Which level of the single ionized carbon has

Question:

Which level of the single ionized carbon has

the same energy as the ground state energy of hydrogen atom?

  1. (1) 1

  2. (2) 6

  3. (3) 4

  4. (4) 8


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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