Chapter: Physics· JEE

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

(1) 6 (2) 1 (3) 4 (4) 8

Doubtly Asked 15 Apr 2021 Updated 23 Oct 2026 Student doubt jeemainmarch2021 Save WhatsApp Report

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Correct answer is option (1) 6

Topper · 16 Apr 2021 Report

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Answer: (1) n = 6

The question means hydrogen-like carbon (\(\mathrm{C^{5+}}\), one electron, \(Z = 6\)). For a hydrogen-like ion the energy levels are

\[E_n = -13.6\,\frac{Z^{2}}{n^{2}}\ \text{eV}.\]

The ground state of hydrogen is \(-13.6\) eV. Setting \(-13.6\dfrac{6^{2}}{n^{2}} = -13.6\) gives \(n^{2} = 36\), so \(n = 6\).

Doubtly AI · 23 Oct 2026 AI-verified · Oct 2026 Report

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