As shown in the figure, a particle of mass m=10^ -10 ~kg , moving...

As shown in the figure, a particle of mass $m=10^{-10} \mathrm{~kg}$, moving with velocity $\mathrm{v}_0=10^5 \mathrm{~m} / \mathrm{s}$ approaches a stationary fixed target with impact parameter $b$ from a large distance. If the fixed rigid target has a core with repulsive central force $F(r)=\frac{K}{r^3}$ where constant $\mathrm{K}>0$ and the particle scatters elastically. The closest distance of approach (if numerically $K=b^2$ ) is