When the ionization energies of a series of isoelectronic atoms and ions are compared, an interesting relationship is observed for some of them. In particular, if the square root of the ionization energy (in kJ mol^-1) for the series Li, Be⁺, B²⁺, C³⁺, N⁴⁺, O⁵⁺, and F⁶⁺ is plotted against the atomic number (Z) of the species, a linear relationship is obtained. The corresponding graph for the series Na, Mg⁺, Al²⁺, Si³⁺, P⁴⁺, S⁵⁺, and Cl⁶⁺ is also linear. The graph is shown below.

The equations for the two lines joining the points are

Explain the origin of these relationships and the differences in the numerical coefficients.

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Second-row elements: VE₁ = 18.4Z - 32.0 Third-row elements: VE 13.7Z 127 = (9.6) (9.7)