Question #a9596
1 Answer
WARNING! Long answer! The minimum energy needed is
Explanation:
The photoelectric effect
When a photon of sufficient energy hits the surface of a metal, some of the energy is used to eject an electron from the surface of the metal (the work function) and the rest goes into the kinetic energy of the electron.
#color(blue)(bar(ul(|color(white)(a/a)E = φ + KEcolor(white)(a/a)|)))" "#
Minimum energy
The energy
#color(blue)(bar(ul(|color(white)(a/a) E = hf color(white)(a/a)|)))" "#
where
Another important formula is
#color(blue)(bar(ul(|color(white)(a/a) fλ = c color(white)(a/a)|)))" "#
where
We can combine these two expressions and get the formula
#color(blue)(bar(ul(|color(white)(a/a) E = (hc)/λ color(white)(a/a)|)))" "#
For a mole of photons,
where
The minimum energy will be that for which the photon has just enough energy to remove the electron with nothing left over (i.e. the work function)
∴
Maximum wavelength
A photon with just enough energy to equal the work function will have the maximum wavelength.