Which one of the following statements is incorrect in relation to ionization enthalpy? (a) Ionization enthalpy

Exercises · 3.37

Q. Which one of the following statements is incorrect in relation to ionization enthalpy?

(a) Ionization enthalpy increases for each successive electron.

(b) The greatest increase in ionization enthalpy is experienced on removal of electron from core noble gas configuration.

(d) Removal of electron from orbitals bearing lower n value is easier than from orbital having higher n value.

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Concept understanding — Effective Nuclear Charge

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}} = Z - S

$Z_{\text{eff}}$ 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:

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 $n=2$ .
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.
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:

Trend	What happens to $Z_{\text{eff}}$	Why
Across a period (left to right)	Increases	Adding protons ( $Z$ up) but electrons go into the same shell (shielding roughly constant). Net pull on outer electrons gets stronger.
Down a group (top to bottom)	Stays roughly constant or decreases slightly	Adding a new shell means much more shielding. The extra protons are almost completely cancelled by the new inner electrons.
Atomic size	Larger $Z_{\text{eff}}$ → smaller atom	Stronger pull pulls electrons closer to nucleus.

Note

This is why fluorine is smaller than lithium, even though fluorine has more protons. The extra protons in fluorine are not fully shielded — the outer electrons feel a much stronger pull.

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. …

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Ionization enthalpy depends on effective nuclear charge and electron shielding. The incorrect statement is (d), because removing an electron from a a lower‑n orbital (closer to the nucleus) is harder, not easier, than from a higher‑n orbital.

The Core Idea: Effective Nuclear Charge ( $Z_{\text{eff}}$ )

Ionization enthalpy is the energy needed to remove an electron from a gaseous atom. The key factor is how strongly the nucleus pulls on that electron. This pull is not simply the full nuclear charge $Z$ — inner electrons shield the outer electron, reducing the attraction. The net pull is the effective nuclear charge:

Z_{\text{eff}} = Z - S

A higher $Z_{\text{eff}}$ means a tighter hold → higher ionization enthalpy. A lower $Z_{\text{eff}}$ means easier removal → lower ionization enthalpy.

Now let’s examine each statement.

Step‑by‑Step Analysis

1. Statement (a): “Ionization enthalpy increases for each successive electron.”

After you remove one electron, the atom becomes a positive ion. The remaining electrons feel a higher $Z_{\text{eff}}$ because there is one less electron to cause repulsion, and the nuclear charge hasn’t changed. So each subsequent electron is harder to pull off.

Example: For Mg:

First ionization enthalpy: $738\ \text{kJ/mol}$
Second: $1451\ \text{kJ/mol}$
Third: $7733\ \text{kJ/mol}$ Yes, it always increases. Statement (a) is correct.

2. Statement (b): “The greatest increase in ionization enthalpy is experienced on removal of electron from core noble gas configuration.”

Consider sodium: electron configuration $1s^2 2s^2 2p^6 3s^1$ .

Removing the $3s$ electron (first IE) is relatively easy — you get a $\text{Na}^+$ ion with a neon core ( $1s^2 2s^2 2p^6$ ).
Removing a second electron means breaking into that stable noble‑gas core. That requires a huge jump in energy. For Na: first IE = $496\ \text{kJ/mol}$ , second IE = $4562\ \text{kJ/mol}$ — nearly a tenfold increase. This pattern holds for all elements: the biggest jump occurs when you start pulling electrons from a filled noble‑gas shell. Statement (b) is correct.

3. Statement (c): “End of valence electrons is marked by a big jump in ionization enthalpy.” …

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Q.Which one of the following statements is incorrect in relation to ionization enthalpy?

The Core Idea: Effective Nuclear Charge (ZeffZ_{\text{eff}}Zeff​)

Step‑by‑Step Analysis

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The Core Idea: Effective Nuclear Charge ( $Z_{\text{eff}}$ )

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