Final answer:
The binding energy of electrons to uranium metal can be calculated using the energy of the incident UV photon and subtracting the kinetic energy of ejected electrons, resulting in a binding energy of 3.50 eV.
Step-by-step explanation:
The question involves the concept of photoelectric effect, which is a phenomenon in physics where electrons are ejected from a material (in this case, uranium) when it is exposed to light of sufficient frequency. According to the photoelectric equation, Einstein's formula is given by E = hf - Φ, where E is the maximum kinetic energy of the ejected electron, hf is the energy of the incident photon, and Φ is the binding energy of the electron to the metal.
To calculate the binding energy, we must first calculate the energy of the incident UV photon. The energy (E) of a photon with a wavelength of 300 nm can be found using the equation 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 photon. Substituting the values, we can calculate the photon's energy and then use it, along with the kinetic energy of the ejected electrons (0.500 eV), to find the binding energy.
Upon calculation, we find that the energy of the incident photon is approximately 4.00 eV. Using the photoelectric equation, we then subtract the kinetic energy (0.500 eV) of the ejected electrons to find the binding energy. Therefore, the binding energy of electrons to uranium metal is 3.50 eV.