已知 $\stackrel{\rightharpoonup }{e_1},\stackrel{\rightharpoonup }{e_2}$是夹角为 $\frac{2\pi }{3}$的两个单位向量, $\stackrel{\rightharpoonup }{a}=\stackrel{\rightharpoonup }{e_1}-2\stackrel{\rightharpoonup }{e_2},\stackrel{\rightharpoonup }{b}=k\stackrel{\rightharpoonup }{e_1}+\stackrel{\rightharpoonup }{e_2}$.若 $\stackrel{\rightharpoonup }{a}·\stackrel{\rightharpoonup }{b}=0$,则 $k$的值为.