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The first three spectral lines of H-atom in the Balmer series are given λ₁, λ₂, λ₃ considering the Bohr atomic model, the wavelengths of first and third spectral lines ((λ₁)/(λ₃)) are related by a factor of approximately x×10⁻¹. The value of x, to the nearest integer, is ______.

Asked in JEE Main 16th March 1st Shift 2021 · Spectral series and wavelengths

Answer: 15

Step-by-step solution

λ₁ (3→2): (5R)/(36); λ₃ (5→2): R(1/4-1/(25))=(21R)/(100).

(λ₁)/(λ₃)=(21/100)/(5/36)=1.51≈15×10⁻¹

→ 15

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