Problem on photoelectric effect

Question: The work function (φ) of some metals is given below. Which of the following metals will show photoelectric effect when light of 300 nm wavelength falls on it?

Metal	Li	Na	K	Mg	Cu	Ag	Fe	Pt	W
Φ (eV)	2.4	2.3	2.2	3.7	4.8	4.3	4.7	6.3	4.75

Solution:

Now first recall the basic of photoelectric effect. In the photoelectric effect, electrons are emitted from solids, liquids or gases when they absorb energy from light. Light contain energy in the form of photon. If an electron within some material absorbs the energy of one photon, it acquires more energy than the work function of the material. (Work function is the energy that bind electron to the material). In such case, electron is ejected from the atom of the material.

Now read the question, here wavelength of the light is given. So we can find out the energy of the light (photon). 

 We know that; h = Planck’s constant = 6.6 x 10^-34 Joule-sec

                   And c= Speed of light = 3 x 10⁸ m/sec                

      

                        

                    

                                                      E = 4.16 eV

Now energy of the light is known. Thus, metals that have lower work function (electron binding energy) than energy of light (4.16 eV), will show photo electric effect. 

So metals that showing photo electric effect will be Li, Na, K and Mg