Question

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

• A. 1
• B. 6
• C. 4
• D. 8

Answer 1

Answer: (B)

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