Chapter 12.1, Problem 28PPS

(a)

To determine

To sketch the cross section from a horizontal slice of a tetragonal crystal and to describe the rotational symmetry.

Answer to Problem 28PPS

The cross section from a horizontal slice of a tetragonal crystal gives a square.

Explanation of Solution

Given Information:

A picture of tetragonal crystal is shown below:

  

Formula Used:

Rotational Symmetry: A shape has rotational symmetry when it still looks the same after some rotations. The number of positions in which a figure can be rotated and still appears exactly as it did before the rotation is called order of symmetry. The angle of turning during rotation is called angle of rotation.

A cross section from a horizontal slice of a tetragonal crystal gives square

A square has 90 and 180 degree rotational symmetry.

Order of symmetry = 4

(b)

To determine

To sketch the cross section from a horizontal slice of a hexagonal crystal and to describe the rotational symmetry.

Answer to Problem 28PPS

The cross section from a horizontal slice of a hexagonal crystal gives a regular hexagon.

Explanation of Solution

Given Information:

A picture of hexagonal crystal is shown below:

  

Formula Used:

Rotational Symmetry: A shape has rotational symmetry when it still looks the same after some rotations. The number of positions in which a figure can be rotated and still appears exactly as it did before the rotation is called order of symmetry. The angle of turning during rotation is called angle of rotation.

A cross section from a horizontal slice of a hexagonal crystal gives a regular hexagon

A regular hexagon has 60, 120 and 180 degree rotational symmetry.

Order of symmetry = 6

(c)

To determine

To sketch a cross section from a horizontal slice of a monoclinic crystal and to describe the rotational symmetry

Answer to Problem 28PPS

The cross section from a horizontal slice of a monoclinic crystal gives a rectangle.

Explanation of Solution

Given Information:

A picture of monoclinic crystal is shown below:

  

Formula Used:

Rotational Symmetry: A shape has rotational symmetry when it still looks the same after some rotations. The number of positions in which a figure can be rotated and still appears exactly as it did before the rotation is called order of symmetry. The angle of turning during rotation is called angle of rotation.

A cross section from a horizontal slice of a monoclinic crystal gives a rectangle.

A rectangle has 180 degree rotational symmetry.

Order of symmetry = 2