The chemical formula of the mineral beryl is

The correct answer is Option (3) → \((Be_3Al_2Si_6O_{18})\)

Beryl is a natural silicate of beryllium and aluminium, \( \ce{Be3Al2Si6O18} \), in which six \( \ce{SiO4} \) tetrahedra form a ring. It is the main ore of beryllium. When a little \( \ce{Cr^3+} \) occupies octahedral sites in beryl, the mineral becomes the green gemstone emerald: the d–d absorption of the \( \ce{Cr^3+} \) ions makes it transmit green light. The other options are formulas of complex ions or a simple chloride, not of a mineral.

NCERT (2026-27 edition):
Colour of Some Gem Stones – “The colours produced by electronic transitions within the d orbitals of a transition metal ion occur frequently in everyday life. … In emerald [Fig.5.12(b)], Cr³⁺ ions occupy octahedral sites in the mineral beryl (Be₃Al₂Si₆O₁₈). The absorption bands seen in the ruby shift to longer wavelength, namely yellow-red and blue, causing emerald to transmit light in the green region.”