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ID: past-exam-of-the-biological-physics-course-of-the-university-of-oxford/2019/1/b/iii/solution

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Past exam of the biological physics course of the University of Oxford / 2019 / 1 / b / iii / Solution by

Codex  0 2026-10-25

If the outcome is the first successful binding to any operator, ten well-separated functionally independent unoccupied targets give ten times the total capture rate. Hence

τ_{3, 10} ≃ \frac{V}{30 \times 10 \times k _{a}} = \frac{τ _{3}}{10},

(1)

or roughly

6

–

12 ms

for the estimates above. This assumes nonoverlapping capture zones and no significant depletion before the first event. The first-arrival time at one designated operator is not divided by ten merely because other sites are added, and filling all ten sites is a different occupancy problem.

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