Problem 45
Question
The correct order of ionic radii of \(\mathrm{Y}^{3+}, \mathrm{La}^{3+}, \mathrm{Eu}^{3+}\) and \(\mathrm{Lu}^{3+}\) is (a) \(\mathrm{Lu}^{3+}<\mathrm{Eu}^{3+}<\mathrm{La}^{3+}<\mathrm{Y}^{3+}\) (b) \(\mathrm{La}^{3+}<\mathrm{Eu}^{3+}<\mathrm{Lu}^{3+}<\mathrm{Y}^{3+}\) (c) \(\mathrm{Y}^{3+}<\mathrm{La}^{3+}<\mathrm{Eu}^{3+}<\mathrm{Lu}^{3+}\) (d) \(\mathrm{Y}^{3+}<\mathrm{Lu}^{3+}<\mathrm{Eu}^{3+}<\mathrm{La}^{3+}\)
Step-by-Step Solution
Verified Answer
The correct order is (d) \(\mathrm{Y}^{3+}<\mathrm{Lu}^{3+}<\mathrm{Eu}^{3+}<\mathrm{La}^{3+}\).
1Step 1: Understanding Ionic Radii
The ionic radius is the measure of an atom's ion in a crystal lattice. It decreases across a period due to an increase in the effective nuclear charge which pulls the electron cloud closer to the nucleus.
2Step 2: Analyze the Elements
The cations given are part of the Lanthanide series and the transition metal Y (yttrium). Their order in the periodic table from left to right is: La (Lanthanum), Ce, Pr, Nd, Pm, Sm, Eu (Europium), Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu (Lutetium). Y (yttrium) is placed before all those elements in the periodic table.
3Step 3: Compare Lanthanide Contraction
Lanthanide contraction is the gradual decrease in the ionic sizes of lanthanide elements (La to Lu). As we move from La to Lu, there is a decrease in ionic radii due to poor shielding effect of the f-electrons. Therefore, Lu
4Step 4: Arrange the Cations by Ionic Radii
Based on the lanthanide contraction and the positioning of Y, the correct order from smallest to largest ionic radius is: \(\mathrm{Lu}^{3+} < \mathrm{Y}^{3+} < \mathrm{Eu}^{3+} < \mathrm{La}^{3+}\). This matches with option (d).
Key Concepts
Lanthanide ContractionPeriodic Table OrderEffective Nuclear Chargef-electron Shielding
Lanthanide Contraction
Lanthanide contraction refers to the subtle, gradual decrease in the ionic radii of the lanthanide series elements as we move from Lanthanum (La) to Lutetium (Lu) in the periodic table.
This phenomenon is due to the presence of poorly shielding f-electrons.
The f-electrons provide less shielding for the nuclear charge compared to d or s electrons.
This results in stronger attraction between the nucleus and the outer electrons, causing the ionic radii to decrease. In essence, as we progress from La to Lu, each successive element experiences a slightly greater nuclear pull on its outer electrons, leading to a smaller ionic radius.
This contraction is significant because it influences various chemical properties and behaviors of the lanthanides.
Lanthanide contraction affects not just the lanthanides themselves, but also elements that follow them in the periodic table, leading to more similar properties between certain transition metals that might otherwise differ significantly.
This phenomenon is due to the presence of poorly shielding f-electrons.
The f-electrons provide less shielding for the nuclear charge compared to d or s electrons.
This results in stronger attraction between the nucleus and the outer electrons, causing the ionic radii to decrease. In essence, as we progress from La to Lu, each successive element experiences a slightly greater nuclear pull on its outer electrons, leading to a smaller ionic radius.
This contraction is significant because it influences various chemical properties and behaviors of the lanthanides.
Lanthanide contraction affects not just the lanthanides themselves, but also elements that follow them in the periodic table, leading to more similar properties between certain transition metals that might otherwise differ significantly.
