Which level of the single ionized carbon has the same energy as the ground state energy of hydrogen atom ?  
Option: 1 6
Option: 2 1
Option: 3 4
Option: 4 8

Answers (1)

The energy of H-atom is \mathrm{E}=-13.6 \times\frac{ \mathrm{Z}^{2 }}{ \mathrm{n}^{2}}
for H-atom Z=1 for the ground state, n=1
\Rightarrow \mathrm{E}=-13.6 \times \frac{1^{2}}{1^{2}}=-13.6 \mathrm{eV}
Now for carbon atom (single ionized), Z=6
\mathrm{E}=-13.6 \frac{\mathrm{Z}^{2}}{\mathrm{n}^{2}}=-13.6 \\ \quad \Rightarrow \mathrm{n}^{2}=6^{2} \Rightarrow \mathrm{n}=6

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