Chapter 3.6, Problem 7PPA

Interpretation Introduction

Interpretation:

The minimum uncertainty in the position of the $\text{25-g}$ bullet traveling at $\text{612 m/s}$ which has the uncertainty in its velocity is $\text{612 m/s ± 1 percent}$ should be calculated using the concept of the Heisenberg uncertainty principle.

Concept Introduction:

The Heisenberg uncertainty principle says that it is impossible to know simultaneously both the momentum ($\text{p}$) and the position ($\text{x}$) of a particle with certainty.

Mathematically,

$\text{Δx}\cdot \text{Δp }\ge \frac{\text{h}}{\text{4π}}$

For a particle having the mass $\text{m}$,

$\text{Δx}\cdot \text{mΔu }\ge \frac{\text{h}}{\text{4π}}$

Where, $\text{Δx and Δu}$ are uncentainty in measuring the position and velocity of the particle respectively; $\text{h}$ is Planck’s constant ($\text{6}{\text{.63 × 10}}^{-\text{34}}\text{ Js}$).

To calculate: Calculate the minimum uncertainty in the position of the $\text{25-g}$ bullet traveling at $\text{612 m/s}$ which has the uncertainty in its velocity is $\text{612 m/s ± 1 percent}$