A gas centrifuge of radius $r = 0.1$ m rotates at angular velocity $\\omega = 3000$ rad/s. A mixture of $^{235}\\text{UF}_6$ ($M_1 = 0.349$ kg/mol) and $^{238}\\text{UF}_6$ ($M_2 = 0.352$ kg/mol) gases is processed at $T = 300$ K. The radial density profile follows $C(r) = C(0) e^{\\frac{M \\omega^2 r^2}{2RT}}$, where $R = 8.314$ J/(mol\cdot K). What is the separation factor $\\alpha = \\frac{(C_2/C_1)_r}{(C_2/C_1)_0}$ at the outer wall?