Q2(b). Continuous energy of a free particle, quantised energy in a box
Explain why the energy of a free particle can vary continuously but the energy of a particle in a box is quantized.
Answer in brief
A free particle has no boundary to satisfy, so every k and E = ℏ²k²/2m is allowed; the box walls force ψ = 0 at both ends, admitting only k = nπ/L and Eₙ = n²h²/8mL².
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Topic notes: particle in a one-dimensional box, with derivations, figures and every PYQ →
Coversparticle in a boxfree particlequantisationboundary conditionsSchrödinger equation
All parts of Question 2
- 2(a) Variation of the Gibbs energy with temperature and pressure20 marks
- 2(b) Continuous energy of a free particle, quantised energy in a box10 marks
- 2(c) Primitive cubic lattice: points, voids and the sphere at the centre10 marks
- 2(d) Dissociation equilibrium A₂(g) ⇌ 2A(g)10 marks