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

Since we know that, energy of hydrogen atom is $E=-13.6\frac{Z^2}{{\mathrm{n}}^2}$

where, Z is the atomic number and n is the energy state.

 $\therefore$For hydrogen atom, $\mathrm{Z}=1 \text{and }\mathrm{n}=1$

$\Rightarrow \mathrm{E}=\frac{-13.6(1{)}^2}{1^2}\Rightarrow \mathrm{E}=-13.6\mathrm{eV}\dots \dots \dots \text{(i)}$ For carbon atom, $\mathrm{Z}=6, \mathrm{n}=?\Rightarrow \mathrm{E}=\frac{-13.6(6{)}^2}{{\mathrm{n}}^2}\dots \dots \text{.}\left(\text{ii}\right)$

According to question, carbon has same energy as the ground state energy of hydrogen atom.

$\therefore$ From Eqs. (i) and (ii), we get $-13.6=\frac{-13.6(6{)}^2}{n^2}\Rightarrow n^2=6^2\Rightarrow n=6$