Question

What is the longest wavelength of light that can cause the release of electrons from a metal that has a work function of 3.40 eV ?

Answer 1

hf = work function + KE
However if you are looking at the max wavelength (or threshold frequency) then there will only be just enough energy for the photoelectrons to be liberated, hence their KE will be 0.
So hf = work function
3.4 x (1.6 x 10^-19) = 5.44 x 10^-19
therefore, hf = 5.44 x 10^-19
f = 5.44 x 10^-19 / planck's constant which is 6.63 x 10^-34
f = 8.205 x 10^14 Hz
c = frequency x wavelength,
wavelength = speed of light/frequency
= (3x10^8)/(8.205x10^14)
= 3.65 x 10^-7 metres