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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 h/4πm × 0.05 nm, is there any problem in defining this value?

Solution:

By applying the uncertainty principle, ΔP = h/4πΔx = (6.626 × 10⁻³⁴) / (4 × 3.1416 × 0.002 × 10⁻⁹) = 2.63 × 10⁻²⁴ kg m/s
The uncertainty in momentum is, h/4πm × 0.002 × 10⁻⁹ = h × 5 × 10¹⁰ / 4 × π × m. This is much larger than the actual momentum, i.e., h/4πm × 0.05 nm. Hence, it cannot be defined.