Final answer:
The work function of a material is the minimum energy required to remove an electron from the surface of that material. Given the wavelength of the incident UV light and the maximum kinetic energy of the ejected photoelectrons, the work function can be calculated using the photoelectric equation. It involves determining the energy of the photons and subtracting the kinetic energy of the ejected electrons.
Step-by-step explanation:
The student has asked about the work function of a material that is being irradiated by ultraviolet light. The formula connecting the work function (φ), the kinetic energy of the ejected photoelectrons (KE), and the energy of the incident photons (E) is given by the photoelectric equation:
E = KE + φ
The energy of a photon is given by E = hc/λ, where h is Planck's constant (6.626 x 10-34 J·s), c is the speed of light (3.00 x 108 m/s), and λ is the wavelength of the light. After calculating the energy of the photon using the given wavelength, we can then use the provided maximum kinetic energy of the photoelectrons to find the work function of the material.
First, the photon energy (E) for a wavelength of 4.00 x 10-7 m is calculated, and this energy is converted from joules to electronvolts (eV). Then using the equation above, we subtract the maximum kinetic energy (30.0 eV) from the photon energy to find the work function.