Julie S. answered • 02/22/20
Master's in Chemistry with 20+ Years of Teaching/Tutoring Experience
The concept you are asking about is called the photoelectric effect. This means that light (photons) can be used to cause a metal to emit electrons. Each metal has a minimum amount of energy required to cause the metal to begin to exhibit the photoelectric effect, this is referred to as the threshold energy. The numbers you provided are the threshold energies for the metals in question, which is basically the minimum energy required to "knock off" an electron from the metal.
The energy of a photon is related to its frequency and wavelength (E = hν, or E = hc/λ). In this case, you are provided with a photon with wavelength 250 nm, which is 2.50 x 10-7 m. These photons have energy
E = ( 6.626 x 10-34 J-s) (3.0 x 108 m/s) / (2.50 x 10-7 m) = 7.95 x 10-19 J
According to the numbers provided, this is more than enough energy to cause either metal to exhibit the photoelectric effect. Any "extra" energy above the threshold energy required to knock them loose can be transmitted to an electron in the form of kinetic energy!
Energy provided by photon - Energy required (threshold energy) =
Energy possessed by the emitted electron (kinetic energy)
The threshold energy for Ti (Φ =6.94 x 10-19 J ) is LESS than that of Si is (Φ = 7.24 x 10-19 J). Therefore, an electron emitted from Ti exhibiting the photoelectric effect has more "extra" energy than one from Si, if they are provided with the same energy photons.
Since electrons have both particle and wave properties, an electron with more Kinetic Energy would have a shorter wavelength. Therefore, the electron emitted from Ti would have more KE and a shorter wavelength, and the electron emitted from Si would have less KE and a longer wavelength.
Hope that helps!
