Answer
$1~u = 1.66\times 10^{-27}~kg$
Work Step by Step
The mass of a $C_{12}$ atom is $12~u$ and one mole of $C_{12}$ has a mass of $0.012~kg$. We can find the conversion factor from atomic units to kg:
$(6.02\times 10^{23})(12~u) = 0.012~kg$
$1~u = \frac{0.012~kg}{(6.02\times 10^{23})(12)}$
$1~u = 1.66\times 10^{-27}~kg$
