Answer:

1.

(I).Items are due to packing of atom/molecules in a crystal.

(a). In three-dimensional space, the equivalent repeat unit is a parallelepiped known as the unit cell.
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(b). The crystal lattice itself is actually an infinite set of equally-spaced point.
1 Mark
(d). The origin in crystal occurs inside crystal.
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(II). Items are due to chosen by the crystllographyer.

(c). In the reciprocal space of crystal, the origin is an arbitrary point chosen by crystallographyer.
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(III). Items are due to chosen by neither (I) or (II).

(e). The Space-Group is a set of elements for which a combination law is defined.
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Comment: You answered this question in unusual order (see model answer).

2.

Laue Classes

In agreement with Neumann's principle,
Comment: Neumann's principle is not something covered in the course material so it cannot possibly be expected in the answer. We have made it clear that the course is 100% self-contained and does not require access to additional course material. In addition, external links are purely for reference only - they do not form part of assignment or examinable course material.
physical experiments do not normally reveal the true symmetry of the crystal: some of them, for example diffraction, show the symmetry one would obtain by adding an inversion centre to the symmetry elements actually present. In particular this happens when the measured quantities do not depend on the atomic positions, but rather on the interatomic vectors, which indeed form a centrosymmetric set. Point groups differing only by the presence of an inversion centre will not be differentiated by these experiments.
1 Mark

In a particular experiment the unit-cell geometry may be such that a ¹ b ¹ c and   a = b = g = 90° within experimental error. Typically the esd' on the angles will be relatively large and so to test for orthorhombic symmetry it is necessary to check, say, that I = (hkl) and I = (h-k-l) to demonstrate that twofold symmetric with respect to a and c, respectively. This is often referred to as a Laue check on the symmetry of the crystal.
Comment: Please read the question and model answer carefully.
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3.

Those point groups which possess no improper rotations are called enantiomorphic. Enantiomorphic molecules have right-handed and left-handed forms. Normally, the condition for enantiomorphic well shows rotary axes and lack of molecular rotary-reflection axes, which means it cannot be superimposed on to its mirror image in any of its possible conformations. So crystallographyer can not find lattice translations and mirror/glide plans in the crystal structure of an enantiomorphic molecule.
Comment: The last part is incorrect: all conventional 3D crystal structures have lattice translations whether they are enatiomorphic or not. Lattice translations are the fundamental characteristic of the simplest space group P1, from which the other 229 are derived.
3 Marks

4.

I.

Comment: This is not the correct approach for this question. Note also that the question only carries 5 marks maximum so that your answer is clearly far too long. Please read model answer to see what was expected here.
An organometallic cobalt compound crystal which accords space group P21/c has central metal atom, Co with co-ordination 0.271, 0.250,0..458.
In the 3-dimention space of this crystal, the view down b has following symmetry operations:

(1). A lattice translation is parallel to a of (1,0,0). The corresponding symmetry operator is 1+x, y, z (i.e. co-ordination 1.271, 0.250, 0.458).
(2). A lattice translation is parallel to c of (0,0,1). The corresponding symmetry operator is x, y, 1+z (i.e. co-ordination 0.271, 0.250, 1.458).
(3). Two lattice translations: one is parallel to a of (1,0,0) and the other parallel to c of (0,0,1). The corresponding symmetry operator is 1+x, y, 1+z (i.e. co-ordination 1.271, 0.250, 1.458).
(4). A two-one screw axis is parallel to b at (½, y, ¼). The corresponding symmetry operator is 1-x, ½+y, ½-z (i.e. co-ordination 0.729, 0.750, 0.042).
(5). A two-one screw axis is parallel to b at (0, y, ¼). The corresponding symmetry operator is -x, ½+y, ½-z (i.e. co-ordination -0.271, 0.75, 0.042).
(6). There is a centre of inversion at the point (½, 0, ½). The corresponding symmetry operator is 1-x, -y, 1-z (i.e. co-ordination 0.729, -0.250, 0.542).
(7). There is a centre of inversion at the point (0, 0, ½). The corresponding symmetry operator is -x, -y, 1-z (i.e. co-ordination -0.271, -0.250, 0.542).
(8). There is a centre of inversion at the point (1/2, 0, 0). The corresponding symmetry operator is 1-x, -y, -z (i.e. co-ordination 0..729, -0.250, -0.458).
(9). There is a point of inversion at the origin (0, 0, 0). The corresponding symmetry operator is -x, -y, -z (i.e. co-ordination -0.271, -0.250, -0.458).
(10). There is a c-glide plane at (x, ¼, z). The corresponding symmetry operator is x, ½-y, ½+z (i.e. co-ordination 0.271, 0.250, 0.958).
(11). There is a c-glide plane at (x, ¼, z) plus a lattice translationparallel to a of (1, 0, 0). The corresponding symmetry operator is 1+x, ½-y, ½+z (i.e. co-ordination 1.271, 0.25, 0.958).

