Alight source of wavelength, l, illuminates a metal and ejects photoelectrons with a maximum kinetic energy of 1 ev. a second light source of wavelength l/2 ejects photoelectrons with a maximum kinetic energy of 4 ev. what is the work function of the metal

Explanation:

From first source, kinetic energy () ejected is 1 eV and wavelength of light is .

From second source, kinetic energy () ejected is 4 eV and wavelength of light is .

Relation between work function, wavelength, and kinetic energy is as follows.

                   K.E =

where,        h = Plank's constant = J.s

                   c = speed of light = m/s

Also, it is known that 1 eV = J

Therefore, substituting the values in the above formula as follows.

                      =  

            1 eV =    

           ........... (1)

                  =  

                         ........... (2)        

Now, divide equation (2) by 2. Therefore, it will become

                  ......... (3)

Now, subtract equation (3) from equation (1), we get the following.

                    =

                          = 2 eV

Thus, we can conclude that work function of the metal is 2 eV.