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)

Question

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) (√3/2) a b c (B) (2/3 √3) (C) (2/√3) (a2 c/b) (D) 1

Tardigrade Admin · Accepted Answer

Ratio =(a b c/6 ×((√3)4 a2) × c)=(2/3 √3) Note: (c/a)=(2 √2/√3) for an ideal hcp [Refer section 1.22(f and g )]

Q. 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)

$\frac{3}{2} ab c$

$\frac{2}{3 3}$

$\frac{2}{3} \frac{a ^{2} c}{b}$

1

Ratio $= \frac{ab c}{6 \times ( \frac{3}{4} a ^{2} ) \times c} = \frac{2}{3 3}$
Note: $\frac{c}{a} = \frac{2 2}{3}$ for an ideal hcp
[Refer section $1.22 (f$ and $g)]$

Q. 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)

23​​abc

33​2​

3​2​ba2c​

1

Ratio =6×(43​​a2)×cabc​=33​2​ Note: ac​=3​22​​ for an ideal hcp [Refer section 1.22(f and g)]

$\frac{3}{2} ab c$

$\frac{2}{3 3}$

$\frac{2}{3} \frac{a ^{2} c}{b}$

Ratio $= \frac{ab c}{6 \times ( \frac{3}{4} a ^{2} ) \times c} = \frac{2}{3 3}$
Note: $\frac{c}{a} = \frac{2 2}{3}$ for an ideal hcp
[Refer section $1.22 (f$ and $g)]$