Periodic Table Order
The arrangement of elements in the periodic table follows a logical sequence based on atomic number, where each element's place tells us about its electronic structure.
For example, in the lanthanide series, the order from La (Lanthanum) to Lu (Lutetium) follows this logical sequence, each with an additional proton and electron. Yttrium (Y), although a transition metal and not a lanthanide, fits into this sequence, but it precedes all the lanthanides. This placement of elements allows us to predict and compare properties such as ionic radii, reactivity, and more, due to the order and pattern in the periodic table.
In our specific exercise, understanding the order helps explain why yttrium (Y) is positioned before the lanthanide series and how this relates to its ionic size compared to other ions. Recognizing this logical order further helps when comparing elements across periods and groups in the periodic table.
For example, in the lanthanide series, the order from La (Lanthanum) to Lu (Lutetium) follows this logical sequence, each with an additional proton and electron. Yttrium (Y), although a transition metal and not a lanthanide, fits into this sequence, but it precedes all the lanthanides. This placement of elements allows us to predict and compare properties such as ionic radii, reactivity, and more, due to the order and pattern in the periodic table.
In our specific exercise, understanding the order helps explain why yttrium (Y) is positioned before the lanthanide series and how this relates to its ionic size compared to other ions. Recognizing this logical order further helps when comparing elements across periods and groups in the periodic table.
Effective Nuclear Charge
Effective nuclear charge refers to the net positive charge experienced by an electron in a multi-electron atom.
It is calculated as the difference between the total nuclear charge and the shielding effect caused by other electrons. When electrons are added to the outer shells, especially those poorly shielded, the inner electrons don't significantly shield the outer electrons from the full effect of the protons in the nucleus. This means that as atomic number increases, without effective shielding, the effective nuclear charge felt by outer electrons increases, pulling them closer to the nucleus and decreasing ionic radii.
In the context of the lanthanides and yttrium, as more protons are added going from lanthanum to lutetium, this increased effective nuclear charge contributes to the lanthanide contraction we discussed earlier.
It is calculated as the difference between the total nuclear charge and the shielding effect caused by other electrons. When electrons are added to the outer shells, especially those poorly shielded, the inner electrons don't significantly shield the outer electrons from the full effect of the protons in the nucleus. This means that as atomic number increases, without effective shielding, the effective nuclear charge felt by outer electrons increases, pulling them closer to the nucleus and decreasing ionic radii.
In the context of the lanthanides and yttrium, as more protons are added going from lanthanum to lutetium, this increased effective nuclear charge contributes to the lanthanide contraction we discussed earlier.
f-electron Shielding
The f-electron shielding effect comes into play significantly with the lanthanide series. Unlike s or p electrons, f-electrons are deeply buried within the atom's electron cloud and do not efficiently shield the outer electrons from the increased nuclear charge.
As a result, the electrons in outer orbits feel a stronger attraction to the nucleus than they would if there were more effective shielding. This insufficient shielding is why as we move across the lanthanide series, each successive atom experiences a slightly stronger nuclear pull, contributing to the reduction in radii and leading to the notable lanthanide contraction.
Understanding f-electron shielding is crucial for explaining why there is a size reduction across the lanthanides and how it affects chemical properties and reactivity. Additionally, poor f-electron shielding is a key factor in why the lanthanide series behaves as it does and affects the elements that follow it in the periodic table.
As a result, the electrons in outer orbits feel a stronger attraction to the nucleus than they would if there were more effective shielding. This insufficient shielding is why as we move across the lanthanide series, each successive atom experiences a slightly stronger nuclear pull, contributing to the reduction in radii and leading to the notable lanthanide contraction.
Understanding f-electron shielding is crucial for explaining why there is a size reduction across the lanthanides and how it affects chemical properties and reactivity. Additionally, poor f-electron shielding is a key factor in why the lanthanide series behaves as it does and affects the elements that follow it in the periodic table.
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