Photoelectric Example

Source: "Theory and problems of Modern Physics", Ronald Gautreau,Problem 9.13

Problem: The emitter in a photoelectric tube has a threshold wavelength of $6000\,\mathrm {\AA}$. Determine the wavelength of the light incident on the tube if the stopping potential for this light is 2.5 V.

Solution: The work function is

$eW_{0}=h\nu _{th}={\frac {hc}{\lambda }}={\frac {1240\times 10^{3}{\text{ eV}}\cdot \mathrm {\AA} }{6000\,\mathrm {\AA} }}=2.07{\text{ eV}}$

The photoelectric equation then gives

$ev_{s}=h\nu -eW_{0}={\frac {hc}{\lambda }}-eW_{0}$

$2.5{\text{ eV}}={\frac {1.24\times 10^{3}{\text{ eV}}\cdot \mathrm {\AA} }{\lambda }}-2.07{\text{ eV}}\Rightarrow \lambda =2713\,\mathrm {\AA}$