Final answer:
The photoelectric effect occurs when the incident light's wavelength is less than or equal to the metal's cut-off wavelength. Thus, electrons are emitted only if the wavelength of the incoming light is equal to or shorter than the specific threshold for that metal.
option c is the correct
Step-by-step explanation:
The photoelectric effect will take place only if the wavelength λ of incident light is less than or equal to the cut-off wavelength λ0 of the metal.
The work function of a metal is the minimum energy needed to remove an electron from the metal surface, which can be converted into a cut-off wavelength using the equation that relates energy (E), frequency (ν), and wavelength (λ), E = hν, where h is Planck's constant, and ν = c/λ with 'c' being the speed of light. Substituting for the energy in terms of the work function (Φ), we have Φ = hc/λ0. Considering frequency and wavelength are inversely proportional, for photoelectric emission to occur, the incident light must have a wavelength λ ≤ λ0. Therefore, the correct option is C λ≤λ0.