How to Determine the Uncertainty in the Physical Property of an Object – Part 1

The uncertainty principle, aka Heisenberg’s indeterminacy/uncertainty principle states that there is a limit to the precision with which certain pairs of physical properties, viz., position (Δx) and momentum (Δp), can be simultaneously known.


It is one of the fundamental concepts in quantum mechanics.

Question:

A golf ball has a mass of 40 g, and a speed of 45 m/s. If the speed can be measured within accuracy of 2%, calculate the uncertainty in the position.

Solution:



Click/tap to enlarge the image

H = Planck constant, m = Mass, Δv = Uncertainty in the velocity

The uncertainty in the position calculated is ~ 1018 times smaller than the diameter of a typical atomic nucleus. For large particles, the uncertainty principle sets no meaningful limit to the precision of measurements.

Quandary on quantum mechanics❓ Let Chemaficionado know in the comments below or at mychemistryhomework@gmail.com❗

References:

(1)    Brown, C.; Ford, M. Higher Level Chemistry, 2nd ed.; Pearson Education: Harlow, Essex, 2014.

(2)    Ncert. Chemistry : Textbook for Class XI - Part.I; National Council Of Educational Research And Training: New Delhi.

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