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Wave Optics

Question
CBSEENPH12039849

An electron of a stationary hydrogen atom passes from the fifth energy level to ground level. The velocity that the atom acquired as a result of photon emission will be

  • fraction numerator 24 hR over denominator 25 space straight m end fraction
  • fraction numerator 25 hR over denominator 24 space straight m end fraction
  • fraction numerator 25 space straight m over denominator 24 space hR end fraction
  • fraction numerator 24 space straight m over denominator 25 space straight h space straight R end fraction

Solution

A.

fraction numerator 24 hR over denominator 25 space straight m end fraction Here comma space straight E subscript 5 space minus straight E subscript 1 space equals space hc over straight lambda
and space
fraction numerator straight R space hc over denominator 25 end fraction space equals space straight R space hc space equals space hc over straight lambda
24 over 25 straight R space equals space 1 over straight lambda
space straight P space equals straight h over straight lambda
straight v equals straight h over mλ
space equals space 24 over 25 Rh over straight m