 Solution

ID: past-exam-of-the-chemistry-course-of-the-year-4-of-the-natural-sciences-course-of-the-university-of-cambridge/2022/paper-2/section-e/26/b/ii/solution

The particle centre can move approximately

ℓ - σ

from the cell centre towards each of its four nearest fixed neighbours. Approximating the actual curved boundary by a square gives

a_{c} ≃ [2 (ℓ - σ)]^{2} = 4 (ℓ - σ)^{2} .

This is the area accessible to the centre, not the geometrical area enclosed by the fixed particle centres or an area computed using

σ /2

. Two equal particles must keep their centres at least

σ

apart.

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