All Problems

Wave Properties of particles. Schrodinger Equation.

Problem 6.71

An electron with kinetic energy \(T \approx 4 \mathrm{eV}\) is confined within a region whose linear dimension is \(l=1 \mu \mathrm{m}\). Using the uncertainty principle, evaluate the relative uncertainty of its velocity.

Reveal Answer
Δv/v/l2mT=1104\Delta v / v \sim \hbar / l \sqrt{2 m T}=1 \cdot 10^{-4}