# Y Intercept of photoelectric effect graph?

In a graph of KE=hf-W (the photoelectric effect equation), why is the work function equal to the y intercept? I mean I can see why it is using the equation (y=mx-c) but conceptually, why is the work function - the minimum energy required to cause emission of electrons - the y intercept of this graph?

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Couldn't you figure this out yourself? –  Ron Maimon Nov 7 '11 at 17:27

The equation requires that u have to give at least an energy equal to the wave function of the metal to eject an electron, if that condition is not met then nothing will happen,

so the work function is the EXTRAPOLATED INTERCEPT of the graph,

as it can be clearly seen that when f=0 , KE = -w , which is impossibe as KE cannot be negative,

so the graph never intersects the X axis, its only the extended or extrapolated graph(on which professors show with a dotted line) which intersects it.

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The photoelectric effect graph just says that the outgoing electron is emitted with the energy of the photon minus the ionization energy, the energy it takes to rip an electron from the metal. Energy out equals energy in minus energy consumed in ionization.

The energy of the photon is proportional to f. If you make f zero, you are looking at the y- intercept. Then you make the energy of the photon zero, so that the outgoing electron (if there were one) would have minus the ionization energy. The ionization energy is called the "work function" only in elementary textbooks, it is not a function of anything. But this means that the negative of the y-intercept is the ionization energy.

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I still can't really conceptualize what is happening - what do you mean 'if you make the energy of the photon zero the outgoing electron would have minus the ionization energy'? Obviously that is the case looking at the equation (subbing in f=0) but why is that the case in reality? –  Parachuting Panda Nov 7 '11 at 8:23
@Parachuting Panda: It has nothing to do with reality--- if you shine close-to-zero frequency light nothing happens electrons don't come out. This is just substituting in a variable in a regime where the equation makes no sense. It's just something that has nothing to do with actual physics, it's just the mathematical intercept of the graph. –  Ron Maimon Nov 7 '11 at 8:30
Okay, so if you didn't know the E=hf-W equation, how would you know that the y intercept is the work function? –  Parachuting Panda Nov 7 '11 at 8:36
@Parachuting Panda: You wouldn't. –  Ron Maimon Nov 7 '11 at 17:26