Find the number of electrons ejected from a metal given total energy

Question

Here's the problem:  When a metal was exposed to light at a frequency of 4.07× 1015 s–1, electrons were emitted with a kinetic energy of 3.30× 10–19 J. What is the maximum number of electrons that could be ejected from this metal by a burst of light (at some other frequency) with a total energy of 3.39× 10–7 J?

Answer 1

You can find the work function of the metal which is the energy required to free the electron from the metal surface:

 

KE_max = hf - W where

 

h is Planck's constant, 6.63 x 10^-34 J·s

 

f is the frequency

 

KE_max is the maximum kinetic energy

 

W is the work function.

 

 

3.30 x 10^-19 J = (6.63 x 10^-34)(4.07 x 10¹⁵) - W

 

W = 2.37 x 10^-18 J

 

 

The maximum number of electrons released would be the total energy divided by the work function--just enough energy to release them.

 

3.39 x 10^-7 / 2.37 x 10^-18 = 1.43 x 10¹¹ electrons.