If the position of the electron is measured within an accuracy of ±0.002 nm, calculate the uncertainty in the momentum of the electron. Suppose the momentum of the electron is h4πm×0.05nm, is there any problem in defining this value?
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Solution
By applying the uncertainty principle, ΔP=h4πΔx=6.626×10−344×3.1416×0.002×10−9=2.63×10−23kgm/s
The uncertainty in momentum is, h4πm×0.002×10−9=h×5×10114×π×m.
This is much larger than the actual momentum, i.e, h4πm×0.05nm. Hence, it cannot be defined.