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Structure Of Atom

Question
CBSEENCH11008400

If uncertanity in position and momentum are equal, then uncertaninty in velocity is 

  • fraction numerator 1 over denominator 2 straight m end fraction square root of straight h over straight pi end root
  • square root of fraction numerator straight h over denominator 2 straight pi end fraction end root
  • 1 over straight m square root of h over pi end root
  • square root of straight h over straight pi end root

Solution

A.

fraction numerator 1 over denominator 2 straight m end fraction square root of straight h over straight pi end root

According to Heisenberg's uncertainty principle, it is impossible to determine simultaneously the position and momentum of moving a particle, ie.
left parenthesis increment straight x right parenthesis space straight x space left parenthesis increment straight p right parenthesis space greater or equal than fraction numerator straight h over denominator 4 straight pi end fraction
Here comma space increment straight x space equals space increment straight p space equals space straight m. increment straight v
increment straight v squared space equals space fraction numerator straight h over denominator straight m squared 4 straight pi end fraction
increment straight v space equals space fraction numerator 1 over denominator 2 straight m end fraction square root of straight h over straight pi end root
The uncertainty principle in terms of energy and time is given as
increment straight E. increment straight t space greater or equal than space fraction numerator straight h over denominator 4 straight pi end fraction