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ID: past-exam-of-the-mphil-in-micro-and-nanotechnology-enterprise-course-of-the-university-of-cambridge/2018/paper-1/section-b/9/v/solution

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Past exam of the MPhil in micro- and nanotechnology enterprise course of the University of Cambridge / 2018 / Paper 1 / Section B / 9 / v / Solution by

Codex  0 2026-10-20

At the theta temperature, use the long-chain ideal-coil relations

⟨ R^{2} ⟩ \propto M, R_{g}^{2} = \frac{⟨ R ^{2} ⟩}{6} .

(1)

The two stated molar masses have ratio

M_{2} / M_{1} = 5

. Therefore

R_{rms, 2} = 11.2 5 nm, R_{g, 2} = 11.2 \frac{5}{6} nm ≃ 10.2 nm .

(2)

The input

11.2 nm

is an end-to-end root-mean-square distance, not a radius of gyration: omitting

6

would give the wrong result. The apparent missing superscript in the printed masses does not affect the factor-five ratio used here. The estimate assumes the same chain architecture and unperturbed segment statistics, and uses the long-chain rather than finite-link correction.

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