# Explain how Heisenberg's uncertainty principle accounts for the fact that electrons cannot exist inside an atomic nucleus.

> IB DP Physics Higher Level (2023 syllabus) — E.2 Quantum physics (HL only) · Explain · 4 marks

> The diameter of a typical atomic nucleus is of the order 10⁻¹⁴ m. An electron has a rest mass of 9.11 × 10⁻³¹ kg.

## Mark scheme (4 marks)

1. If an electron were confined within the nucleus, its positional uncertainty Δx would be of the order of the nuclear diameter (~10⁻¹⁴ m).
2. By the uncertainty principle ΔxΔp ≥ ℏ/2 (or h/4π), a small Δx requires a correspondingly large minimum uncertainty in momentum Δp.
3. The large momentum uncertainty implies a minimum momentum (and hence minimum kinetic energy) far exceeding the rest-mass energy of the electron, making confinement energetically impossible.
4. Therefore the uncertainty principle rules out electron confinement inside a nucleus, as no physical mechanism can supply the necessary energy to maintain such confinement.

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