Final answer:
The difference in work function for the two surfaces can be calculated using the photoelectric effect formula by Einstein. The difference is given by subtracting the work functions associated with the respective surfaces, which is equal to the difference in maximum kinetic energies of ejected electrons.
Step-by-step explanation:
The question you asked is about the difference in work function for two surfaces upon which light is shone, resulting in the ejection of electrons with different maximum kinetic energies. To calculate this difference, we use the concept of the photoelectric effect, which is explained by Einstein's equation:
KE = hf - φ
where KE is the maximum kinetic energy of the ejected electrons, hf is the energy of the incident photons (with h being Planck's constant and f the frequency of radiation), and φ is the work function of the surface.
Given that the light of frequency 6.60 x 10⁾¹⁴ Hz (frequency of incident radiation) ejects electrons from surface (a) with a maximum kinetic energy that is 2.80 x 10⁻⁹ J (maximum kinetic energy) greater than that from surface (b), we can express the maximum kinetic energy for each surface as:
KEₑ = hf - φₑ
KEₒ = hf - φₒ
Given that KEₑ - KEₒ = 2.80 x 10⁻⁹ J, we can write:
(hf - φₑ) - (hf - φₒ) = 2.80 x 10⁻⁹ J
φₒ - φₑ = 2.80 x 10⁻⁹ J
The difference in work functions (φₒ - φₑ) is therefore 2.80 x 10⁻⁹ J. You can convert this value to electronvolts (eV) if necessary, using the conversion factor 1 eV = 1.602 x 10⁻⁹ J.