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Question: In the table given below, dimensions and angles of various crystals are given. Complete the table by...

In the table given below, dimensions and angles of various crystals are given. Complete the table by filling the blanks.

Type of crystalDimensionAngles
(A).Cubica = b = cα=β=γ=p‾\alpha = \beta = \gamma = \underline{p}
(B)Tetragonalq‾\underline{q}α=β=γ=90∘\alpha = \beta = \gamma = 90{^\circ}
(C)Orthorhombica≠b≠ca \neq b \neq cq‾\underline{q}
(D)HexagonalS‾\underline{S}α=β=90∘,γ=t‾\alpha = \beta = 90{^\circ},\gamma = \underline{t}

P q r s t

A

90∘α=b≠cα=β=γ=90∘a=b≠c120∘90{^\circ}\alpha = b \neq c\alpha = \beta = \gamma = 90{^\circ}a = b \neq c120{^\circ}

B

120∘α=b=cα=90∘,β=γ=120∘a≠b≠c90∘120{^\circ}\alpha = b = c\alpha = 90{^\circ},\beta = \gamma = 120{^\circ}a \neq b \neq c90{^\circ}

C

90∘α≠b≠cα=β=γ=120∘a=b≠c90∘90{^\circ}\alpha \neq b \neq c\alpha = \beta = \gamma = 120{^\circ}a = b \neq c90{^\circ}

D

120∘α≠b≠cα≠β≠γ≠90∘a≠b=c120∘120{^\circ}\alpha \neq b \neq c\alpha \neq \beta \neq \gamma \neq 90{^\circ}a \neq b = c120{^\circ}

Answer

90∘α=b≠cα=β=γ=90∘a=b≠c120∘90{^\circ}\alpha = b \neq c\alpha = \beta = \gamma = 90{^\circ}a = b \neq c120{^\circ}

Explanation

Solution

For cubic, a = b = c,

α=β=γ=90∘\alpha = \beta = \gamma = 90{^\circ}

Tetragonal, α=b≠c,α=β=γ=90∘\alpha = b \neq c,\alpha = \beta = \gamma = 90{^\circ}

Orthorhombic ,

a≠b≠c,α=β=γ=90∘a \neq b \neq c,\alpha = \beta = \gamma = 90{^\circ}

Hexagonal ,

a=b≠c,α=β=90∘,γ−120∘a = b \neq c,\alpha = \beta = 90{^\circ},\gamma - 120{^\circ}