Question:
Which level of the single ionized carbon has the same energy as the ground state energy of hydrogen atom?
Correct Option: , 2
Solution:
Energy of H-atom is $\mathrm{E}=-13.6 \mathrm{Z}^{2} / \mathrm{n}^{2}$
for $H$-atom $Z=1$ \& for ground state, $n=1$
$\Rightarrow \mathrm{E}=-13.6 \times \frac{1^{2}}{1^{2}}=-13.6 \mathrm{eV}$
Now for carbon atom (single ionised), $Z=6$
$E=-13.6 \frac{Z^{2}}{n^{2}}=-13.6$
$\Rightarrow n^{2}=6^{2} \Rightarrow n=6$
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