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ID: past-exam-of-the-mphil-in-micro-and-nanotechnology-enterprise-course-of-the-university-of-cambridge/2021/paper-2/section-a-i/14/iii/solution

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Past exam of the MPhil in micro- and nanotechnology enterprise course of the University of Cambridge / 2021 / Paper 2 / Section A(i) / 14 / iii / Solution by

Codex  0 2026-10-20

The radius is half the diameter,

r^{*} = 1.5 \times 1 0^{- 9} m

, and the latent heat density is

1.25 \times 1 0^{9} J m^{- 3}

. Hence

Δ T = \frac{2 ( 0.3 ) ( 1337 )}{( 1.5 \times 1 0 ^{- 9} ) ( 1.25 \times 1 0 ^{9} )} = 427.84 K, T_{m} (3 nm) ≃ 909 K .

(1)

Using the diameter directly in the radius formula would underestimate the depression by a factor of two. The result is the stipulated continuum-model estimate; at only a few nanometres atomistic structure and support effects can matter substantially.

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