The work functions of Aluminium and Gold are 4.1 eV and 5.1 eV respectively. The ratio of the slope of the stopping potential versus frequency plot for Gold to that of Aluminium is
To determine the ratio of the slope of the stopping potential versus frequency plot for Gold to that of Aluminium, we need to use the photoelectric equation:
E = h \nu - \phi.
Where:
E is the energy of the emitted photoelectron,
h is the Planck's constant,
\nu is the frequency of the incident light,
\phi is the work function of the material.
The stopping potential V_0 can be determined from the energy of the emitted electron as E = eV_0, where e is the charge of an electron. Therefore:
eV_0 = h \nu - \phi.
Rearranging the equation gives the relation for the stopping potential:
Here, the slope of the stopping potential versus frequency plot is given by \left( \frac{h}{e} \right), which is invariant of the material's work function. Therefore, the ratio of the slopes is 1.
