Answer to Question #123227 in Quantum Mechanics for asghar ali

Question

Q#2: in the photo electric effect, electromagnetic radiation incident on a metal surface may eject electron, but only if the frequency of the radiation exceeds a threshold value.
Show that this frequency threshold can be understood if the mechanism for the photoelectric effect involves an interaction between a photon and an electron, and if the energy needed to eject the electron has a minimum value.
The minimum energy needed to eject an electron from the surface of magnesium is 3. 68ev.show that light with a frequency below 8.89*1014 Hz cannot produce photoelectrons from magnesium, no matter how intense the illumination may be.

Answer 1

Given, work function $\phi=3.68eV,$ Frequency of light is $\nu=8.89\times 10^{14}Hz$

Now, by Einstein's photoelectric principle , a single photo electron will ejected if

$$h\nu-\phi>0$$

But, In this case, we have

$$h\nu=3.67eV$$

Which is clearly sates that

$$K=h\nu-\phi<0$$

Hence, no matter how strong the intensity of given light is , not even a single electron will get out of the surface of Magnesium.