The nuclear charge of an atom is the total positive charge in its nucleus, equal to the number of protons (atomic number Z) multiplied by the elementary charge (e = 1.6 × 10⁻¹⁹ C). In a multi-electron atom, the outer electrons do not experience the full nuclear charge because inner electrons partially 'shield' them — the charge actually felt by an outer electron is called the effective nuclear charge (Zeff).
Nuclear charge = atomic number (Z) × elementary charge (e)
Effective nuclear charge: Zeff = Z − S
S = shielding constant; depends on electron configuration
Slater's rules: same-shell electrons contribute 0.35; (n-1) electrons contribute 0.85
Zeff increases across a period → smaller atomic radius, higher ionisation energy
Shielding = inner electrons partially blocking outer electrons from full nuclear charge
Nuclear charge (Z) = number of protons in the nucleus × elementary charge
Nuclear charge = Z × e where e = 1.6 × 10⁻¹⁹ C (elementary charge)
Examples:
Neutral atom: number of electrons = number of protons (Z) So the net charge of a neutral atom = 0
In a multi-electron atom, not all electrons are at the same distance from the nucleus. Inner-shell electrons partially block the nuclear charge from being felt by outer electrons. This is called the shielding effect or screening effect.
Effective nuclear charge: Zeff = Z − S
where:
The shielding constant S can be estimated using Slater's Rules:
Example — Zeff for 2p electron of Fluorine (Z=9, configuration 1s² 2s² 2p⁵): Same shell (2s and other 2p) = 6 electrons × 0.35 = 2.10 1s shell = 2 electrons × 0.85 = 1.70 S = 2.10 + 1.70 = 3.80 Zeff = 9 − 3.80 = 5.20
Across a period (left to right):
Down a group:
Nuclear charge vs Effective nuclear charge — Key difference:
Nuclear charge is the total positive charge in the nucleus of an atom, equal to the atomic number Z multiplied by the elementary charge. For example, oxygen (Z=8) has nuclear charge +8. In a neutral atom, the nuclear charge equals the electron charge in magnitude, giving a net charge of zero.
Effective nuclear charge (Zeff) is the net nuclear charge experienced by an outer electron after accounting for the shielding by inner electrons. Zeff = Z − S, where S is the shielding constant. Zeff is always less than Z in multi-electron atoms because inner electrons partially cancel the nuclear attraction.
Higher effective nuclear charge (Zeff) means the nucleus pulls electrons more strongly. Effects: (1) Smaller atomic radius — electrons are held closer, (2) Higher ionisation energy — harder to remove electron, (3) Higher electronegativity — stronger pull on bonding electrons, (4) Higher electron affinity — stronger attraction for extra electron. These are why properties change across a period.
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