An electron is not free but is confined to a region of size nm

PHYSICS · Multi-part · Fermi University Physics · Quantum Mechanics · Origins of quantum theory · Origins of quantum theory

Quantum Mechanics: From the Photon to the Hydrogen Atom, Ch Matter waves and wave-particle duality

Problem

An electron is not free but is confined to a region of size Δx=0.20\Delta x = 0.20 nm, about the length of a small molecule. Use the uncertainty relation in its estimating form, taking the spread of momentum to be of order Δp∼ℏ/Δx\Delta p \sim \hbar/\Delta x and the electron to be non-relativistic, with ℏ=1.055×10−34\hbar = 1.055\times10^{-34} J s and me=9.109×10−31m_e = 9.109\times10^{-31} kg. ((a)) Estimate the momentum Δp\Delta p. ((b)) Estimate the least kinetic energy the electron can have, in eV (11 eV =1.602×10−19= 1.602\times10^{-19} J).

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