Kinetic Energy and Stopping Potential

Einstein's relation E_c,max = hν − W₀ is that of a straight line. If we plot the maximum kinetic energy of the electrons as a function of the frequency of the light, we get:

   E_c,max
     ^
     |               /
     |              /   slope = h
     |             /
     |            /
   0 +-----------•------------> ν
     |          /|
     |         / ν₀ (threshold frequency)
   -W₀ ......•

Three direct readings: the slope of the line is h (the Planck constant, the same for all metals!); the intersection with the horizontal axis gives the threshold frequency ν₀; the extension of the line crosses the vertical axis at −W₀. A single experiment therefore gives h and the work function of the metal.

How do we measure E_c,max? We apply a voltage that slows down the electrons. We increase it up to the value U₀, the stopping potential, at which even the fastest electrons are stopped: the current drops to zero. Their kinetic energy is then exactly balanced:

   E_c,max = e·U₀        (e = elementary charge)

So measuring a voltage is enough to know the energy of the electrons. By repeating this for several frequencies, Millikan plotted the line above and measured h with remarkable precision — confirming Einstein despite his own initial skepticism. Remember: frequency → energy (through the slope h), intensity → number.