For a certain metal, when monochromatic light of wavelength \( \lambda \) is incident, the stopping potential for photoelectrons is \( 3V_{0} \). When the same metal is illuminated by light of wavelength \( 2\lambda \), then the stopping potential becomes \( V_{0} \). The threshold wavelength for photoelectric emission for the given metal is \( \alpha \lambda \). The value of \( \alpha \) is________.
