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Question

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×0.05 nm, is there any problem in defining this value?

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Solution

By applying the uncertainty principle,
ΔP=h4πΔx=6.626×10344×3.1416×0.002×109=2.63×1023 kg m/s
The uncertainty in momentum is,
h4πm×0.002×109=h×5×10114×π×m.

This is much larger than the actual momentum, i.e, h4πm×0.05 nm. Hence, it cannot be defined.

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