A hydrogen-like ion has one electron. The energy needed to remove that electron when it is in the first excited state ($n = 2$) is $30.6\ \text{eV}$. How much energy, in $\text{eV}$, is needed to lift the electron of this ion from its ground state to the orbit $n = 3$? Use $E_n = -13.6\,\dfrac{Z^2}{n^2}\ \text{eV}$ and give the answer to the nearest integer.