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Q3.36:
The size of isoelectronic species — $F^{-}$, $Ne$ and $Na^{+}$ is affected by

Solution :

Step 1: Analyzing the Electronic Configuration

To determine the properties of the species $F^{-}$, $Ne$, and $Na^{+}$, we must first identify their total number of electrons. These species are classified as isoelectronic, meaning they possess the same number of electrons despite having different nuclear charges.

  • Fluorine ($F$, $Z=9$): $9 + 1 = 10$ electrons.
  • Neon ($Ne$, $Z=10$): $10$ electrons.
  • Sodium ($Na$, $Z=11$): $11 - 1 = 10$ electrons.

All three species possess a stable electronic configuration of $1s^2 2s^2 2p^6$. [Per the Pauli Exclusion Principle and Aufbau Principle].

Step 2: Defining the Governing Variable: Nuclear Charge ($Z$)

In isoelectronic series, the number of electrons (and consequently the electron-electron repulsion) remains constant. However, the nuclear charge ($Z$), which represents the number of protons in the nucleus, varies significantly:

Species Nuclear Charge ($Z$) Number of Electrons
$F^{-}$ $9$ $10$
$Ne$ $10$ $10$
$Na^{+}$ $11$ $10$

Step 3: Calculating Effective Nuclear Charge ($Z_{eff}$)

The size of an atom or ion is primarily determined by the magnitude of the electrostatic force of attraction between the nucleus and the outermost electrons. This is expressed by the effective nuclear charge ($Z_{eff}$). As the nuclear charge ($Z$) increases while the electron count remains constant, the nucleus exerts a stronger pull on the electron cloud. [Based on Coulomb's Law, $F = k \frac{q_1 q_2}{r^2}$].

Step 4: Visualization of Ionic/Atomic Radii

F⁻ (1.33 Å) Ne (1.12 Å) Na⁺ (0.95 Å)

Step 5: Synthesizing the Conclusion

The variation in size among isoelectronic species is inversely proportional to the nuclear charge. Specifically:

  • Higher $Z$ leads to a stronger inward pull on the valence shell.
  • This results in a decrease in the ionic/atomic radius.
  • Therefore, the size is fundamentally affected by the nuclear charge ($Z$).

Final Solution: The size of isoelectronic species is affected by the nuclear charge ($Z$). As the nuclear charge increases, the inward pull on the electron cloud increases, leading to a decrease in the ionic or atomic radius.


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