Identify the least stable ion amongst the following : (1) \(\mathrm{Ne}^{-}\) (2) \(\mathrm{F}^{-}\) (3) \(\mathrm{B}^{-}\) (4) \(\mathrm{C}^{-}\)

Understanding the electron configuration of ions is crucial in determining their stability. An electron configuration is a distribution of electrons of an atom or molecule in atomic or molecular orbitals. Here's how to break it down:

• Electrons fill atomic orbitals in a specific sequence known as the Aufbau principle: 1s, 2s, 2p, 3s, 3p, and so on.
• Each orbital can hold a specific number of electrons: s-orbitals hold 2, p-orbitals hold 6, d-orbitals hold 10, and f-orbitals hold 14.
• The electrons in the outermost shell are referred to as valence electrons, which play a key role in determining the chemical properties of an element.

When an ion forms, it either gains or loses electrons to achieve a more stable electron configuration. For example, the neon ion \(\text{Ne}^{-}\) has one extra electron, making its electron configuration 1s² 2s² 2p⁷. This configuration is unstable because neon normally has a full outer shell (1s² 2s² 2p⁶), so adding an extra electron disrupts that balance.
Understanding how electrons are arranged in atoms helps predict the chemical behavior and stability of ions.

Effective nuclear charge (Z\textsubscript{eff}) is another important factor in understanding ion stability. Z\textsubscript{eff} is the net positive charge experienced by an electron in a multi-electron atom. This concept explains why certain ions are more stable than others. Here’s how it works:

• In a multi-electron atom, electrons are attracted to the nucleus due to electrostatic forces but are also repelled by other electrons (electron-electron repulsion).
• The effective nuclear charge is calculated by subtracting shielding effects (caused by inner-shell electrons) from the total positive charge of the nucleus.
• Higher Z\textsubscript{eff} means a stronger attraction between the nucleus and the valence electrons, resulting in a more stable configuration.

For example, in the fluoride ion (F\textsuperscript{-}), the effective nuclear charge felt by the extra electron is relatively strong compared to the boron ion (B\textsuperscript{-}). This makes F\textsuperscript{-} more stable because the added electron is more effectively held by the nucleus, achieving a noble gas configuration.
Analyzing Z\textsubscript{eff} helps explain why some ions, like \(\text{Ne}^{-}\), are less stable as the extra electrons significantly reduce Z\textsubscript{eff} due to strong electron-electron repulsions.

Ion stability is the result of a combination of electron configuration and effective nuclear charge. Generally, the more stable ions have a full valence shell, similar to the noble gas configuration. Factors affecting ion stability include:

• Electron configuration: Stable ions usually have electron configurations similar to the nearest noble gas. For instance, F\textsuperscript{-} is stable because its configuration matches that of neon.
• Effective nuclear charge: Ions with a higher Z\textsubscript{eff} are more stable because the nucleus attracts electrons more effectively. For example, \(\text{Ne}^{-}\) is less stable because an additional electron beyond the stable noble gas configuration decreases the Z\textsubscript{eff} significantly.
• Electron-electron repulsions: Highly negative ions (with extra electrons) suffer from increased repulsive forces among electrons, leading to reduced stability.

Considering these factors, we can analyze the given ions:

• \(\text{Ne}^{-}\) is the least stable because the extra electron exceeds the stable noble gas configuration, causing strong electron repulsions.
• \(\text{F}^{-}\) is stable as it achieves a noble gas configuration.
• \(\text{B}^{-}\) and \( \text{C}^{-} \) are less stable but not as unstable as \(\text{Ne}^{-}\).

Thus, based on these principles, \(\text{Ne}^{-}\) is the least stable ion, confirming our initial conclusion.