= Solution
The <diffusion coefficient> relates particle flux to concentration gradient through <Fick's first law>, $\mathbf j=-D\nabla c$. For unbiased isotropic motion in $d$ dimensions it can equivalently be defined by the long-time <mean squared displacement>:
$$
\boxed{D=\lim_{t\to\infty}\frac{\langle|\mathbf r(t)-\mathbf r(0)|^2\rangle}{2dt}.}
$$
An uncorrelated <random walk> with jump length $a$ and total jump rate $\Gamma$ has $\langle r^2\rangle=\Gamma a^2t$, hence $D=\Gamma a^2/(2d)$; correlations introduce a multiplicative correlation factor. The factor $d$ counts the directions sharing the total displacement. It does not mean that the same material's single-coordinate diffusivity changes merely by choosing to observe fewer coordinates: $\langle x^2\rangle=2Dt$ in every Cartesian direction of the same isotropic system.
At $500$ K, silver iodide is in its fast-ion-conducting $\alpha$ phase. For an order-of-magnitude estimate, take a jump length $a\sim3$ Å and an effective successful jump rate $\Gamma\sim10^{11}\ \mathrm{s^{-1}}$. Then
$$
\boxed{D\sim\frac{(3\times10^{-10})^2(10^{11})}{6}
\sim1.5\times10^{-9}\ \mathrm{m^2\,s^{-1}}.}
$$
Thus \b[$D$ of order $10^{-9}\ \mathrm{m^2\,s^{-1}}$] is a reasonable estimate for this <superionic conductor>. The length and rate are explicitly assumed material scales; the question supplies neither a measured conductivity nor jump data, so an exact numerical coefficient cannot be deduced from <temperature> alone. The estimate is not presented as an experimentally measured value.
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