Question
The work function of a metal is eV. Light of wavelength nm falls on the surface. Find the maximum kinetic energy of photoelectrons. Take eV nm.
Solution — Step by Step
Using with eV nm:
This is the trick that saves time — keep in eV nm and in nm; the answer comes out in eV directly.
Final answer: eV.
If the question asked for the stopping potential, that’s just V.
Why This Works
Einstein’s photoelectric equation: each photon delivers energy to a single electron. Part of it (, the work function) goes into freeing the electron from the metal; the rest becomes kinetic energy. Photons below threshold () cause no emission, regardless of intensity.
The threshold wavelength is . For this metal, nm. Since , emission happens.
Alternative Method
Compute everything in joules: J. Convert work function: J. Then J eV. Slower but mechanically equivalent.
Memorise eV nm. With this single number, you can compute photon energies in your head for any visible-light wavelength. JEE timing rewards this kind of shortcut.
Common Mistake
Students sometimes write instead of . The work function is the energy COST to escape, not a bonus — so it subtracts. Also: is the maximum, since some electrons lose energy to the metal lattice on the way out.