Q.(i) Define electron gain enthalpy.

The Intuition: Why Don't Electrons Just Fly Away?

Imagine you're holding a magnet near a pile of paperclips. The closer the magnet, the stronger the pull. Now imagine you put a sheet of cardboard between the magnet and the paperclips. The pull weakens — the cardboard "shields" the paperclips from the full force of the magnet.

An atom works similarly. The nucleus (positive charge) pulls on the electrons (negative charge). But an electron is not alone — there are other electrons buzzing around between it and the nucleus. Those inner electrons act like the cardboard sheet: they shield or screen the outer electron from feeling the full positive charge of the nucleus.

So an outer electron doesn't "see" the full nuclear charge $Z$ (the atomic number). It sees a smaller, effective charge — the net positive pull after accounting for the repulsion from inner electrons.

That's effective nuclear charge, denoted $Z_{\text{eff}}$.

The Precise Statement

$Z_{\text{eff}}$ is always less than $Z$ (except for hydrogen, which has no other electrons to shield — there $Z_{\text{eff}} = Z$).

What Determines the Shielding Constant $S$?

Not all electrons shield equally. The key rules:

1. Inner electrons shield outer electrons very effectively. An electron in the $n=1$ shell completely blocks about 1 unit of charge from an electron in $n=2$.
2. Electrons in the same shell shield poorly. They're at roughly the same distance, so they don't block much of the nucleus from each other.
3. Outer electrons do not shield inner electrons at all. An electron farther out cannot block the nucleus from one closer in.

There are detailed rules (Slater's rules) to calculate $S$ numerically, but the core idea is simple: the more electron shells between an electron and the nucleus, the more shielding, and the lower $Z_{\text{eff}}$.

Why Does This Matter?

$Z_{\text{eff}}$ explains three fundamental patterns in the periodic table:

A Concrete Example: Sodium vs. Chlorine

Sodium ($Z = 11$): Electron configuration $1s^2 2s^2 2p^6 3s^1$

The outermost electron (3s) is shielded by the 10 inner electrons ($1s^2 2s^2 2p^6$). Roughly, $S \approx 10$, so $Z_{\text{eff}} \approx 11 - 10 = 1$. The outer electron feels a pull equivalent to just one proton. …