Question

Draw a plot of frequency \( \nu \) of incident radiations as a function of stopping potential \( V_0 \) for a given photoemissive material. What information can be obtained from the value of the intercept on the stopping potential axis?

Hint:

The stopping potential intercept gives the work function of the material, and the slope provides the ratio \( \frac{e}{h} \).

Answer 1

A plot of frequency \( u \) versus stopping potential \( V_0 \) for a photoemissive material yields a straight line, described by the photoelectric equation: \[ E_k = hu - \phi \]. Here, \( E_k \) denotes the kinetic energy of the emitted photoelectron, \( h \) is Planck's constant, \( u \) is the incident radiation frequency, and \( \phi \) is the material's work function. The stopping potential \( V_0 \) is linked to the electron's kinetic energy by: \[ E_k = eV_0 \], where \( e \) is the electron's charge. Equating these expressions for \( E_k \) results in: \[ eV_0 = hu - \phi \]. This equation can be rewritten as \( u = \frac{eV_0 + \phi}{h} \), demonstrating that the plot of \( u \) against \( V_0 \) is a straight line. The slope of this line is \( \frac{e}{h} \), and the intercept is \( \frac{\phi}{h} \). The \( V_0 \)-axis intercept directly indicates the work function \( \phi \), and the slope is proportional to \( \frac{e}{h} \).