Final answer:
The photoelectric effect describes the ejection of electrons from materials exposed to light. To find the maximum wavelength of light that can eject electrons from sodium, the work function is needed, which can be calculated from related data. Using the relationship λ_max = hc/φ, the maximum wavelength can then be compared with the given options.
Step-by-step explanation:
The question deals with the photoelectric effect, which is a phenomenon in physics where electrons are ejected from a material when it's exposed to light of sufficient energy. The maximum wavelength that can cause an electron to be ejected is related to the work function of the material, which is the minimum energy required to remove an electron. By applying the equation for the photoelectric effect, we can link the energy of the incident photons (E=h and E=hc/λ) to the work function and the kinetic energy of the emitted electrons.
In this specific context, we aren't directly given the work function of sodium, but we have related information from which we can deduce it. We know that a 400-nm violet light ejects photoelectrons with a maximum kinetic energy of 0.860 eV from a sodium photoelectrode. First, we must convert the wavelength to energy using the equation E = hc/λ, where h is Planck's constant, c is the speed of light, and λ is the wavelength. Next, we subtract the kinetic energy of the ejected electrons to find the work function (φ).
Now, to find the maximum wavelength that can still cause ejection of electrons, we use the relationship: λ_max = hc/φ. The option with the longest wavelength that will provide just enough energy to overcome the work function (and no excess kinetic energy) will be the correct answer. Comparing the calculated maximum wavelength with the answer options, we can find the respective correct option.