’ Answer: 1.67 eV
Explanation: The energy of a photon is given by:
$$E = hf$$
where h is Planck’s constant and f is the frequency of the photon. The frequency of a photon is inversely proportional to its wavelength:
$$f = \frac{c}{\lambda}$$
where c is the speed of light. So, the energy of a photon is inversely proportional to its wavelength.
The work function of a metal is the minimum energy required to remove an electron from the metal. So, the maximum kinetic energy of the photoelectrons is the energy of the photon minus the work function:
$$K_max = E - \phi$$
Plugging in the values, we get:
$$K_max = \frac{hc}{\lambda} - \phi = \frac{(6.626 \times 10^{-34} J\cdot s)(3 \times 10^8 m/s)}{500 \times 10^{-9} m} - 2.5 eV = 1.67 eV$$
