# 17.2.4 KEmax-f Graph

So far, the photon model has been faultless in providing qualitative explanations for the experimental observations. But it is not physics until we start measuring and verifying the numbers.

So we conduct the photoelectric effect experiment using emitters made of different types of metal. We measure the maximum kinetic energy (KEmax) at different light frequencies f. We then plot the graph of KEmax against f, one for each type of metal. Guess what we get?

Parallel lines! You are staring at the quantitative proof of the photoelectric equation

$\displaystyle K{{E}_{{\max }}}=hf-\Phi$

The gradient of those parallel lines corresponds to the Planck’s constant, $\displaystyle h=6.63\times {{10}^{{-34}}}\text{ J s}$. And the y-intercepts of each graph corresponds to the work function F  of each metal!

So what do you think now? Is light a wave or a stream of photons? The photoelectric effect endorses the photon theory totally. But what about the double-slit experiment? Doesn’t it still lend irrefutable support to the wave theory? Hmm. Obviously, we are not finished yet.

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