The following figure shows five silicon atoms that are part of a silicon lattice. The two atoms shown within the pink-dashed region are a bonded lattice pair. Which, if any, of the electrons of either of the atoms of the pair is a free electron? (A) Electron two only, (B) electrons one and five only, (C) all of the labeled electrons, (D) none of the labeled electrons.
In our diagram, we see that six of the electrons within this pink-dashed line are indicated. Here we see electron one, here is the electron labeled electron two, here is number three, four, five, and six. We want to figure out which of these, if any, is a free electron. Recall that a free electron is one that energetically is not bound to any particular atom. In that sense, a free electron exists outside of the electron orbitals of an atom. To identify free electrons in our diagram, we’ll look for those electrons shown by blue dots that are not located on the black circles that indicate electron energy levels.
Looking first at electron one, we see that this electron is located at the intersection of the orbitals of two silicon atoms. This electron is shared between these atoms, and it is a bound electron rather than a free one. Since electron one is not a free electron, we can eliminate answer option (C), which says that all of the labeled electrons are free.
Next, we look at electron two. This blue dot, we notice, does not lie along any of the black circles. It exists outside of those circles. And indeed, we can even see an opening called a vacancy where this electron may have existed. Currently though, electron two does exist outside the orbit of any particular atom. Therefore, it is a free electron. Looking back at our answer options, this means that option (B) that only electrons one and five are free or (D) that none of the labeled electrons are free are both incorrect.
Before settling on our final answer though, let’s look at the remaining electrons. Electron three exists on a black circle, as does electron four, indicating that they are bound electrons. Electron five exists at the overlap between two black circles. This electron is bound and it is shared. The same is true for electron six, which is shared between our central silicon atom and the atom directly below it. Answer choice (A) then is our final answer. Of all of the six electrons indicated, it’s only electron two that is a free electron.