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Q. Given, the mass of electron is 9.11×1031kg, Planck's constant is 6.626×1034Js, the uncertainty involved in the measurement of velocity within a distance of 0.1˚A is

AIPMTAIPMT 2006Structure of Atom

Solution:

By Heisenberg's uncertainty principle
Δx×Δpxh4π
or Δx×Δ(mvx)h4π
Δx×Δvxh4πm
Δp= uncertainty in momentum
Δx= uncertainty in position
Δv= uncertainty in velocity
m= mass of particle
Given that,
Δx=0.1˚A=0.1×1010m
m=9.11×1031kg
h= Planck's constant =6.626×1034Js
π=3.14
Thus,
Δv×0.1×1010=6.626×10344×3.14×9.11×1031
Δv=6.626×10344×3.14×9.11×1031×0.1×1010ms1
=5.785×106ms1
=5.79×106ms1