Chapter 1, Problem 1B.5AST

Interpretation Introduction

Interpretation:

The minimum uncertainty in the position of a proton that is accelerated in a cyclotron to a speed within $3.0\times {10}^{2}km.s^{-1}$ has to be calculated.

Concept Introduction:

Uncertainty principle:

Uncertainty principle states that if the location of a particle is known to within an uncertainty $\Delta x$, then the linear momentum, p, parallel to the x – axis can be known simultaneously only to within an uncertainty $\Delta p.$

Mathematically, $\Delta p\times \Delta x\ge \frac{1}{2}\hslash$

Where, $\Delta x$ is the uncertainty in position and $\Delta p$ is the uncertainty in momentum.