Solve this multiple-choice question and choose the correct option.

Concept/ApproachFor H-atom, En = −x/n² if x is the ionization energy from n = 1 (since E1 = −x). Thus, E₂ = −x/4 and E₃ = −x/9. Step-by-stepΔE (2 → 3) = E₃ − E₂ = (−x/9) − (−x/4) = x(−1/9 + 1/4) = x(5/36). Final Answer5x/36

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Bohr–hydrogen energy levels: If the ionization energy of hydrogen from the ground state equals x kJ mol⁻¹, what energy is required to excite an electron from n = 2 to n = 3? Use Eₙ ∝ −1/n² and compute ΔE between levels. Choose the correct option.

Difficulty: Easy

5x/36
5x
7.2x
x/6

Correct Answer: 5x/36

Explanation:

Concept/ApproachFor H-atom, E_n = −x/n² if x is the ionization energy from n = 1 (since E₁ = −x). Thus, E₂ = −x/4 and E₃ = −x/9.

Step-by-stepΔE (2 → 3) = E₃ − E₂ = (−x/9) − (−x/4) = x(−1/9 + 1/4) = x(5/36).

Final Answer5x/36

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