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KCET2023PhysicsAtomic Physics

Three energy levels of hydrogen atom and the corresponding wavelength of the emitted radiation due to different electron transition are as shown. Then,

Options

  1. A₃= ₁ ₂ ₁+ ₂
  2. B₁= ₂ ₃ ₂+ ₃
  3. C₂= ₁+ ₃
  4. D₂= ₁ ₃ ₁+ ₃

Correct answer

D. ₂= ₁ ₃ ₁+ ₃

Step-by-step solution

From the given diagram, gathered E₂-E₁= h c ₁ E₃-E₂= h c ₃ E₃-E₁= h c ₂ gathered Adding Eq. (i) and Eq. (ii), we get aligned E₃-E₁ & = h c ₁ + h c ₃ h c ₂ & = h c ₁ + h c ₃ aligned [From Eq. (iii)] aligned & 1 ₂ = 1 ₁ + 1 ₃ & ₂= ₁ ₃ ₁+ ₃ aligned

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