Final answer:
The question deals with the photoelectric effect, where light ejects electrons from a metal's surface. To identify the metal, one must calculate the work function using the kinetic energy of the emitted electrons and the frequency of the incident light.
Step-by-step explanation:
The question concerns the photoelectric effect, a phenomenon in physics where electrons (called photoelectrons) are ejected from a metal surface when it is exposed to light of a certain frequency or wavelength that is above the metal's threshold frequency. You've given a light with a wavelength of 190 nm incident on an unknown metal, and the most energetic electrons emitted have 4.0 eV of kinetic energy.
To identify which metal this could be, one needs to calculate the work function of the metal. This involves using the equation for the photoelectric effect: KE = hf - Φ, where KE is the kinetic energy of the ejected electrons, h is Planck's constant, f is the frequency of the incident light, and Φ represents the work function (also known as the binding energy) of the metal.
First, we need to convert the wavelength of 190 nm into frequency using the equation c = λf, where c is the speed of light, λ is the wavelength, and f is the frequency. Once we have the frequency, we can plug it into Planck's equation to find the energy of the photons. Subsequently, we'll use the initial energy of the photons to determine the work function. By comparing this calculated work function with the known work functions of various metals, we can identify the most likely metal of the surface.