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Question:

Assume that you are travelling at a speed of 90 km/h in a small car with a mass of 1050 kg. If the uncertainty in the velocity of the car is 1 m/s, what is the uncertainty in the position of the car?

Δx≥1×10⁻³³m

Δx≥2×10⁻³³m

Δx≥2×10⁻³²m

Δx≥4×10⁻³³m

Solution:

From Heisenberg uncertainty principle,
Δx ≥ h/(4π(mΔv))
Δx ≥ 6.626×10⁻³⁴ Js/(4 × 3.14 × 1050 kg × 0.9 m/s × (1000 m/km) × (3600 s/h))
Δx ≥ 2×10⁻³³ m
The uncertainty in the position of the car is far smaller than the uncertainty in the position of an electron in a hydrogen atom (3×10⁻¹⁰ m) and far too small a value to have any measurable consequences. Hence, option B is correct.