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

1. 1
2. 6
3. 4
4. 8

Correct answer: 6

Solution

For a one-electron ion E = -13.6 Z^2/n^2 eV. Carbon has Z = 6, so E = -13.6*36/n^2. Setting this equal to the hydrogen ground state (-13.6 eV) gives n^2 = 36, i.e. n = 6.

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