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CHEM 121 Studioby Learn4Less · UBC CHEM 121

CHEM 121 glossary

Zero-point energy

The lowest possible energy of a confined particle, which is never zero. For a particle in a box it is E1=h2/8mL2E_1 = h^2/8mL^2, because n=0n = 0 is not allowed; a confined particle is never at rest, as the uncertainty principle requires.

Particle-in-a-box wavefunction ψWavefunction between walls at x = 0 and x = L with 1 lobe and 0 interior nodes (marked with circles).V = ∞V = ∞0Lxψ

ψ1\psi_1: the ground state, with energy E1>0E_1 > 0.

Example

An electron in a 0.100 nm box has E1=(6.626×10−34)28(9.109×10−31)(1.00×10−10)2=6.02×10−18E_1 = \dfrac{(6.626\times10^{-34})^2}{8(9.109\times10^{-31})(1.00\times10^{-10})^2} = 6.02\times10^{-18} J, 100 times that of a 1.00 nm box.

See alsoParticle in a boxGround stateHeisenberg uncertainty principle