Answer
$1.66\times10^{-10}m$.
Work Step by Step
The energy levels are given by the equation $E_n=\frac{n^2 h^2}{8mL^2}$.
The ground state has n=1. Solve for L. From the problem statement, $E_1=13.6 eV=2.18\times10^{-18}J$.
$$L=\frac{h}{\sqrt{8mE_1}}=1.66\times10^{-10}m $$
