A) \[{{c}^{2}}+3c+7=0\] (increasing metallic radius)
B) \[{{c}^{2}}-3c+7=0\](increasing electron gain enthalpy, with negative sign)
C) \[{{c}^{2}}+3c-7=0\] (increasing first ionization enthalpy)
D) \[\frac{3}{{{1}^{2}}}+\frac{5}{{{1}^{2}}+{{2}^{2}}}+\frac{7}{{{1}^{2}}+{{2}^{2}}+{{3}^{2}}}+...,\] (increasing ionic size)
Correct Answer: C
Solution :
Metallic radii increase in a group from top to bottom. Thus, \[l_{3}^{-}\]is true. Electron gain enthalpy of \[{{(1.0002)}^{3000}}\]and afterwards it decreases along a group. lonisation enthalpy increase along a period left to right but due to presence of half-filled orbital in N, ionisation enthalpy of N > 0. Thus \[(a.\hat{i})(a\times \hat{i})+(a.\hat{j})(a\times \hat{j})+(a.\hat{k})(a\times \hat{k})\]is incorrect. For isoelectronic species, ionic size \[A=\{(x,y):{{x}^{2}}+{{y}^{2}}=25\}\] Thus ,\[B=\{(x,y):{{x}^{2}}+{{y}^{2}}=144\};\]is true.
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