Variation in Atomic and Ionic Sizes — Revision Notes

⚡ 30-Second Revision

Atomic Radius Trend (Across a Period) — Decrease $\rightarrow$ Constant $\rightarrow$ Slight Increase (e.g., 3d series). \n- Atomic Radius Trend (Down a Group): 3d to 4d (Increase); 4d to 5d (Near Constant due to Lanthanoid Contraction). \n- Lanthanoid Contraction Cause: Poor shielding by 4f electrons. \n- Lanthanoid Contraction Consequences: Similar sizes of 4d & 5d elements (e.g., Zr/Hf); similar chemical properties; higher densities of 5d elements. \n- Ionic Radius Trend: Cations < Parent Atom. Higher positive charge $\implies$ smaller ionic radius ($Fe^{2+} > Fe^{3+}$). Decreases across a series for same charge ($Cr^{2+} > Mn^{2+}$).

2-Minute Revision

The size of transition elements, measured as atomic or ionic radius, follows specific patterns. Across a transition series (e.g., 3d), atomic radii initially decrease due to increasing effective nuclear charge ($Z_{eff}$).

In the middle, they become relatively constant as increasing $Z_{eff}$ is balanced by increasing electron-electron repulsion. Towards the end, a slight increase occurs due to enhanced electron-electron repulsion in filled d-orbitals.

Down a group, radii increase from 3d to 4d series. However, a critical exception is the near identical sizes of 4d and 5d elements (e.g., Zr and Hf). This is due to lanthanoid contraction, caused by the poor shielding of 4f electrons, which leads to a higher $Z_{eff}$ for 5d elements.

Consequences include similar chemical properties for 4d/5d pairs and higher densities for 5d elements. Ionic radii generally decrease with increasing positive charge for the same element and decrease across a series for ions of the same charge.

5-Minute Revision

Understanding the variation in atomic and ionic sizes of transition elements is crucial. Atomic radius, typically metallic radius for d-block, is influenced by effective nuclear charge ($Z_{eff}$), shielding effect, and electron-electron repulsion.

\n\nAcross a Period (e.g., 3d series, Sc to Zn): \n1. Initial Decrease (Sc to Cr/Mn): $Z_{eff}$ increases, d-electrons shield poorly, pulling outer electrons closer. \n2. Near Constancy (Fe, Co, Ni): Balance between increasing $Z_{eff}$ and increasing electron-electron repulsion among d-electrons.

\n3. Slight Increase (Cu to Zn): Enhanced electron-electron repulsion in fully filled d-orbitals dominates. \n\nDown a Group: \n1. 3d to 4d Series: Atomic radii increase due to the addition of a new electron shell.

\n2. 4d to 5d Series: Atomic radii are remarkably similar (e.g., Zr (160 pm) and Hf (159 pm)). This is Lanthanoid Contraction. \n * Cause: Poor shielding of 4f electrons (which are filled from Ce to Lu, before 5d).

The diffuse 4f orbitals are ineffective at screening the increasing nuclear charge, leading to a higher $Z_{eff}$ for subsequent 5d elements. \n * Consequences: \n * Similar Sizes: 4d and 5d elements in the same group have nearly identical radii.

\n * Similar Chemical Properties: Due to similar sizes and $Z_{eff}$. \n * Higher Densities: 5d elements have much higher atomic masses but similar volumes, leading to higher densities. \n * Higher Ionization Enthalpies: Stronger nuclear pull makes it harder to remove electrons.

\n\nIonic Radii: \n* Cations are smaller than their parent atoms. \n* For the same element, higher positive oxidation state means smaller ionic radius (e.g., $Fe^{3+}$ < $Fe^{2+}$). \n* Across a series, for a given oxidation state, ionic radii generally decrease due to increasing $Z_{eff}$ (e.

g., $Cr^{2+}$ > $Mn^{2+}$ > $Fe^{2+}$). \n\nKey Takeaway: Master lanthanoid contraction and its consequences, and the non-uniform trend across a transition series.

Prelims Revision Notes

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Atomic Radii Trends in Transition Elements:\n * Across a Period (e.g., 3d series: Sc to Zn):\n * Initial decrease (Sc to Cr/Mn) due to increasing $Z_{eff}$ (d-electrons shield poorly). \n * Near constancy (Fe, Co, Ni) due to balance between increasing $Z_{eff}$ and increasing electron-electron repulsion. \n * Slight increase (Cu to Zn) due to dominant electron-electron repulsion in filled d-orbitals.\n * Down a Group:\n * 3d to 4d series: Increase in size (new shell added). \n * 4d to 5d series: Near identical sizes. This is Lanthanoid Contraction.\n2. Lanthanoid Contraction:\n * Definition: Steady decrease in atomic/ionic radii across the lanthanoid series (Ce to Lu). \n * Cause: Very poor shielding effect of 4f electrons. 4f orbitals are diffuse and ineffective at screening the increasing nuclear charge for outer electrons. This leads to a higher effective nuclear charge experienced by 5d and 6s electrons. \n * Consequences:\n * Similar Atomic/Ionic Radii: 4d and 5d elements in the same group have almost identical sizes (e.g., Zr (160 pm) and Hf (159 pm); Nb and Ta). \n * Similar Chemical Properties: Due to similar sizes and $Z_{eff}$ values, 4d and 5d elements in the same group show strong chemical resemblances. \n * Higher Densities of 5d Elements: Higher atomic masses combined with similar volumes (due to contraction) lead to significantly higher densities for 5d elements. \n * Higher Ionization Enthalpies: Stronger nuclear pull makes electron removal harder. \n * Higher Electronegativity: Increased nuclear attraction on valence electrons.\n3. Ionic Radii:\n * Cations are always smaller than their parent atoms. \n * For the same element, ionic radius decreases with increasing positive oxidation state (e.g., $Fe^{2+}$ > $Fe^{3+}$). \n * Across a transition series, for a given oxidation state, ionic radii generally decrease due to increasing $Z_{eff}$ (e.g., $Cr^{2+}$ > $Mn^{2+}$ > $Fe^{2+}$).

Vyyuha Quick Recall

To remember the trend across a 3d series: Decrease, Constant, Increase. Think: 'DCI' (like a detective agency) for d-block sizes. \nFor Lanthanoid Contraction consequences: Similar Sizes, Similar Chemistry, Higher Density. Think: '3S-HD' (like a high-definition movie with three S's).