Alight source of wavelength λ illuminates a metal and ejects photoelectrons with a maximum kinetic energy of 2.00 ev. a second light source with half the wavelength of the first ejects photoelectrons with a maximum kinetic energy of 6.00 ev. what is the work function of the metal?

Explanation:

Energy from a light source (photons):

E=h*c/λ

Photoelectric effect and Work function (W):

E=W+Ek

Ek: maximum kinetic energy from photoelectrons

then:

h*c/λ=W+Ek

Case 1:

 (1)

Case 2:

but  

 (2)

If we divide (2) by (1):

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .