 Solution

ID: past-exam-of-the-short-options-paper-shared-by-prelims-and-parts-a-and-b-of-the-physics-course-of-the-university-of-oxford/2017/s16/2/1/solution

n_{0} /2

, so the left side of Saha's equation is

n_{0} /2

. Its logarithm changes by

d lo g n_{0} = (3/2 + R / (k_{B} T^{'})) d lo g T^{'}

. To first order,

\frac{Δ n _{0}}{n _{0}} ≃ (\frac{3}{2} + \frac{R}{k _{B} T ^{'}}) \frac{Δ T ^{'}}{T ^{'}} .

This holds for small fractional changes and the supplied ground-state partition approximation, not an exact finite-difference identity.

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