The following orbital energies ($E$) are compared. Identify the correct sets (I) E 2 (H) = E 2 (H) (II) E 3 (H) = E 3 (He) (III) E 2 s(H)

Question

The following orbital energies ($E$) are compared. Identify the correct sets   (I) E 2 (H) = E 2 (H) (II) E 3 (H) = E 3 (He) (III) E 2 s(H) < E 2 s(He) (IV) E 3 s(He) < E 3 s(H)

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Step 1: Understanding Orbital Energy Comparisons - The energy levels of hydrogen-like atoms depend on the principal quantum number and nuclear charge. - For hydrogen ($H$), energy levels follow: $$ E_n = -\frac{13.6}{n^2} \text{ eV} $$ - For helium ($He^+$), the energy levels are modified by the nuclear charge $Z$: $$ E_n = -\frac{13.6 Z^2}{n^2} \text{ eV} $$ Step 2: Evaluating the Given Statements - (I) $E_2(H) = E_2(H)$: This is trivially true. - (II) $E_3(H) = E_3(He)$: Incorrect, as energy levels differ for different atomic numbers. - (III) $E_{2s}(H)<E_{2s}(He)$: Incorrect, as higher nuclear charge in $He$ causes lower energy. - (IV) $E_{3s}(He)<E_{3s}(H)$: True, since helium has a stronger nuclear charge, lowering energy levels. Thus, the correct answer is $ \mathbf{(4)} $ I, IV only.

Answer

Answer

I, II, III, IV

Answer

III, IV only

Answer

<div>I, IV only

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The following orbital energies (\(E\)) are compared. Identify the correct sets
(I) E₂(H) = E₂(H)
(II) E₃(H) = E₃(He)
(III) E₂s(H) < E₂s(He)
(IV) E₃s(He) < E₃s(H)

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The Correct Option is D

Solution and Explanation

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The following orbital energies (\(E\)) are compared. Identify the correct sets (I) E2(H) = E2(H)(II) E3(H) = E3(He)(III) E2s(H) < E2s(He)(IV) E3s(He) < E3s(H)