For a coordination number of four, the radius of Mn⁷⁺ has been estimated to be 39 pm. Estimate the charge density for the Mn⁷⁺ ion. Express your answer in C mm^–3. How does this compare with the charge density of Be²⁺ given in Table 21.4? Would you expect the bonding in Mn₂O₇ to be primarily ionic or primarily covalent? Explain.

Table 21.4

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TABLE 21.4 Some Properties of Group 2 (Alkaline Earth) Metals Be 4 111 41 Atomic number Atomic (metallic) radius, pm Ionic (M²¹) radius, pmª Electronegativity Charge density of M²+ (C mm ³) First ionization energy, kJ mol-¹ Electrode potential Eº, Vb Melting point, °C Boiling point, °C Density, g cm-3 at 20 °C Hardnessd Electrical conductivityd Flame color 1.5 1108 899.4 -1.85 1278 2970€ 1.85 ~5 39.7 None Mg 12 160 86 1.2 120 737.7 -2.356 648.8 1090 1.74 2.0 35.6 None Ca 20 197 114 1.0 52 589.7 -2.84 839 1483.6 1.55 1.5 40.6 Orange-red Sr 38 215 132 1.0 33 549.5 -2.89 769 1383.9 2.54 1.8 6.90 Scarlet Ba 56 222 149 0.9 23 502.8 -2.92 729 1637 3.60 ~2 3.20 Green