The ratio of the ionization enthalpy of hydrogen and beryllium three positive is
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The energy of a one electron atom or ion in a given quantum state is (to a first approximation) proportional to the square of the nuclear charge, Z^2. The ionization energy is also proportional to Z^2, since that is the difference between the ground state of the atom/ion and the energy of the separated ion plus electron.
The charge of Be^(4+) is four times that of H^+, so the ionization energy of Be^(3+) is 4^2 or 16 times that of H.
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