1. Use the hydrogen-like energy formula

For a hydrogen-like ion, the energy of the $n$th level is

$E_n=-\frac{13.6Z^2}{n^2}\,\text{eV}$

where $Z$ is the atomic number.

2. Identify the ion

Single ionized carbon is $\mathrm{C}^+$.

Carbon has atomic number $Z=6$. However, the formula above applies strictly to hydrogen-like ions (single-electron systems), such as $\mathrm{C}^{5+}$, not $\mathrm{C}^+$.

So the intended question is almost certainly about a hydrogen-like carbon ion, for which we take $Z=6$.

3. Ground state energy of hydrogen

For hydrogen, $Z=1$ and ground state means $n=1$:

$E_1(\mathrm{H})=-13.6\,\text{eV}$

4. Set the carbon ion energy equal to hydrogen ground state energy

For hydrogen-like carbon,

$E_n=-\frac{13.6\times 6^2}{n^2}=-\frac{13.6\times 36}{n^2}$

We want

$-\frac{13.6\times 36}{n^2}=-13.6$

Cancelling $-13.6$ on both sides:

$\frac{36}{n^2}=1$

$n^2=36$

$n=6$

5. Check options

• A: $8$ ❌
• B: $6$ ✅
• C: $1$ ❌
• D: $4$ ❌

Therefore, the required level is $n=6$.