Question

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

• A. $8$
• B. $1$
• C. $6$
• D. $4$

Answer 1

The correct option is C $6$

Energy in $n^{\text{th}}$ state for hydrogen-like atom :
$E_n=-13.6\frac{Z^2}{n^2}$

According to the question :

$E_n$ of Carbon $=E_1$ of Hydrogen

$\Rightarrow -13.6\times \frac{6^2}{n^2}=-13.6\times \frac{1^2}{1^2}$

$\Rightarrow n=6$

Therefore, $\left(C\right)$ is the required answer.