# Millikan’s Photoelectric Experiment and Measurement of Planck’s Constant

The experimental arrangement of Millikan’s method to determine Planck’s constant ‘h’ is shown below.  The apparatus consists of an evacuated chamber (vaccum) where different alkali metals are placed on a rotating table so that experiment can be performed for different surfaces like Sodium, Potassium, Lithium etc without evacuating the chamber. The metals are very reactive so they may form a film over the surface so a scraper (knife) is inserted to surface. A sensitive galvanometer G and a voltmeter V are also connected to detect the current and measure the Pd across the metallic surface and the collector (which collects the electron).

Millikan’s Photoelectric experiment

The Pd across the arrangement can be varied by rheostat. A light radiation o suitable frequency f (f > f0) is made incident on the metallic surface are collected at the other surface which faces the metallic surface. The galvanometer shows deflection due to photoelectric current.

We know from Einstein’s photoelectric equation:

$$hf = \phi + \frac{1}{2}mv_{max}^{2}………(i)$$

The potential difference across the arrangement is slowly increased until the galvanometer shows zero deflection. This corresponding potential difference is called stopping potential (eVs). Then kinetic energy becomes equal to the stopping potential. So,

$$\frac{1}{2}mv_{max}^{2} = \text{eV}_{s}……..(ii)$$

From  equation (i) and (ii),

$$hf = \phi + \text{eV}_{s}$$

$$or, V_s = \frac{hf}{e} + \left ( \frac{-\phi}{e} \right )……..(iii)$$

Here, Φ and hf0 is constant for a given metal. So, the euqaion (iii) represent the equation of straight line y = mx +c.

Now, the frequency of incident radiation is changed and the corresponding value of stopping potential is measured. If we plot a graph between incident reuency (f) and stopping potential (Vs) we obtain a straight line having negative intercept whose slope gives the measure of h/e and intercept gives the measure of Φ/e.

A graph between frequency and stopping potential

If we perform the experiment by exposing different surfaces like Na, Cs, K, etc to the radiation, straight line having same slope but different intercepts are obtained as shown in the graph above. This means that ‘h’ is a universal constant and ϕ varies from surface to surface.

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