Final answer:
To find the wavelength of a 14 eV photon in nm, use the equation λ = c/f. Rearrange the equation to solve for frequency, f = E/h. Plug the frequency into the equation for wavelength, λ = c/f, and convert the result to nm.
Step-by-step explanation:
The given relationship to use in this question is E = hf, where E is the energy of a single photon, h is Planck's constant, and f is the frequency of the photon. We can relate the frequency to the wavelength using the equation c = λν, where c is the speed of light and λ is the wavelength. Rearranging the equation to solve for wavelength, we get λ = c/f.
To find the wavelength of a 14 eV photon in nm, we need to solve for the frequency first. Since we know the energy (14 eV) and Planck's constant (4.14x10^-15 eV·s), we can rearrange the equation to solve for frequency: f = E/h. Substituting the values, we get f = (14 eV)/(4.14x10^-15 eV·s). Finally, we can plug the frequency into the equation for wavelength to find the result: λ = (3.00x10^8 m/s) / f. Converting the result to nm, we get the wavelength of the 14 eV photon.