We know thatphoton energy = minimum energy needed to free an electron + max kinetic energy of emitted photoelectronAs we have been asked for the maximum wavelength , we know these photoelectrons just have enough energy to leave the surface of the potassium, but they will not have any kinetic energy. Therefore:photon energy = min energy needed to free electron (work function) E = hf = work function as v = f * wavelengthwork function = (hv)/wavelength, therefore rearranging we get wavelength = (hv) / work function wavelength = (6.63x10-34 x 3.00x108)/(3.65x10-19)= 5.4493x10-7m = 5.45x10-7m (to 3s.f)