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An electron of a stationary hydrogen atom (mass = m ) jumps from the fifth energy level to the ground level. As a result, the atom emits a photon and recoils with some velocity. The velocity that the atom acquires as a result of photon emission is [ h = Planck's constant, R = Rydberg's constant]

Options

  1. A24 hR 25 m
  2. B25 hR 24 m
  3. C24 m 25 hR
  4. D25 m 24 hR

Correct answer

A. 24 hR 25 m

Step-by-step solution

Here, E 5 − E 1 = hc λ − ( Rhc 5 2 − Rhc ) = hc λ (where R = Rydberg's constant, h = Planck's constant and c = speed of light in vacuum) ⇒ 24 25 R = 1 λ But P = h λ ⇒ v = h mλ = 24 Rh 25 m

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