Multiple Choice
Which of the following best defines the effective nuclear charge (Z_{eff}) experienced by an electron in a multi-electron atom?
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10. Periodic Properties of the Elements
Periodic Trend: Effective Nuclear Charge
Multiple Choice
Rank the effective nuclear charge (Z_ext{eff}) experienced by a valence electron in the following atoms: Na, Mg, Al. Which of the following correctly orders them from lowest to highest Z_ext{eff}?
A
Al < Mg < Na
B
Na < Mg < Al
C
Na < Al < Mg
D
Mg < Na < Al
Verified step by step guidance1
Recall that the effective nuclear charge, \(Z_{\text{eff}}\), experienced by a valence electron is given by the equation \(Z_{\text{eff}} = Z - S\), where \(Z\) is the atomic number (number of protons) and \(S\) is the shielding constant representing the repulsion from other electrons.
Identify the atomic numbers for the elements: Sodium (Na) has \(Z=11\), Magnesium (Mg) has \(Z=12\), and Aluminum (Al) has \(Z=13\).
Consider the electron configurations to estimate shielding: Na is \([\text{Ne}] 3s^1\), Mg is \([\text{Ne}] 3s^2\), and Al is \([\text{Ne}] 3s^2 3p^1\). Since all have valence electrons in the third shell, the inner shells provide similar shielding.
Since the shielding \(S\) is roughly similar for these valence electrons, the effective nuclear charge \(Z_{\text{eff}}\) mainly depends on the increasing nuclear charge \(Z\) as you move from Na to Al.
Therefore, the order of \(Z_{\text{eff}}\) from lowest to highest is \(\text{Na} < \text{Mg} < \text{Al}\), because the increasing number of protons pulls the valence electrons closer with less relative shielding.
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