What happens when a fast-moving electron hits water?
This question is important for understanding the effects of ionizing radiation, but it’s also just cool. I learned the answer here:
• H. Haberland and K. H. Bowen, Solvated electron clusters, Springer Series in Chemical Physics 56 (1994), 134–153.
There are four stages. To get a feel for these, it helps to remember that a femtosecond is 10-15 seconds. This is roughly the time it takes for light to travel a third of a micron—about 5000 times the radius of a hydrogen atom.
In 10 to 20 femtoseconds, our electron slows down due to its interaction with water molecules. It transfers energy to these molecules by knocking their electrons to higher energy levels or even knocking them off entirely. It does this until its energy has dropped to about 5 electron volts.
This is still quite energetic: for comparison, a lone electron at room temperature would have an energy of about 0.037 electron volts. Still, at this point we say the electron is thermalized. From now on it exchanges energy with water mainly by exciting motions of the water molecules.
Metals have a conduction band, a range of energies such that electrons with these energies can move freely. But materials called dielectrics, which do not conduct electricity well, also have a conduction band! The difference is that for metals, the conduction band has an energy low enough that electrons can easily jump into it. For dielectrics, the conduction band has an energy so high that it’s usually unoccupied.
Water is a dielectric. So, its conduction band is mostly empty. But even after our fast-moving electron is thermalized, it still has enough energy to occupy the conduction band! So, it moves along through the water!
It does this for about 110 to 180 femtoseconds until it finds a more localized state with about the same energy it has. You see, an electron in the conduction band has a wavefunction that’s very spread out. But there are also some states of about the same energy where the wavefunction is not so spread out. These are called shallow trap states. ‘Trap state’ means that the electron is stuck in one place. ‘Shallow’ means that the energy is still fairly high—there are also ‘deep trap states’.
All this sounds a bit abstract. What are these shallow trap states actually like? I think the electron finds itself a home in a little region that momentarily happens not to contain water molecules.
Next, the water molecules around the newly trapped electron start reacting to its electric field. As this happens, the energy of the electron decreases. People say the electron “digs its own trap”. I like that metaphor!
This takes about 240 femtoseconds. When this is done, we have what’s called a solvated electron:
This picture is by Michael Tauber. The electron looks huge, but that’s just because its wavefunction is fairly spread out. He says this picture shows the ‘first and second coordination shells’ around the solvated electron.
In the final stage, the electron combines with a positively charged ion. How long this takes depends radically on how many positively charged ions happen to be around.
For example, even in pure water there are some lone protons floating around. Not many! At 25 degrees Celsius, there is one lone proton per half billion molecules of water. But eventually the electron may combine with one of those and form a hydrogen atom.
In reality, it’s not quite that simple. A proton floating around in water will almost surely have already attached itself to a water molecule, forming a hydronium ion, H3O+:
And hydronium is still positively charged, so it will attract electrons in other water molecules. It will stick on to them in various various ways, the two most famous being the Eigen cation H₉O₄⁺:
and the Zundel cation H₅O₂⁺:
These in turn are still positively charged, so they attract more water molecules, making bigger and bigger structures, which I discussed in detail here:
• Water, Azimuth, 29 November 2013.
Here’s a picture of one, called the protonated 21-water cluster:
Presumably when our lone electron meets these structures, they fall apart like a house of cards! I don’t know.