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.
IIT JEE
Chemistry
Difficulty: Easy
Choose an option
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A5x/36
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B5x
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C7.2x
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Dx/6
Answer
Correct Answer: 5x/36
Explanation
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