Question

in order to understand the periodic trend of atomic radius across a row, we need to understand the concept of effective nuclear charge (z_eff). z_eff is the charge that valence electrons experience after core electrons shield the nuclear charge. valence electrons do not shield each other from the charge. z_eff is calculated using the following equation: z_eff = atomic number(z) - core electrons (s). complete the table and calculate zeff for the following elements. 4. as you go across a row (period) in the periodic table, does the positive charge experienced by the valence electrons (z_eff) increase decrease, or stay the same? 5. would the attraction of valence electrons of argon to its nucleus be the same, greater than, or less than the attraction of the valence electrons of sodium to a sodium nucleus? created by emily heider

Explanation:

Step1: Determine electron configuration

• Na (Sodium): Atomic number \(Z = 11\). Electron configuration is \(1s^{2}2s^{2}2p^{6}3s^{1}\).
• Al (Aluminum): Atomic number \(Z = 13\). Electron configuration is \(1s^{2}2s^{2}2p^{6}3s^{2}3p^{1}\).
• P (Phosphorus): Atomic number \(Z = 15\). Electron configuration is \(1s^{2}2s^{2}2p^{6}3s^{2}3p^{3}\).
• Cl (Chlorine): Atomic number \(Z = 17\). Electron configuration is \(1s^{2}2s^{2}2p^{6}3s^{2}3p^{5}\).
• Ar (Argon): Atomic number \(Z = 18\). Electron configuration is \(1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}\).

Step2: Calculate number of valence electrons

• Valence electrons are in the outermost shell.
• Na: \(3s^{1}\), so \(1\) valence electron.
• Al: \(3s^{2}3p^{1}\), so \(3\) valence electrons.
• P: \(3s^{2}3p^{3}\), so \(5\) valence electrons.
• Cl: \(3s^{2}3p^{5}\), so \(7\) valence electrons.
• Ar: \(3s^{2}3p^{6}\), so \(8\) valence electrons.

Step3: Calculate number of core electrons

• Core electrons = Total electrons - Valence electrons.
• Na: \(11 - 1=10\) core electrons.
• Al: \(13 - 3 = 10\) core electrons.
• P: \(15 - 5=10\) core electrons.
• Cl: \(17 - 7 = 10\) core electrons.
• Ar: \(18 - 8=10\) core electrons.

Step4: Calculate \(Z_{eff}\)

• Using formula \(Z_{eff}=Z - \text{core electrons}\).
• Na: \(Z_{eff}=11 - 10 = 1\).
• Al: \(Z_{eff}=13 - 10=3\).
• P: \(Z_{eff}=15 - 10 = 5\).
• Cl: \(Z_{eff}=17 - 10=7\).
• Ar: \(Z_{eff}=18 - 10 = 8\).

Step5: Answer question 4

• As we go across a row (period) in the periodic table, \(Z_{eff}\) increases. Because atomic number \(Z\) increases while core electrons remain the same (\(Z_{eff}=Z-\text{core electrons}\), and core electrons are constant for elements in the same period).

Step6: Answer question 5

• The attraction of valence electrons to the nucleus is related to \(Z_{eff}\).
• \(Z_{eff}\) for Ar (\(8\)) is greater than \(Z_{eff}\) for Na (\(1\)). So the attraction of valence electrons of argon to its nucleus is greater than the attraction of the valence electrons of sodium to a sodium nucleus.

Answer:

	Na	Al	P	Cl	Ar
# Valence electrons	\(1\)	\(3\)	\(5\)	\(7\)	\(8\)
# Core electrons	\(10\)	\(10\)	\(10\)	\(10\)	\(10\)
\(Z_{eff}\)	\(1\)	\(3\)	\(5\)	\(7\)	\(8\)

1. \(Z_{eff}\) increases as we go across a row (period) in the periodic table.

1. The attraction of valence electrons of argon to its nucleus is greater than the attraction of the valence electrons of sodium to a sodium nucleus.