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Question:

Some energy levels of a molecule are shown in the figure. The ratio of the wavelengths r = λ₁/λ₂, is given by:

r=34

r=43

r=13

r=23

Solution:

E=hc/λ ⇒ λ=hc/E ⇒ λ ∝ 1/E
From Figure,
Energy of photon of wavelength λ₂ ΔE₂ = -E - (-3/3E) ΔE₂ = E
Energy of photon of wavelength λ₁ ΔE₁ = -E - (-6/6E) ΔE₁ = E
∴ λ₁/λ₂ = ΔE₂/ΔE₁ = (E)/(E/3) = 3
r = λ₁/λ₂ = 1/3
Hence option (1) is correct.