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

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

JEE MainJEE Main 2021Atoms

Solution:

Energy of $H$ -atom is $E =-13.6 Z ^{2} / n ^{2}$
for $H$ -atom $Z =1 \&$ for ground state, $n =1$
$\Rightarrow E =-13.6 \times \frac{1^{2}}{1^{2}}=-13.6 \,eV$
Now for carbon atom (single ionised), $Z=6$
$E =-13.6 \frac{ Z ^{2}}{ n ^{2}}=-13.6 $ (given)
$\Rightarrow n ^{2}=6^{2} \Rightarrow n =6$