Final answer:
Emeralds are rare because they form under very specific conditions that are not commonly met, and the incorporation of chromium into the beryl lattice is uncommon. The unique green color of emeralds, as with the red color of rubies, results from trace chromium impurities within the lattice, but differences in the host lattice lead to different light absorption and transmission properties.
Step-by-step explanation:
Gem beryl, such as emerald, is rare because its formation requires specific geological conditions that are infrequent. Emerald is formed when beryl, a crystal composed of beryllium aluminosilicate (Be3Al2Si6O18), incorporates trace amounts of chromium (Cr3+) into its structure. The replacement of Al3+ ions with Cr3+ ions at just one percent concentration turns the mineral green, creating the precious gemstone known as emerald. The rarity of these conditions and the scarcity of chromium available to be incorporated into the beryl lattice result in the rarity of gem-quality emerald crystals.
Ruby is another gemstone that owes its color to the presence of chromium impurities. Both ruby and emerald are colored due to small amounts of Cr3+ impurities in octahedral sites within a colorless metal oxide lattice. However, they exhibit different colors because the Cr-O distances in their host lattices are different, altering the way they absorb and transmit light. In rubies, which is alumina (Al2O3) with Cr3+ replacing Al3+, the shorter Cr-O distances increase d orbital-ligand interactions, causing rubies to absorb green light and transmit or reflect red light, which gives them their characteristic red color. In contrast, the longer Cr-O distances in emerald, due to the larger silicate rings in its crystal lattice, result in decreased d orbital-ligand interactions, causing emeralds to absorb light of a longer wavelength (red) and transmit or reflect green light.