Question Video: Identifying Bonded Lattice Pairs in a Silicon Lattice Physics • 9th Grade

The following figure shows five silicon atoms that are part of a silicon lattice. Only the electrons in the outer shells of the atoms are shown. Which of the following show atoms that are bonded lattice pairs? [A] Both the atoms whose nuclei are shown within the region indicated by the brown dashed line and the atoms whose nuclei are shown within the region indicated by the pink solid line [B] Only the atoms whose nuclei are shown within the region indicated by the pink solid line [C] Only the atoms whose nuclei are shown within the region indicated by the brown dashed line [D] Neither the atoms whose nuclei are shown within the region indicated by the brown dashed line nor the atoms whose nuclei are shown within the region indicated by the pink solid line

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Video Transcript

The following figure shows five silicon atoms that are part of a silicon lattice. Only the electrons in the outer shells of the atoms are shown. Which of the following show atoms that are bonded lattice pairs? (A) Both the atoms whose nuclei are shown within the region indicated by the brown dashed line and the atoms whose nuclei are shown within the region indicated by the pink solid line. (B) Only the atoms whose nuclei are shown within the region indicated by the pink solid line. (C) Only the atoms whose nuclei are shown within the region indicated by the brown dashed line. (D) Neither the atoms whose nuclei are shown within the region indicated by the brown dashed line, nor the atoms whose nuclei are shown within the region indicated by the pink solid line.

In our diagram, we see five silicon atoms arranged in a lattice. Two of those atoms, this atom here and this one here, are indicated by this pink solid line. Likewise, a different pair of atoms, this atom and the central atom in the lattice, are indicated by a brown dashed line. We want to identify which, if any, of these pairs are bonded lattice pairs. The keyword here is bonded, that is, that there is a bond resulting in electron sharing between a pair of atoms.

In order to fit all four of our answer options on screen at the same time, let’s write condensed versions of answer options (A) and (B). Answer option (A) held that only atoms indicated by the pink solid line are a bonded lattice pair, while option (B) said that both of the atom pairs indicated by the pink solid line and the brown dashed line are bonded lattice pairs.

Let’s look at these pairs in turn, starting with the pair in the pink solid line. In this representation of silicon atoms, the black circle around each nucleus represents the valence electron energy level of that atom. In order for a pair of atoms to be a bonded lattice pair, they must both exist in the lattice and their valence electron energy levels must overlap with one another so that electron sharing can occur. We see though that for the atoms indicated by the pink solid line, this is not possible. Those electron energy levels do not overlap. Therefore, no valence electrons can be shared between the two atoms indicated by the pink solid line. They are not therefore a bonded lattice pair. And we can eliminate any answer options that say that they are. This includes answer option (A) as well as option (B).

We next consider the pair of silicon atoms indicated by the brown dashed line. As we’ve seen, this pair involves the atom on the left and the silicon atom at the center of the lattice. If we look at the valence electron orbitals for these two atoms, we see that this path does overlap for these adjacent atoms. This means a covalent bond can form between these atoms, and electron sharing will occur. Indeed, we see two such shared electrons, this one here at the intersection of their orbitals and this one here. These two atoms then do form a bonded lattice pair.

Therefore, answer option (D) that neither of these pairs of atoms forms a bonded lattice pair is not correct. But option (C) is correct. Only the atoms whose nuclei are shown within the region indicated by the brown dashed line form a bonded lattice pair. We choose answer choice (C).

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