Physics-
General
Easy

Question

When a hydrogen atom emits a photon in going from n =5  to n = 1, its recoil speed is almost

  1. 10 to the power of negative 4 end exponent m s to the power of negative 1 end exponent
  2. 8 cross times 10 squared m s to the power of negative 1 end exponent
  3. 2 cross times 10 to the power of negative 2 end exponent ms to the power of negative 1 end exponent
  4. 4 m s to the power of negative 1 end exponent

The correct answer is: 4 m s to the power of negative 1 end exponent


    Energy of photon emitted,

    E equals 13.6 open parentheses 1 over 1 squared minus 1 over 5 squared close parentheses eV equals 13.6 cross times 24 over 25 eV

    Momentum of photon equals E over c

    The momentum of hydrogen atom is equal and opposite to the momentum of photon. If  is the mass of hydrogen atom open parentheses equals 1.67 cross times 10 to the power of negative 27 end exponent kg close parentheses

    and  v is recoil speed of hydrogen atom , then

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell mv equals straight E over straight c end cell row cell straight v equals straight E over mc equals fraction numerator 13.01 cross times 1.6 cross times 10 to the power of negative 19 end exponent over denominator 1.67 cross times 10 to the power of negative 27 end exponent cross times 3 cross times 10 to the power of 8 end fraction end cell row cell straight v equals 4.15 ms to the power of negative 1 end exponent end cell end table

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