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Chapter 9: Problem 93

In multielectron atoms many of the periodic trends can be explained in terms of \(Z_{\text {eff }}\) Consider the following statements and discuss whether or not the statement is true or false. (a) Electrons in a \(p\) orbital are more effective than electrons in the \(s\) orbitals in shielding other electrons from the nuclear charge. (b) \(\mathrm{Z}_{\text {eff }}\) for an electron in an \(s\) orbital is lower than that for an electron in a \(p\) orbital in the same shell. (c) \(Z_{\text {eff }}\) is usually less than \(Z.\) (d) Electrons in orbitals having \(\ell=1\) penetrate better than those with \(\ell=2.\) (e) \(\mathrm{Z}_{\text {eff }}\) for the orbitals of the elements \(\mathrm{Na}(3 s)\) \(\mathrm{Mg}(3 s), \mathrm{Al}(3 p), \mathrm{P}(3 p),\) and \(\mathrm{S}(3 p)\) are in the order \(Z_{\text {eff }}(\mathrm{Na})<\mathrm{Z}_{\text {eff }}(\mathrm{Mg})>\mathrm{Z}_{\text {eff }}(\mathrm{Al})<\mathrm{Z}_{\text {eff }}(\mathrm{P})>\mathrm{Z}_{\text {eff }}(\mathrm{S}).\)

Short Answer

Expert verified
The correct answers are: (a) False, (b) False, (c) True, (d) True, (e) False. The explanation for each statement relies on understanding how the effective nuclear charge and electron shielding work in multi-electron atoms.

Step by step solution

01

Evaluate Statement (a)

Statement (a) says that electrons in a \(p\) orbital are more effective in shielding other electrons from the nuclear charge than electrons in the \(s\) orbital. However, this is actually false. Electrons in the \(s\) orbital are closer to the nucleus and hence more effective at shielding than those in the \(p\) orbital.
02

Evaluate Statement (b)

Statement (b) claims that the effective nuclear charge for an electron in an \(s\) orbital is lower than that for an electron in a \(p\) orbital in the same shell. This is false. Electrons in an \(s\) orbital experience a higher effective nuclear charge than those in a \(p\) orbital in the same shell because \(s\) electrons are closer to the nucleus.
03

Evaluate Statement (c)

Statement (c) states that \(Z_{\text {eff }}\) is usually less than \(Z.\) This is true. The effective nuclear charge is less than the actual nuclear charge because of shielding by other electrons in the atom.
04

Evaluate Statement (d)

Statement (d) says that electrons in orbitals having \(\ell=1\) penetrate better than those with \(\ell=2.\) This is true. The value of \(\ell\), the azimuthal quantum number, reflects the shape of the orbital; \(\ell=1\) represents \(p\) orbitals and \(\ell=2\) represents \(d\) orbitals. \(p\) orbitals penetrate closer to the nucleus compared to \(d\) orbitals, due to their shapes and node structures.
05

Evaluate Statement (e)

Statement (e) provides a specific order for the effective nuclear charge for orbitals of different elements. This order implies that \(Z_{\text {eff }}(\mathrm{Na})<\mathrm{Z}_{\text {eff }}(\mathrm{Mg})>\mathrm{Z}_{\text {eff }}(\mathrm{Al})<\mathrm{Z}_{\text {eff }}(\mathrm{P})>\mathrm{Z}_{\text {eff }}(\mathrm{S}).\) However, the correct order is \(Z_{\text {eff }}(\mathrm{Na})<\mathrm{Z}_{\text {eff }}(\mathrm{Mg})<\mathrm{Z}_{\text {eff }}(\mathrm{Al})<\mathrm{Z}_{\text {eff }}(\mathrm{P})<\mathrm{Z}_{\text {eff }}(\mathrm{S})\), so statement (e) is false.

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Most popular questions from this chapter

Some electron affinities are negative quantities, and some are zero or positive. Why is this not also the case with ionization energies?

Compare the elements \(\mathrm{Na}, \mathrm{Mg}, \mathrm{O},\) and \(\mathrm{P}.\) (a) Place the elements in order of increasing ionization energy. (b) Place the elements in order of increasing electron affinity.

Use principles established in this chapter to arrange the following atoms in order of increasing value of the first ionization energy: $\mathrm{Sr}, \mathrm{Cs}, \mathrm{S}, \mathrm{F}, \mathrm{As}.$

A method for estimating electron affinities is to extrapolate \(Z_{\text {eff }}\) values for atoms and ions that contain the same number of electrons as the negative ion of interest. Use the data in the table on the next page to answer the questions that follow. $$\begin{array}{lll} \hline \begin{array}{l} \text { Atom or lon: } \\ \text { I(kJmol }^{-1} \text {) } \end{array} & \begin{array}{l} \text { Atom or lon: } \\ \text { I(kJmol }^{-1} \text {) } \end{array} & \begin{array}{l} \text { Atom or lon: } \\ \text { I(kJmol }^{-1} \text {) } \end{array} \\ \hline \text { Ne: 2080 } & \text { F: 1681 } & \text { O: } 1314 \\ \text { Na }^{+}: 4565 & \text { Ne }^{+}: 3963 & \text { F }^{+}: 3375 \\ \text { Mg }^{2+} \text { : 7732 } & \text { Na }^{2+}: 6912 & \text { Ne }^{2+}: 6276 \\ \text { A1 }^{\text {3 }^{+}: 11,577} & \text { Mg }^{3+}: 10,548 & \text { Na }^{3+}: 9540 \\ \hline \end{array}$$ (a) Estimate the electron affinity of \(F\), and compare it with the experimental value. (b) Estimate the electron affinities of \(\mathrm{O}\) and \(\mathrm{N}\) (c) Examine your results in terms of penetration and screening.

For each of the following pairs, indicate the atom that has the larger size: (a) Te or Br; (b) \(\mathrm{K}\) or \(\mathrm{Ca} ;\) (c) Ca or Cs; (d) \(\mathrm{N}\) or \(\mathrm{O} ;\) (e) \(\mathrm{O}\) or \(\mathrm{P} ;\) (f) \(\mathrm{Al}\) or \(\mathrm{Au}.\)
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