No, path difference cannot occur if the wavelength of the wave is larger than the distance between the slit and the screen in the context of a double-slit interference pattern.
In a double-slit interference setup, a wave passes through two closely spaced slits and creates an interference pattern on a screen located some distance away. The path difference refers to the difference in the distance traveled by two waves originating from the two slits before they reach a specific point on the screen.
For interference to occur, the path difference between the waves must be within the range of a few wavelengths. If the wavelength of the wave is larger than the distance between the slits and the screen, it means that the wavefronts are relatively spread out compared to the distance between the slits. In such a case, the wavefronts from the two slits will not overlap significantly, and the conditions for interference are not satisfied.
In the double-slit interference pattern, the interference fringes are generated by the constructive and destructive interference of waves with similar wavelengths. If the wavelength is larger than the distance between the slits and the screen, the resulting pattern would not exhibit the characteristic interference fringes associated with double-slit interference.