The recoil speed of a hydrogen atom after it emits a photon in going from n = 5 state to n = 5 state will be

Step-by-step solution

Δ E Releases when photon going from n = 5 to n = Δ E = 13 . 6 - 0 . 54   eV = 13 . 06   eV P i = P f (By linear momentum conservation) 0 = h λ - M v = V Recoil = h λ M                 . . . 1 &   Δ E = h c λ = h c λ M × M ⇒ M c V Recoil V Recoil   = Δ E M c = 13 . 06 × 1 . 6 × 10 - 19 1 . 67 × 10 - 27 × 3 × 10 8 = 4 . 17   m   s - 1