Answer
$$1.60 \times 10^{7} \mathrm{\ m} / \mathrm{s} $$
Work Step by Step
The initial speed of the germanium nucleus is
$$v_{\mathrm{Ge}}=\sqrt{\frac{2 K_{\mathrm{Ge}}}{M_{\mathrm{Ge}}}}=\sqrt{\frac{2\left(110 \times 10^{6} \mathrm{eV}\right)\left(1.60 \times 10^{-19} \mathrm{J} / \mathrm{eV}\right)}{(83 \mathrm{u})\left(1.661 \times 10^{-27} \mathrm{kg} / \mathrm{u}\right)}}=1.60 \times 10^{7} \mathrm{\ m} / \mathrm{s} $$
