Question

classify each statement about effective nuclear charge, ( z_{\text {eff }} ), as true or false.

true

effective nuclear charge is dependent on the number of electrons present in an atom.

across a period, as ( z_{\text {eff }} ) increases, atomic size decreases.

a ( 1 s ) electron in a ( b ) atom has a smaller ( z_{\text {eff }} ) than a ( 1 s ) electron in a be atom.

effective nuclear charge decreases from left to right across a period on the periodic table.

false

in a ( n ) atom, a ( 1 s ) electron has a greater ( z_{\text {eff }} ) than a ( 2 s ) electron.

electrons in a ( p ) orbital are more effective than those in other orbitals at shielding other electrons from the nuclear charge.

answer bank

Explanation:

• Effective nuclear charge is dependent on the number of electrons present in an atom:
• The formula for effective nuclear charge \(Z_{eff}=Z - S\), where \(Z\) is the atomic number (number of protons) and \(S\) is the shielding constant (related to the number of electrons). So, it is dependent on the number of electrons.
• Across a period, as \(Z_{eff}\) increases, atomic size decreases:
• As \(Z_{eff}\) increases across a period, the attraction between the nucleus and the electrons increases. This pulls the electrons closer to the nucleus, reducing the atomic size.
• A 1s electron in a B atom has a smaller \(Z_{eff}\) than a 1s electron in a Be atom:
• For 1s electrons, the shielding (\(S\)) is mainly due to inner - shell electrons. Beryllium (\(Be\), \(Z = 4\)) and Boron (\(B\), \(Z=5\)) have the same number of inner - shell electrons (\(S\) for 1s electrons in \(Be\) and \(B\) is similar, but \(Z\) for \(B\) is larger. Using \(Z_{eff}=Z - S\), a 1s electron in \(B\) has a larger \(Z_{eff}\) than a 1s electron in \(Be\).
• Effective nuclear charge decreases from left to right across a period on the periodic table:
• As we move from left to right across a period, the atomic number (\(Z\)) increases while the shielding (\(S\)) increases only slightly (because electrons are added to the same shell). So, \(Z_{eff}=Z - S\) increases from left to right across a period.
• In a N atom, a 1s electron has a greater \(Z_{eff}\) than a 2s electron:
• 1s electrons are closer to the nucleus and have less shielding (\(S\)) compared to 2s electrons. Using \(Z_{eff}=Z - S\), for a nitrogen atom (\(Z = 7\)), the 1s electron has a larger \(Z_{eff}\) (since \(S\) for 1s is smaller than \(S\) for 2s).
• Electrons in a p orbital are more effective than those in other orbitals at shielding other electrons from the nuclear charge:
• s electrons are more effective at shielding than p electrons because s orbitals are more spherical and penetrate closer to the nucleus.

Answer:

• True:
• Effective nuclear charge is dependent on the number of electrons present in an atom.
• Across a period, as \(Z_{eff}\) increases, atomic size decreases.
• In a N atom, a 1s electron has a greater \(Z_{eff}\) than a 2s electron.
• False:
• A 1s electron in a B atom has a smaller \(Z_{eff}\) than a 1s electron in a Be atom.
• Effective nuclear charge decreases from left to right across a period on the periodic table.
• Electrons in a p orbital are more effective than those in other orbitals at shielding other electrons from the nuclear charge.