Final answer:
Halving the wavelength of light incident on a photoelectric surface increases the stopping potential due to the photoelectric effect, as photon energy and frequency are inversely related to wavelength.
Step-by-step explanation:
If the wavelength λ is incident on a photoelectric surface and the resulting stopping potential is V0, halving the wavelength would result in an increase of the stopping potential. This is due to the photoelectric effect, where photons with a higher frequency (and thus a shorter wavelength, since frequency and wavelength are inversely proportional) impart more energy to the ejected photoelectrons.
According to the equation E = hf - Φ, where E is the maximum kinetic energy of photoelectrons, h is Planck's constant, f is the frequency of the incident light, and Φ is the work function of the material, doubling the frequency due to halving the wavelength would result in a higher kinetic energy for each photoelectron and therefore would require a greater stopping potential to halt the photoelectric current. In essence, the stopping potential would increase if the wavelength of the incident light is reduced to half its original value given that other conditions remain constant.