Views down c:

(1). There is a lattice translation parallel to b of (0, 1, 0). The corresponding symmetry operator is x, 1+y, z (i.e. co-ordination 0.271, 1.25, 0.458).
(2). There is a lattice translation parallel to a of (1, 0, 0). The corresponding symmetry operator is 1+x, y, z (i.e. co-ordination 1.271, 0.25, 0.458).
(3). There are two lattice translations: one is parallel to a of (1, 0, 0) and the other is parallel to b of (0, 1, 0). The corresponding symmetry operator is 1+x, 1+y, z (i.e. co-ordination 1.271, 1.25, 1.458).
(4). There is a two-one screw axis parallel to b at (½, y, ¼). The corresponding symmetry operator is 1-x, ½+y, ½-z (i.e. co-ordination 0.729, 0.750, 0.042).
(5). There is a two-one screw axis parallel to b at (0, y, ¼). The corresponding symmetry operator is -x, ½+y, ½-z (i.e. co-ordination -0.271, 0.750, 0.042).
(6). There is a centre of inversion at the point (½, ½, 0). The corresponding symmetry operator is 1-x, 1-y, -z (i.e. co-ordination 0.729, 0.750, -0.458).
(7). There is a centre of inversion at the point (½, 0, 0). The corresponding symmetry operator is 1-x, -y, -z (i.e. co-ordination 0..271, -0.25, -0.458).
(8). There is a centre of inversion at the point (0, ½, 0). The corresponding symmetry operator is -x, 1-y, -z (i.e. co-ordination -0.729, 0.25, -0.458).
(9). There is a centre of inversion at the origin (0, 0, 0). The corresponding symmetry operator is -x, -y, -z (i.e. co-ordination -0.271, -0.25, -0.458).
(10). There is a c-glide plane at (x, ¼, z). The corresponding symmetry operator is x, ½-y, ½+z (i.e. co-ordination 0.271, 0.25, 0.958).
(11). There is a c-glide plane at (x, ¼, z) plus a lattice translation parallel to a of (1, 0, 0). The corresponding symmetry operator is 1+x, ½-y, ½+z (i.e. co-ordination 1.271, 0.25, 0.958).

Views down a:

(1). There is a lattice translation parallel to b of (0, 1, 0). The corresponding symmetry operator is x, 1+y, z (i.e. co-ordination 0.271, 1.25, 0.458).
(2). There is a two-one screw axis parallel to b at (0, y, ¼). The corresponding symmetry operator is -x, ½+y, ½-z (i.e. co-ordination -0.271, 0.75, 0.042).
(3). There is a centre of inversion at the point (0, ½, ½). The corresponding symmetry operator is -x, 1-y, 1-z (i.e. co-ordination -0.271, 0.250, 0.042).
(4). There is a centre of inversion at the point (0, 0, ½). The corresponding symmetry operator is -x, -y, 1-z (i.e. co-ordination -0.271, -0.25, 0.542).
(5). There is a c-glide plane at (x, ¼, z). The corresponding symmetry operator is x, ½-y, ½+z (i.e. co-ordination 0.271, 0.250, 0.958).
Therefore, co-ordinations Co atoms within the unit cell present above possible co-ordinations.

II.

In the crystal structures of organic and organometallic compounds, it is very common for the molecules to occupy general positions within the unit cell unless the molecule possesses a point-group symmetry witch can coexist with some of the point-group symmetry elements of the space group. When atoms are positioned on point-group symmetry elements of a space group, they are said to be on special positions. According to that, in above crystal Co atoms are not sited on point-group symmetry element of a P2₁/c space group.
Comment: The final part is excellent.
4 Marks

5.

In 1,2-dichloroethanein conformation only rotation symmetry element is present. Hence, the molecular point symmetry for this particular conformation is -1.
Comment: See model answer for correct solution to this problem.
1 Mark

6.

I.
There are three types of symmetry element present in the diagram presented in problem set 4
(1). Two-fold element
(2). Mirror element
(3). a-glide element
Comment: Excellent, but figures not really needed.
3 Marks

II.
The position of symmetry-related objects within the unit cell is specified in following diagram.

III.
For each symmetry-related object specified in (II) above, there are four pairs of handedness (i.e. original object and Z, g and h, B and C, and J and K) due to the mirror symmetry element.
Comment: True, but which is which in terms of handedness.
1 Mark

IV.
The crystal system probably belongs to P2ma, because there are three symmetry elements in the space group and it also is primitive space group which has been specifiey.
Comment: A space group is not a "crystal system" and the space group is actually Pma2 (the order of the symmetry elements in the symbol is critical)
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Additional comments: I am a little concerned as to whether you really understood the questions or the course material. This particular assignment tests understanding and you have scored less than half marks. Also, you do not ask any questions concerning the course material. If there are parts of the course that you do not understand (or even where the English language confuses you?), please email us.