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Ujwal Saraf
Asked: 2022-11-10T07:48:55+05:30 In:

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

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

  1. 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)`

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