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AP EAMCET201921 Apr 2019Evening ShiftPhysicsAtomic PhysicsActual

When a hydrogen atom emits a photon during a transition from n = 4 to n = 2 , its recoil speed is about

Options

  1. A4 . 28   m   s - 1
  2. B0 . 814   m   s - 1
  3. C2 . 07   m   s - 1
  4. D0 . 407   m   s - 1

Correct answer

B. 0 . 814   m   s - 1

Step-by-step solution

The expression for the momentum of the photon, p = h λ m v = h λ v = h m λ From the formula for the Bohr's for H-atom, 1 λ = R 1 n 1 2 - 1 n 2 2 Substitute the given values in the above equation. 1 λ = 1 . 097 × 10 7   1 2 2 - 1 4 2 ⇒     λ = 4 . 86 × 10 - 7   m The recoil speed of photon is, v = h m λ = 6 . 62 × 10 - 34 1 . 6 × 10 - 27 × 4 . 86 × 10 - 7 ⇒     v = 0 . 8513   m   s - 1

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