The ratio of the volume of a tetragonal lattice unit cell to that of a hexagonal lattice unit cell is (both having same respective lengths)

Options

A. `(2)/sqrt(3)`
B. `sqrt(3)/(2)abc`
C. `(sqrt(3)a^(2))/(2bc)`
D. `((2a^(2)c))/sqrt(3)b`

Explanation

Volume of a lattice is given by:
`V=abc(1-cos^(2)alpha-cos^(2)beta-cos^(2)gamma-2cos alpha cos beta cos gamma)^((1)/(2))`
`V_("tetragonal")=a^(2)c` (because `a=bcancel=c,alpha=beta=gamma=90^(@)`)
`V_("hexagonal")=a^(2)cxx(sqrt(2))/(2)`(because `a=bcancel=c,alpha=beta=90^(@),gamma=120^(@)`)
`therefore(V_("tetragonal"))/(V_("hexagonal"))=(a^(2)cxx2)/(sqrt(3)xxa^(2)xxc)=(2)/sqrt(3)`