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