Among the following elements, which has the largest ratio of second ionisation enthalpy to first ionisation enthalpy, $\mathrm{I}{\mathrm{E}}_2/I{\mathrm{E}}_1$?

Removing the first electron from $\mathrm{Na}$ leaves a noble-gas core ($\mathrm{Na}{}^{+}$, $\mathrm{Ne}$-like), so the second electron must come from a complete inner shell. $\mathrm{I}{\mathrm{E}}_2/I{\mathrm{E}}_1$ is about $4562/496\approx 9.2$ for Na, against only about 2 for Mg, Ca and Ba, where the second electron is the other valence electron.