How the gem stones ruby exhibits red colour and emerald exhibits green colour ?

Explanation

Ruby is aluminium oxide `(Al_2O_3)` containing about 0.5-1% `Cr^(3+)` ion `(d^3)`. This chromium (III) is an octahedral complex incorporated into the alumina lattice. The d-d transitions in `Cr^(3+)` give the red colour to ruby. Emerald is the beryl mineral `(3BeO.Al_2O_3. 6SiO_2)` having some `Cr^(3+)` ions at octahedral sites. The absorption bands seen in the ruby shift to longer wavelength, namely yellow-red and blue, causing emerald to reflect green colour.