isoelectronic, meaning they all have the same number of electrons. Each of these species has a total of 10 electrons, corresponding to the electron configuration of neon (Ne).

### Step 2: Understand the concept of effective nuclear charge (Z_eff)
The effective nuclear charge is the net positive charge experienced by an electron in a multi-electron atom. It accounts for the shielding effect of inner electrons. The greater the effective nuclear charge, the more strongly the nucleus can attract the electrons, leading to a smaller atomic radius.

### Step 3: Compare the nuclear charges of the species
- \( O^{2-} \): The atomic number of oxygen is 8, so the nuclear charge (Z) is +8.
- \( F^{-} \): The atomic number of fluorine is 9, so the nuclear charge (Z) is +9.
- \( Na^{+} \): The atomic number of sodium is 11, so the nuclear charge (Z) is +11.

### Step 4: Analyze the effect of nuclear charge on size
As the effective nuclear charge increases from \( O^{2-} \) to \( F^{-} \) to \( Na^{+} \), the size of the species decreases. This is because the increased positive charge in the nucleus pulls the electrons closer, reducing the size of the electron cloud.

### Step 5: Conclusion
The size of the isoelectronic species \( O^{2-}, F^{-}, \) and \( Na^{+} \) is affected primarily by the effective nuclear charge. As the effective nuclear charge increases, the size of the species decreases.

### Final Answer
The size of the isoelectronic species \( O^{2-}, F^{-}, \) and \( Na^{+} \) is affected by the effective nuclear charge.

---