What is the approximate uncertainty in the position of a proton (1.673 $\times$ 10^-27 kg)in a particle accelerator if its velocity is known to about ±2.5 m/s (total uncertainty is 5.0 m/s)?

Question

Quizplus · Accepted Answer

The uncertainty in position Δx is given by the Heisenberg uncertainty principle as:
ΔxΔp≥ℏ2
where Δp is the uncertainty in momentum given by Δp=mv, m is the mass of the proton, and v is the velocity. Therefore,
Δx≥ℏ2mΔv
Substituting the values, we get:
Δx≥ (6.626×10^-34)/(2 × 1.673×10^-27 × 2.5) = 3.19×10^-10 m
Rounding off to one significant figure, the uncertainty in position is approximately 3.2×10^-10 m or 3.2 Å. The best choice is B, which gives this value.

What Is the Approximate Uncertainty in the Position of a Proton