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JEE Main 2021 (17 Mar, Shift 1) · Energy of the Electron & Energy Levels

Energy of the Electron & Energy Levels question from JEE Main 2021 (17 Mar, Shift 1)

Q36JEE Main 2021 · 17 MAR · SHIFT 1Medium

Energy of the Electron & Energy Levels

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

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Answer: (b)

Treat the carbon ion as hydrogen-like with $Z = 6$ : $E_n = -13.6\,\frac{36}{n^2}$ eV.
Set equal to $-13.6$ eV: $\frac{36}{n^2} = 1 \Rightarrow n = 6$
So the answer is (b) 6.

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