The Photoelectric Effect

In the last segment on quantized energy, I explained why the idea that energy comes in little packets (quanta) was proposed to explain blackbody radiation. However, blackbody radiation isn’t the only experimental result that requires quantized energy to explain. A more puzzling one is the photoelectric effect.

The photoelectric effect is that when light is shines on metallic surfaces, electrons are emitted. Physicists have created an apparatus to do more experiments on this effect. Basically, light (or any type of electromagnetic radiation) shines on one metallic plate (the cathode) and a distance away from it is another metal plate, which can absorb electrons (the anode). Then wires, resistors, etc are added to create a voltage across these plates, and physicists run experiments to test the connection between the current in the system (caused by the electrons emitted from the photoelectric effect) and the voltage. A positive voltage causes electrons to be attracted to the anode, but a negative voltage repels the electrons from the anode. When the voltage is negative, only the electrons that are emitted with enough initial kinetic energy to overcome the voltage difference make it to the anode. (For those of you who like math, that situation is described by: (1/2)mv²=eV, where e is the charge of an electron and the velocity is the initial velocity.)

Now, classically there is no problem with the photoelectric effect. Newton’s Laws allow for the transfer of energy. However, our understanding of Newton’s Laws, the nature of atoms, and the assumption that energy is continuous combine to make certain predictions.

1) There should be a maximum voltage such that all the emitted electrons make it to the anode (since a positive voltage attracts the electrons). Increasing the voltage beyond this does not increase the current any further.

2) Also, if one increases the intensity of the light hitting the cathode, corresponding to increasing the amount of energy hitting the cathode, while keeping the frequency of the light constant, this should increase the maximum kinetic energy of the electrons emitted. In less technically language, as the light hitting the cathode transfers more energy, the electrons should be emitted with higher speeds. Thus, there should be no minimum voltage beyond which no electrons are emitted- at any voltage, if you increase the intensity of the light enough, there should eventually be an electron emitted with enough kinetic energy to make it to the anode.

3) Finally, under the classical theory with the continuous spectra of energy, one can calculate the length of time light of a given intensity needs to shine on the cathode before enough energy is gathered for an electron to be emitted. Lower intensities should have a longer delay than higher intensities, but eventually an electron should be emitted.

These are the predictions given by classical theory, depending on Newton’s Laws, the understanding that electrons orbit the nucleus of atoms and require energy to be emitted, and the claim that light energy is continuous (doesn’t come in quanta).

But, then, what did they actually observe? Of the three predictions, only (1) was verified experimentally. However, regarding (2), physicists noted that there was a minimum voltage (V0) beyond which no electrons were emitted (however long they waited). Even worse, for (3), physicists noted that either the electrons were emitted immediately (to their instruments- in a tiny, tiny, tiny fraction of a second), or not at all (however long they waited); their predictions of several hours were completely rebutted by experimental evidence. Something had to go: Newton’s Laws, the understanding that electrons orbit the nucleus of atoms are require energy to be emitted, or the claim the light energy comes in continuous amounts. Whatever goes, too, has to replaced by something that explain these results, which have been verified literally millions of times in labs over the world (including in many college classes). Rejecting Newton’s Laws undermines everything we know of physics, and rejecting this understanding of the atom undermines chemistry. (1)

Fortunately, along came a brilliant man, who applied Planck’s idea of quantized energy to solve this problem and won a Nobel Prize in physics for it…the one, the only Einstein! For as opposed as Einstein was the quantum mechanics once the field took off, he was one of the founding fathers, and it was for this contribution, and not for relativity, that he won his Nobel Prize. So, let’s see how quantized energy can rescue physics and chemistry from certain destruction yet again.

If we suppose that these packets of energy are real, then they also exist for electromagnetic radiation (including light), and Einstein proposed calling these packets of energy “photons” for electromagnetic radiation. At first people cried “foul!”- didn’t we settle it long ago that light was a wave? After all, it has interference, diffraction, and travels faster in denser materials. However, remember all that was disproven was that light couldn’t be matter- it couldn’t have mass AND have a volume. There’s no reason why light can’t be a wave and also massless packets, whatever that means. So Einstein basically said, yes, light is a wave, but what if we say this wave is equivalent to little massless packets of energy (photons)? (Recall that the assumption that energy is quantized does not conflict with Newton’s Laws, but simply something else that can interact with them and change what is derived from them.)

So Einstein said:

(Recall E=hυ is from Planck’s explanation of blackbody radiation, υ is often used for f.)

φ is a characteristic of the material of the surface; it’s essentially the energy needed to remove the electron of the orbit.

So, according the quantum theory, these photons strike electrons and transfer their energy to them.  If they give the electrons enough energy, the electrons escape from their orbits and are emitted.  For a given frequency of light, the extra energy a photon transfers to the electron (beyond escaping the orbit) is converted to a specific amount of kinetic energy.  This means that there is a limit on the initial maximum kinetic energy an electron can leave with, and if that’s not enough to overcome voltage to get to the anode, then the electron won’t make it.  Ever. Thus, Newton’s Laws plus the quantized energy predicts that there will be a minimum voltage (remember negative voltages repel the electrons) beyond which no electrons will make it to the anode- which is what is observed #2!  Now, for the timing- can the quantized theory explain that?  Well, if the energy is great enough, as soon as the photon strikes the electron it was emitted.  This will happen with the first photon that hits an electron; they don’t need to accumulate over time.  Thus, there is no measurable lag.  However, if the energy of a photon isn’t enough to give the electron enough kinetic energy to escape, photons striking the electron won’t knock it out, no matter how long you wait.  (2) There will never be a situation where you will have a steady supply of electrons emitted after several hours because the energy doesn’t accumulate continuously until an electron is emitted.  (3)

So between this and the blackbody radiation, I hope that I’ve convinced you that energy comes in discrete packets (or that you’ve got to rebuild all of physics), or at the very least explained why physicists can believe such a claim. In case not, though, I’m going to briefly mention Compton scattering. Basically, he shone radiation at an electron at rest, measured the scattering angle of the electron, and basically was able to show that the electron was struck with something with a specific momentum- different than if it was constantly pushed by something with a constant momentum, like a classical wave would predict.

Of course, if you don’t accept quantization of energy, you’re going to have to have some sort of better explanation for things than Newton’s Laws (or a better assumption that can be combined with them to explain blackbody radiation and the photoelectric effect, which means you’d better think you know more about physics than Einstein), give up all of chemistry, and reject molecular biology. What?!!! Yes- using the theory of quantized energy, they used the atoms in a crystal as a diffraction grating for x-rays, and called it x-ray diffraction. Know of any great discoveries that depended on x-ray diffraction? Yep- the double-helix shape of DNA. Quantum mechanics is underneath a lot more than modern physics.

Next, of course, you’d like to read about: The Bohr model of the atom.

1) Note how basic this knowledge of the atom was; current atomic theory (and therefore all of the chemistry) is based on quantum mechanics and wasn’t developed yet when these experiments were done, but the idea of an electron was around even though they were still forming the model of the atom.

2) But wait, you say, what if several photons strike the electron at once? Yes, this can happen, but given the relative sizes of electrons and photons, the statistical odds of more than one photon striking an electron at precisely the same amount of time is essentially nil. And even if it happened once or twice, you wouldn’t be able to sustain a current- the statistical odds are just too low.

3) In case you’re wondering what happens to the energy of the photon when it strikes the electron but doesn’t give it enough kinetic energy to escape, it’s converted into other forms of energy like heat.

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