Suppose the ionization energy of a hydrogen-like ion A is greater...

The ionization energy of a hydrogen-like ion in the ground state is given by $I = 13.6 Z^2$ eV.

Given $I_A > I_B$, we have $Z_A > Z_B$.

For the ground state, the principal quantum number is $n = 1$.

The electron speed is $u \propto Z$, which implies $u_A > u_B$.

The orbital angular momentum is $L = \dfrac{nh}{2\pi}$, which implies $L_A = L_B$.

The total energy is $E = -13.6 Z^2$ eV, which implies $E_A < E_B$.

The orbit radius is $r \propto \dfrac{1}{Z}$, which implies $r_A < r_B$.