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# A matchbox exhibits which type of geometry? Choose the correct option.A.Cubic GeometryB.Orthorhombic GeometryC.Monoclinic GeometryD.Tetragonal Geometry

Last updated date: 25th Jun 2024
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Hint:The matchbox has a three dimensional structure where three of the sides, which is length, breadth and height are unequal, and the angles at the corners are all perpendicular.
-The geometry of any structure can be determined by the length of the sides and the angles possessed between them.

Out of $14$ Bravais crystal lattices, the seven lattice systems are used to distinguish one type of crystal from another existing in nature. These space lattices have a, b and c as the dimensions of the lattice and three different angles $\alpha \beta \gamma$ denote the corresponding angles.
Hence, we can observe from the given following example below that since a matchbox has unequal sides and the angles formed by the sides are mutually perpendicular to each other. So we can say that
$\alpha =\beta =\gamma =90{}^\circ$

We know that in case of a matchbox the length breadth and height have different dimensions, and the angles are all perpendicular. Given below is a diagram of a matchbox to get an idea about its shape. The sides, length breadth and height have different values. So, these criteria are fulfilling the characteristics of an orthorhombic lattice structure, which has a structure similar to that of a matchbox.

If we consider option A, we can see that it mentions that a matchbox has a cubic structure. But we know that the cubic structure has dimensions equal to one another, as in the value of a b and c are equal. We can say that a cubic structure is a three dimensional square.
Now if we consider option B, it says that the matchbox has an orthorhombic structure, which seems like the appropriate option as they both have similar characteristics.
If we consider option C, it says matchbox has a monoclinic structure which is not true as, in monoclinic structure, a is perpendicular to b and c but b and c are not perpendicular to each other, whereas in case of matchbox, all the three sides are perpendicular to each other.
So option B is the correct answer.

Note:
-A matchbox has the geometry as that of an orthorhombic lattice as the sides a, b and c have different lengths and all of them have angles equal to $90{}^\circ$.
-The cubic lattice is basically a square in three dimensions, where all the sides are of equal lengths and all the angles are perpendicular to one another.