The ratio of the wavelengths of the light absorbed by a Hydrogen atom when it undergoes n = 2 → n =

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Question

The ratio of the wavelengths of the light absorbed by a Hydrogen atom when it undergoes n = 2 → n = 3 and n = 4 → n = 6 transitions, respectively, is

Accepted Answer

Correct Answer: A — 1/4Step-by-step Solution:Using the Rydberg formula: 1/λ ∝ ΔE ∝ (1/ni² − 1/nf²), so λ ∝ 1/ΔE.Transition 1 (n=2→3): ΔE₁ ∝ (1/4 − 1/9) = (9−4)/36 = 5/36Transition 2 (n=4→6): ΔE₂ ∝ (1/16 − 1/36) = (9−4)/144 = 5/144Ratio: λ₁/λ₂ = ΔE₂/ΔE₁ = (5/144)/(5/36) = 36/144 = 1/4Shortcut: The n=4→6 transition is exactly the n=2→3 transition scaled by factor 2 (multiply all n by 2). Since ΔE ∝ 1/n², energy gaps scale as 1/4, so wavelength ratio = 1/4.Key Concepts:Rydberg Formula: 1/λ = RH × Z² × (1/ni² − 1/nf²)Energy and wavelength: E = hc/λ → λ ∝ 1/ΔEBohr's model: En = −13.6/n² eV for hydrogen

The ratio of the wavelengths of the light absorbed by a Hydrogen atom when it undergoes n = 2 → n = 3 and n = 4 → n = 6 transitions, respectively, is

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The ratio of the wavelengths of the light absorbed by a Hydrogen atom when it undergoes n = 2 → n = 3 and n = 4 → n = 6 transitions, respectively, is

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