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Question

Uncertainty in the position of an electron (mass = 9.1×1031 kg) moving with a velocity of 300 m/s accurate upto 0.001% will be:
  1. 5.76×103 m
  2. 1.92×102 m
  3. 3.84×103 m
  4. 19.2×104 m


Solution

The correct option is B 1.92×102 m
We know that from Heisenberg's Uncertainity principle,
Δx × Δp  h4π
where Δx is uncertainity in position
           Δp is uncertainity in momentum
             h is Planck's constant
Here, p = mv 
where p =momentum of particle
           m = mass of particle
           v = velocity of particle.
Δp = Δ(mv)
Δp = m(Δv) ; since m is constant.
Δxmin = h4πm×Δv

= 6.626×10344π×(9.1×1031)×(300×0.001100)
= 1.93×102 m



 

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