For a certain metal, when monochromatic light of wavelength $\lambda$ is incident, the stopping potential for photoelectrons is $3 \mathrm{~V}_0$. When the same metal is illuminated by light of wavelength $2 \lambda$, then the stopping potential becomes $\mathrm{V}_0$. The threshold wavelength for photoelectric emission for the given metal is $\alpha \lambda$. The value of $\alpha$ is $\_\_\_\_$。