Tin exists in two allotropic forms: Gray tin has a diamond structure, and white tin has a close-packed structure. One of these allotropic forms is a semiconductor with a small band gap while the other is a metal. Which one is which? Which form would you expect to have the longer \(\mathrm{Sn}-\mathrm{Sn}\) bond distance?

Gray tin has a diamond structure, which is a type of covalent semiconductor. In this structure, covalent bonds are formed between tin atoms, leading to a small band gap due to the presence of localized electron states. White tin has a close-packed structure, which is typical of metals. In this structure, the tin atoms are densely packed with strong metallic bonds that allow free movement of electrons. This leads to strong electrical conductivity, which is a characteristic of metals. Thus, gray tin is the semiconductor with a small band gap, and white tin is the metal.

Next, we can compare the Sn-Sn bond distances in the two allotropic forms to determine which one has the longer bond distance. In general, a longer bond distance indicates weaker bonding between the atoms. For gray tin with a diamond structure, the covalent bonds formed between the tin atoms lead to a more rigid and localized bonding arrangement. On the other hand, the close-packed structure of white tin leads to strong metallic bonds formed by delocalized electrons. Since covalent bonds are typically formed in semiconductors like gray tin, and metallic bonds are typically formed in metals like white tin, we can infer that the Sn-Sn bond distance is longer in gray tin due to the weaker covalent bonding compared to the stronger metallic bonding in white tin. In conclusion, gray tin is the semiconductor with a small band gap while white tin is the metal. Gray tin is expected to have a longer Sn-Sn bond distance than white tin due to the weaker covalent bonding.