Which level of the single ionized carbon has the same energy as the ground state energy of hydrogen atom?

Energy of carbon in  $n^{th}$ state = energy of hydrogen atom in ground state

$$\begin{gathered} -\frac{13.6z_c^2}{n^2}=-\frac{13.6z_h^2}{{n_g}^2} \\ \Rightarrow -\frac{13.6(6{)}^2}{n^2}=-\frac{13.6(1{)}^2}{(1{)}^2} \\ \Rightarrow n^2=6^2 \\ \Rightarrow n=6 \end{gathered}$$