Final answer:
The question involves calculating the stopping potential and the wavelength of incident light in relation to the photoelectric effect for aluminium, using the known work function of 4.2 eV.
Step-by-step explanation:
The question concerns the calculation of stopping potential and incident light wavelength in the context of the photoelectric effect where the work function for the aluminium surface is provided as 4.2 eV. According to the photoelectric effect, electrons are emitted from a material's surface when light of a certain frequency shines upon it. The stopping potential is the potential difference needed to stop the maximum energy electrons emitted by the light from reaching the anode.
The energy of the incoming photon can be calculated using Planck's equation, E = hν, where h is Planck's constant and ν is the frequency of the light. Alternatively, E can also be calculated by converting the wavelength λ of the light through the relation c = νλ, with c being the speed of light. The maximum kinetic energy (KE) of the emitted electron is then given by KE = E - work function. For a stopping potential V, eV (where e is the elementary charge) equals the maximum kinetic energy of the ejected electron.
To find the amount of potential difference required to stop the emission of electrons by light of a specific wavelength, we would use the equation KE = eV = hc/λ - work function, and solve for V. For a stopping potential of 0, we'd find the wavelength for which the photon energy is just equal to the work function. For the aluminium with a work function of 4.2 eV, one would have to calculate for different wavelengths, such as 2000 Å, to determine the corresponding stopping potential.