One method for calculating Zeff is to use the equation
where E is the energy necessary to remove an electron from an atom and n is the principal quantum number of the elec-tron. Use this equation to calculate Zeff values for the highest-energy electrons in potassium (E = 418.8 kJ/mol) and krypton (E = 1350.7 kJ/mol).

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Identify the given values for potassium and krypton: E (ionization energy) and n (principal quantum number). For potassium, E = 418.8 kJ/mol and n = 4. For krypton, E = 1350.7 kJ/mol and n = 4.

Substitute the given values for potassium into the equation: \(Z_{eff} = \sqrt{\frac{(418.8)(4^2)}{1312}}\).

Simplify the expression inside the square root for potassium: \(Z_{eff} = \sqrt{\frac{(418.8)(16)}{1312}}\).

Substitute the given values for krypton into the equation: \(Z_{eff} = \sqrt{\frac{(1350.7)(4^2)}{1312}}\).

Simplify the expression inside the square root for krypton: \(Z_{eff} = \sqrt{\frac{(1350.7)(16)}{1312}}\).

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주요 개념

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Effective Nuclear Charge (Zeff)

Effective nuclear charge (Zeff) refers to the net positive charge experienced by an electron in a multi-electron atom. It accounts for the shielding effect of inner electrons that reduces the full nuclear charge felt by outer electrons. Understanding Zeff is crucial for predicting atomic properties such as ionization energy and atomic size.

Ionization Energy (IE)

Ionization energy (IE) is the energy required to remove an electron from an atom or ion in its gaseous state. It is a key factor in determining the reactivity of an element, as elements with low ionization energies tend to lose electrons easily, while those with high ionization energies hold onto their electrons more tightly. The values of IE vary across the periodic table.

Principal Quantum Number (n)

The principal quantum number (n) indicates the energy level of an electron in an atom and is a key factor in determining the electron's distance from the nucleus. Higher values of n correspond to electrons that are further from the nucleus and generally have higher energy. In the context of Zeff calculations, n is squared to reflect the increased energy associated with higher energy levels.