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Chapter 7: Problem 13

(a) What is meant by the term effective nuclear charge? (b) How does the effective nuclear charge experienced by the valence electrons of an atom vary going from left to right across a period of the periodic table?

Short Answer

Expert verified
(a) Effective nuclear charge refers to the net positive charge experienced by an electron in an atom, determined by the difference between the number of protons in the nucleus and the shielding effect of lower-energy orbitals' electrons. (b) As we move from left to right across a period in the periodic table, the effective nuclear charge experienced by the valence electrons increases due to the increasing number of protons in the nucleus and a relatively constant shielding effect.

Step by step solution

01

(Explanation of Effective Nuclear Charge)

(Effective nuclear charge refers to the net positive charge experienced by an electron in an atom. It is determined by the difference between the number of protons in the nucleus (which defines the nuclear charge) and the shielding effect of electrons between the nucleus and the electron in question. The shielding effect occurs because electrons in lower-energy orbitals create a repulsive force that shields the outer electrons from the full pull of the nucleus.)
02

(Variation of Effective Nuclear Charge across a Period)

(As we move from left to right across a period in the periodic table, the effective nuclear charge experienced by the valence electrons increases. This is because the number of protons in the nucleus increases, resulting in a higher nuclear charge overall. Additionally, as we move across a period, electrons are added to the same energy level, thus the shielding effect remains relatively constant. Consequently, electrons experience a stronger net positive charge, or a greater effective nuclear charge, as we move from left to right across a period.)
03

(Summary)

(In summary, effective nuclear charge is the net positive charge experienced by an electron in an atom, which is influenced by the number of protons in the nucleus and the shielding effect of other electrons. When moving from left to right across a period in the periodic table, the effective nuclear charge experienced by the valence electrons increases due to the increasing nuclear charge and a relatively constant shielding effect.)

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Most popular questions from this chapter

Chlorine reacts with oxygen to form \(\mathrm{Cl}_{2} \mathrm{O}_{7}\). (a) What is the name of this product (see Table \(2.6\) )? (b) Write a balanced equation for the formation of \(\mathrm{Cl}_{2} \mathrm{O}_{7}(l)\) from the elements. (c) Under usual conditions, \(\mathrm{Cl}_{2} \mathrm{O}_{7}\) is a colorless liquid with a boiling point of \(81^{\circ} \mathrm{C}\). Is this boiling point expected or surprising? (d) Would you expect \(\mathrm{Cl}_{2} \mathrm{O}_{7}\) to be more reactive toward \(\mathrm{H}^{+}(a q)\) or \(\mathrm{OH}^{-}(a q)\) ? (e) If the oxygen in \(\mathrm{Cl}_{2} \mathrm{O}_{7}\) is considered to have the \(-2\) oxidation state, what is the oxidation state of the \(\mathrm{Cl}\) ? What is the electron configuration of \(\mathrm{Cl}\) in this oxidation state?

(a) If the core electrons were totally effective at screening the valence electrons and the valence electrons provided no screening for each other, what would be the effective nuclear charge acting on the \(3 s\) and \(3 p\) valence electrons in \(\mathrm{P}\) ? (b) Repeat these calculations using Slater's rules. (c) Detailed calculations indicate that the effective nuclear charge is \(5.6+\) for the \(3 s\) electrons and \(4.9+\) for the \(3 p\) electrons. Why are the values for the \(3 s\) and \(3 p\) electrons different? (d) If you remove a single electron from a P atom, which orbital will it come from?

(a) Why does xenon react with fluorine, whereas neon does not? (b) Using appropriate reference sources, look up the bond lengths of Xe-F bonds in several molecules. How do these numbers compare to the bond lengths calculated from the atomic radii of the elements?

(a) Which ion is smaller, \(\mathrm{Co}^{3+}\) or \(\mathrm{Co}^{4+}\) ? (b) In a lithium-ion battery that is discharging to power a device, for every \(\mathrm{Li}^{+}\)that inserts into the lithium cobalt oxide electrode, \(\mathrm{a} \mathrm{Co}^{4+}\) ion must be reduced to \(\mathrm{Co}^{3+}\) ion to balance charge. Using the \(C R C\) Handbook of Chemistry and Physics or other standard reference, find the ionic radii of \(\mathrm{Li}^{+}, \mathrm{Co}^{3+}\), and \(\mathrm{Co}^{4+}\). Order these ions from smallest to largest. (c) Will the lithium cobalt electrode expand or contract as lithium ions are inserted? (d) Lithium is not nearly as abundant as sodium. If sodium ion batteries were developed that function as lithium ion ones, do you think "sodium cobalt oxide" would still work as the electrode material? Explain. (e) If you don't think cobalt would work as the redox-active partner ion in the sodium version of the electrode, suggest an alternative metal ion and explain your reasoning.

Moseley established the concept of atomic number by studying X rays emitted by the elements. The \(X\) rays emitted by some of the elements have the following wavelengths: $$ \begin{array}{lc} \hline \text { Element } & \text { Wavelength } \\ \hline \mathrm{Ne} & 14.610 \\ \mathrm{Ca} & 3.358 \\ \mathrm{Zn} & 1.435 \\ \mathrm{Zr} & 0.786 \\ \mathrm{Sn} & 0.491 \\ \hline \end{array} $$ (a) Calculate the frequency, \(\nu\), of the \(\mathrm{X}\) rays emitted by each of the elements, in Hz. (b) Plot the square root of \(\nu\) versus the atomic number of the element. What do you observe about the plot? (c) Explain how the plot in part (b) allowed Moseley to predict the existence of undiscovered elements. (d) Use the result from part (b) to predict the \(\mathrm{X}\)-ray wavelength emitted by iron. (e) A particular element emits X rays with a wavelength of \(0.980 \AA\). What element do you think it is?
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